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| -rw-r--r-- | Engineering_Physics_by_V_Yadav/3-Diffraction.ipynb | 1494 | ||||
| -rw-r--r-- | Engineering_Physics_by_V_Yadav/4-Polarization.ipynb | 850 | ||||
| -rw-r--r-- | Engineering_Physics_by_V_Yadav/5-Nuclear_Physics.ipynb | 263 | ||||
| -rw-r--r-- | Engineering_Physics_by_V_Yadav/6-Semiconductors_and_Nano_Physics.ipynb | 92 | ||||
| -rw-r--r-- | Engineering_Physics_by_V_Yadav/7-Fiber_Optics.ipynb | 372 | ||||
| -rw-r--r-- | Engineering_Physics_by_V_Yadav/8-Laser.ipynb | 184 |
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diff --git a/Engineering_Physics_by_V_Yadav/1-Quantum_Mechanics.ipynb b/Engineering_Physics_by_V_Yadav/1-Quantum_Mechanics.ipynb new file mode 100644 index 0000000..d0faa3a --- /dev/null +++ b/Engineering_Physics_by_V_Yadav/1-Quantum_Mechanics.ipynb @@ -0,0 +1,1358 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 1: Quantum Mechanics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.10: de_Broglie_wavelength_associated_with_moving_proton.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.10: Page-1.8 (2009)\n", +"clc; clear;\n", +"m = 1.67e-027; // Mass of the proton, kg\n", +"c = 3e+08; // Speed of light, m/s\n", +"v = 1/20*c; // Velocity of the proton, m/s\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"lambda = h/(m*v); // de Broglie wavelength of the neutron, m\n", +"printf('\nThe de Broglie wavelength associated with moving proton = %5.3e m', lambda);\n", +"\n", +"// Result \n", +"// The de Broglie wavelength associated with moving proton = 2.645e-14 m\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.11: Wavelength_of_matter_wave_associated_with_moving_proton.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.11: Page-1.8 (2009)\n", +"clc; clear;\n", +"m = 1.67e-027; // Mass of the proton, kg\n", +"v = 2e+08; // Velocity of the proton, m/s\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"lambda = h/(m*v); // de Broglie wavelength of the neutron, m\n", +"printf('\nThe wavelength of matter wave associated with moving proton = %5.3e m', lambda);\n", +"\n", +"// Result \n", +"// The wavelength of matter wave associated with moving proton = 1.984e-15 m \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.12: de_Broglie_wavelength_of_an_electron_accelerated_through_a_given_potential.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.12: Page-1.17 (2009)\n", +"clc; clear;\n", +"m = 9.1e-031; // Mass of the electron, kg\n", +"q = 1.6e-019; // Charge on an electron, C\n", +"V = 50; // Accelearting potential, V\n", +"E = q*V; // Energy gained by the electron, J\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"lambda = h/sqrt(2*m*E); // de Broglie wavelength of the electron, m\n", +"printf('\nThe de Broglie wavelength of the electron accelearted through a given potential = %5.3e m', lambda);\n", +"\n", +"// Result \n", +"// The de Broglie wavelength of the electron accelearted through a given potential = 1.736e-10 m \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.13: Interplanar_spacing_of_the_crystal.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.13: Page-1.17 (2009)\n", +"clc; clear;\n", +"theta = 45; // Diffraction angle, degrees\n", +"h = 6.626e-034; // Planck's constant\n", +"m = 1.67e-027; // Mass of a neutron, kg\n", +"n = 1; // Order of diffraction\n", +"k = 1.38e-023; // Boltzmann constant, J/mol/K\n", +"T = 27+273; // Absolute room temperature, K\n", +"E = 3/2*k*T; // Energy of the neutron, J\n", +"lambda = h/sqrt(2*m*E); // de-Broglie wavelength of neutrons, m\n", +"// From Bragg's law, 2*d*sin(theta) = n*lambda, solving for d\n", +"d = n*lambda/(2*sind(theta));\n", +"printf('\nThe interplanar spacing of the crystal = %4.2f angstrom', d/1e-010);\n", +"\n", +"// Result \n", +"// The interplanar spacing of the crystal = 1.03 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.14: Interplanar_spacing_using_Bragg_law.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.14: Page-1.18 (2009)\n", +"clc; clear;\n", +"theta = 70; // Glancing angle at which reflection occurs, degrees\n", +"h = 6.626e-034; // Planck's constant\n", +"m = 9.1e-031; // Mass of a electron, kg\n", +"e = 1.6e-019; // Electronic charge, C\n", +"V = 1000; // Accelerating potential, V\n", +"n = 1; // Order of diffraction\n", +"E = e*V; // Energy of the electron, J\n", +"lambda = h/sqrt(2*m*E); // de-Broglie wavelength of electron, m\n", +"// From Bragg's law, 2*d*sin(theta) = n*lambda, solving for d\n", +"d = n*lambda/(2*sind(theta)); // Interplanar spacing, m\n", +"printf('\nThe interplanar spacing of the crystal = %6.4e m', d);\n", +"\n", +"// Result \n", +"// The interplanar spacing of the crystal = 2.0660e-11 m \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.15: de_Broglie_wavelength_of_electron_accelerated_at_V_volts.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.15: Page-1.18 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant\n", +"m = 9.1e-031; // Mass of a electron, kg\n", +"e = 1.6e-019; // Electronic charge, C\n", +"V = 1; // For simplicity the accelerating potential is assumed to be unity, V\n", +"E = e*V; // Energy of the electron, J\n", +"lambda = h/sqrt(2*m*E); // de-Broglie wavelength of electron, m\n", +"printf('\nde-Broglie wavelength of electron accelerated at V volts = %5.2f/sqrt(V) angstrom', lambda/1e-010);\n", +"\n", +"// Result \n", +"// de-Broglie wavelength of electron accelerated at V volts = 12.23/sqrt(V) angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.16: de_Broglie_wavelength_of_electron_accelerated_from_rest.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.16: Page-1.18 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant\n", +"m = 9.1e-031; // Mass of a electron, kg\n", +"e = 1.6e-019; // Electronic charge, C\n", +"V = 100; // Accelerating potential for electron, V\n", +"E = e*V; // Energy of the electron, J\n", +"lambda = h/sqrt(2*m*E); // de-Broglie wavelength of electron, m\n", +"printf('\nde-Broglie wavelength of electron accelerated at %d volts = %6.4e m', V, lambda);\n", +"\n", +"// Result \n", +"// de-Broglie wavelength of electron accelerated at 100 volts = 1.2231e-10 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.17: The_wavelength_associated_with_moving_mass.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.17: Page-1.19 (2009)\n", +"clc; clear;\n", +"m = 10e-03; // Mass of the body, kg\n", +"v = 110; // Velocity of the mass, m/s\n", +"h = 6.6e-034; // Planck's constant\n", +"lambda = h/(m*v); // de-Broglie wavelength of electron, m\n", +"printf('\nThe wavelength associated with mass moving with velocity %d m/s = %1.0e m', v, lambda);\n", +"\n", +"// Result \n", +"// The wavelength associated with mass moving with velocity 110 m/s = 6e-34 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.18: Wavelength_of_an_electron_from_its_kinetic_energy.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.18: Page-1.19 (2009)\n", +"clc; clear;\n", +"m = 9.1e-031; // Mass of the electron, kg\n", +"Ek = 1.27e-017; // Kinetic energy of electron, J\n", +"h = 6.6e-034; // Planck's constant\n", +"lambda = h/sqrt(2*m*Ek); // de-Broglie wavelength of electron, m\n", +"printf('\nThe wavelength associated with moving electron = %4.2f angstrom', lambda/1e-010);\n", +"\n", +"// Result \n", +"// The wavelength associated with moving electron = 1.37 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.19: Kinetic_energy_of_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.19: Page-1.19 (2009)\n", +"clc; clear;\n", +"m = 9.1e-031; // Mass of the electron, kg\n", +"h = 6.6e-034; // Planck's constant\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"lambda = 9.1e-012; // de-Broglie wavelength of electron, m\n", +"// We have lambda = h/(m*v), solving for v\n", +"v = h/(m*lambda); // Velocity of the electron, m/s\n", +"K = 1/2*m*v^2; // Kinetic energy of electron, J\n", +"printf('\nThe kinetic energy of electron having wavelength %3.1e m = %4.2e eV', lambda, K/e);\n", +"\n", +"// Result \n", +"// The kinetic energy of electron having wavelength 9.1e-12 m = 1.81e+04 eV \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.1: Energy_of_the_particle_from_de_Broglie_wavelength.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.1:Page-1.5 (2009)\n", +"clc; clear;\n", +"lambda = 2.1e-010; // de Broglie wavelength of the particle, m\n", +"m = 1.67e-027; // Mass of the particle, kg\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"// From de Broglie relation, lambda = h/sqrt(2*m*E), solving for E\n", +"E = h^2/(2*m*lambda^2*e); // Energy of the particle, eV\n", +"printf('\nThe energy of the particle from de Broglie wavelength = %5.3e eV', E);\n", +"\n", +"// Result \n", +"// The energy of the particle from de Broglie wavelength = 1.863e-002 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.20: Speed_of_proton_for_an_equivalent_wavelength_of_that_of_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.20: : Page-1.19 (2009)\n", +"clc; clear;\n", +"m_e = 9.1e-031; // Mass of the electron, kg\n", +"m_p = 1.67e-027; // Mass of the proton, kg\n", +"v_e = 1; // For simplicity assume velocity of electron to be unity, m/s\n", +"// From de-Broglie relation, \n", +"// lambda_p = lambda_e = h(m*v_p), solving for v_p\n", +"v_p = m_e*v_e/m_p; // Velocity of the proton, m/s\n", +"// As lambda_e = h/sqrt(2*m_e*K_e) and lambda_p = h/sqrt(2*m_p*K_p), solving for K_e/K_p\n", +"K_ratio = m_p/m_e; // Ratio of kinetic energies of electron and proton\n", +"\n", +"printf('\nThe speed of proton for an equivalent wavelength of that of electron = %3.1e ve', v_p);\n", +"printf('\nRatio of kinetic energies of electron and proton = %3.1e, therefore Ke > Kp', K_ratio);\n", +"\n", +"// Result \n", +"// The speed of proton for an equivalent wavelength of that of electron = 5.4e-04 ve\n", +"// Ratio of kinetic energies of electron and proton = 1.8e+03, therefore Ke > Kp " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.21: de_Broglie_wavelength_of_the_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.21: Page-1.20 (2009)\n", +"clc; clear;\n", +"V = 50; // Potential difference, V\n", +"m = 9.1e-031; // Mass of the electron, kg\n", +"e = 1.6e-019; // Electronic charge, C\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"lambda = h/sqrt(2*m*e*V); // From de-Broglie relation,\n", +"printf('\nde-Broglie wavelength of the electron = %4.2f angstrom', lambda/1e-010);\n", +"\n", +"// Result \n", +"// de-Broglie wavelength of the electron = 1.73 angstrom" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.23: Minimum_accuracy_to_locate_the_position_of_an_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.23:: Page-1.31 (2009)\n", +"clc; clear;\n", +"v = 740; // Speed of the electron, m/s\n", +"m = 9.1e-031; // Mass of the electron, kg\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"p = m*v; // Momentum of the electron, kg-m/s\n", +"frac_v = 0.05/100; // Correctness in the speed \n", +"delta_p = p*frac_v; // Uncertainty in momentum, kg-m/s\n", +"delta_x = h/(4*%pi)*1/delta_p; // Uncertainty in position, m\n", +"\n", +"printf('\nThe minimum accuracy to locate the position of an electron = %4.2e m',delta_x);\n", +"\n", +"// Result \n", +"// The minimum accuracy to locate the position of an electron = 1.56e-04 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.24: Uncertainty_in_energy_of_an_emitted_photon.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.24: : Page-1.31 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"h_cross = h/(2*%pi); // Reduced Planck's constant, Js\n", +"delta_t = 1e-010; // Uncertainty in time, s\n", +"// From Energy-time uncertainty, \n", +"// delta_E*delta_t = h_cross/2, solving for delta_E\n", +"delta_E = h_cross/(2*delta_t); // Uncertainty in energy of an emitted photon, J \n", +"\n", +"printf('\nThe uncertainty in energy of an emitted photon = %5.3e eV', delta_E/1.6e-019);\n", +"\n", +"// Result \n", +"// The uncertainty in energy of an emitted photon = 3.283e-06 eV" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.25: Minimum_uncertainty_in_velocity_of_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.25: : Page-1.31 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"delta_x_max = 1e-007; // Uncertainty in length, m\n", +"m = 9.1e-031; // Mass of an electron, kg\n", +"// From Position-momentum uncertainty, \n", +"// delta_p_min = m*delta_v_min = h/delta_x_max, solving for delta_v_min\n", +"delta_v_min = h/(delta_x_max*m); // Minimum uncertainty in velocity of electron, m/s\n", +"\n", +"printf('\nThe minimum uncertainty in velocity of electron = %4.2e m/s', delta_v_min);\n", +"\n", +"// Result \n", +"// The minimum uncertainty in velocity of electron = 7.25e+03 m/s " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.26: Minimum_uncertainty_in_momentum_and_minimum_kinetic_energy_of_proton.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.26: Page-1.32 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"delta_x_max = 8.5e-014; // Uncertainty in length, m\n", +"m = 1.67e-027; // Mass of proton, kg\n", +"// From Position-momentum uncertainty, \n", +"// delta_p_min*delta_x_max = h, solving for delta_p_min\n", +"delta_p_min = h/delta_x_max; // Minimum uncertainty in momentum of electron, kg-m/s\n", +"p_min = delta_p_min; // Minimum momentum of the proton, kg.m/s\n", +"delta_E = p_min^2/(2*m); \n", +" \n", +"printf('\nThe minimum uncertainty in momemtum of proton = %4.2e kg-m/s', p_min);\n", +"printf('\nThe kinetic energy of proton = %6.3e eV', delta_E/1.6e-019);\n", +"\n", +"// Result \n", +"// The minimum uncertainty in momemtum of proton = 7.76e-21 kg-m/s\n", +"// The kinetic energy of proton = 1.128e+05 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.27: Uncertainty_in_momentum_of_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.27:: Page-1.32 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"E = 0.15*1e+03*e; // Energy of the electron, J\n", +"m = 9.1e-031; // Mass of electron, kg\n", +"delta_x = 0.5e-010; // Position uncertainty of electron, m\n", +"p = (2*m*E)^(1/2); // Momentum of the electron, kg-m/s\n", +"// delta_x*delta_p = h/(4*%pi), solving for delta_p\n", +"delta_p = h/(4*%pi*delta_x); // Uncertainty in momentum of electron, kg-m/s\n", +"frac_p = delta_p/p*100; // Percentage uncertainty in momentum of electron, kg-m/s\n", +"\n", +"printf('\nThe percentage uncertainty in momentum of electron = %2d percent', frac_p);\n", +"\n", +"// Result \n", +"// The percentage uncertainty in momentum of electron = 15 percent " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.28: Uncertainty_in_position_of_the_particle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.28:: Page-1.33 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"delta_v = 7.54e-015; // Uncertainty in velocity of the particle, m/s\n", +"m = 0.25e-06; // Mass of particle, kg\n", +"// delta_x*delta_p = h/(4*%pi), solving for delta_x\n", +"delta_x = h/(4*%pi*m*delta_v); // Position uncertainty of particle, m\n", +"\n", +"printf('\nThe position uncertainty of particle = %4.2e m', delta_x);\n", +"\n", +"// Result \n", +"// The position uncertainty of particle = 2.79e-14 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.29: Uncertainty_in_position_of_the_moving_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.29:: Page-1.33 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"v = 450; // Velocity of the electron, m/s\n", +"delta_v = v*0.05/100; // Uncertainty in velocity of the particle, m/s\n", +"m = 9.1e-031; // Mass of electron, kg\n", +"// delta_x*delta_p = h/(4*%pi), solving for delta_x\n", +"delta_x = h/(4*%pi*m*delta_v); // Position uncertainty of particle, m\n", +"\n", +"printf('\nThe position uncertainty of moving electron = %4.2e m', delta_x);\n", +"\n", +"// Result \n", +"// The position uncertainty of moving electron = 2.57e-04 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.2: de_Broglie_wavelength_of_the_particle.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.2: Page-1.5 (2009)\n", +"clc; clear;\n", +"m = 1.67e-027; // Mass of the particle, kg\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"E = 1e+011*e; // Energy of the particle, J\n", +"lambda = h/sqrt(2*m*E); // de Broglie wavelength of the particle, m\n", +"printf('\nThe de Broglie wavelength of the particle = %4.2e m', lambda);\n", +"\n", +"// Result \n", +"// The de Broglie wavelength of the particle = 9.06e-017 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.30: Smallest_possible_uncertainty_in_position_of_the_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.30:: Page-1.33 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"c = 3e+08; // Speed of light, m/s\n", +"v = 3e+07; // Velocity of the electron, m/s\n", +"m0 = 9.1e-031; // Rest mass of electron, kg\n", +"m = m0/sqrt(1-v^2/c^2); // Mass of moving electron, kg\n", +"delta_p_max = m*v; // Maximum uncertainty in momentum of the particle, m/s\n", +"// delta_x_min*delta_p_max = h/(4*%pi), solving for delta_x_min\n", +"delta_x_min = h/(4*%pi*delta_p_max); // Minimum position uncertainty of particle, m\n", +"\n", +"printf('\nThe smallest possible uncertainty in position of the electron = %5.3f angstrom', delta_x_min/1e-010);\n", +"\n", +"// Result \n", +"// The smallest possible uncertainty in position of the electron = 0.019 angstrom" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.31: EX1_31.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.31: : Page-1.44 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 9.1e-031; // Electronic mass, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"l = 2e-002; // Length of the side of the cube, m\n", +"E_F = 9*e; // Fermi energy, J\n", +"// As E_F = h^2/(8*m*l^2)*(nx^2 + ny^2 + nz^2) and nx = ny = nz for a cube, solving for nx\n", +"nx = sqrt(E_F*(8*m*l^2)/(3*h^2)); // Value of integer for a cube\n", +"E = h^2/(8*m*l^2)*3*nx^2; // Fermi energy, J\n", +"E1 = h^2/(8*m*l^2)*((nx-1)^2 + nx^2 + nx^2); // Energy of the level just below the fermi level, J\n", +"delta_E = E - E1; // Difference in the energy between the neighbouring levels of Na at the highest state, J\n", +"printf('\nThe energy difference between the neighbouring levels of Na at the highest state = %4.2e eV', delta_E/e);\n", +"// Result \n", +"// The energy difference between the neighbouring levels of Na at the highest state = 1.06e-07 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.32: Energy_of_the_neutron_confined_in_a_nucleus.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.32:: Page-1.45 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 1.67e-027; // Electronic mass, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"nx = 1, ny = 1, nz = 1; // Principle quantum numbers in 3D corresponding to the longest energy state\n", +"lx = 1e-014, ly = 1e-014, lz = 1e-014; // Dimensions of the box to which the neutron is confined, m\n", +"E = h^2/(8*m)*(nx^2/lx^2+ny^2/ly^2+nz^2/lz^2); // Energy of the neutron confined in the nucleus, J\n", +"printf('\nThe energy of the neutron confined in a nucleus = %4.2e eV', E/e);\n", +"// Result \n", +"// The energy of the neutron confined in a nucleus = 6.11e+06 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.33: Energy_of_an_electron_moving_in_one_dimensional_infinitely_high_potential_box.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.33:: Page-1.46 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 9.1e-031; // Electronic mass, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"n = 1; // For simplicity assume principle quantum number to be unity\n", +"l = 2.1e-010; // Length of one dimensional potential box, m\n", +"E = h^2*n^2/(8*m*l^2); // Energy of the electron, J\n", +"printf('\nThe energy of the electron moving in one dimensional infinitely high potential box = %4.2f n^2 eV', E/e);\n", +"// Result \n", +"// The energy of the electron moving in one dimensional infinitely high potential box = 8.48 n^2 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.34: Lowest_energy_of_an_electron_in_a_one_dimensional_force_free_region.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.34:: Page-1.46 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 9.1e-031; // Electronic mass, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"n = 1; // The lowest energy state of electron\n", +"l = 3.5e-010; // Length of one dimensional potential box, m\n", +"E = h^2*n^2/(8*m*l^2); // Energy of the electron in the lowest state, J\n", +"printf('\nThe lowest energy of the electron in a one dimensional force free region = %1d eV', E/e);\n", +"// Result \n", +"// The lowest energy of an electron in a one dimensional force free region = 3 eV" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.35: First_three_energy_levels_of_an_electron_in_one_dimensional_box.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.35:: Page-1.46 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 9.1e-031; // Electronic mass, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"l = 9.5e-010; // Length of one dimensional potential box, m\n", +"// First energy level\n", +"n = 1; // The first energy state of electron\n", +"E1 = h^2*n^2/(8*m*l^2); // Energy of the electron in first state, J\n", +"// Second energy level\n", +"n = 2; // The second energy state of electron\n", +"E2 = h^2*n^2/(8*m*l^2); // Energy of the electron in second state, J\n", +"// Third energy level\n", +"n = 3; // The third energy state of electron\n", +"E3 = h^2*n^2/(8*m*l^2); // Energy of the electron in third state, J\n", +"printf('\nThe energy of the electron in first state = %4.1e J', E1);\n", +"printf('\nThe energy of the electron in second state = %4.1e J', E2);\n", +"printf('\nThe energy of the electron in third state = %4.1e J', E3);\n", +"// Result \n", +"// The energy of the electron in first state = 6.6e-20 J\n", +"// The energy of the electron in second state = 2.7e-19 J\n", +"// The energy of the electron in third state = 6.0e-19 J " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.36: Lowest_two_permitted_energy_values_of_the_electron_in_a_1D_box.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.36:: Page-1.47 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 9.1e-031; // Electronic mass, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"l = 2.5e-010; // Length of one dimensional potential box, m\n", +"// First energy level\n", +"n = 1; // The lowest energy state of electron\n", +"E1 = h^2*n^2/(8*m*l^2); // Energy of the electron in first state, J\n", +"// Second energy level\n", +"n = 2; // The second energy state of electron\n", +"E2 = h^2*n^2/(8*m*l^2); // Energy of the electron in second state, J\n", +"printf('\nThe energy of the electron in lowest state = %5.2f eV', E1/e);\n", +"printf('\nThe energy of the electron in second state = %5.2f eV', E2/e);\n", +"// Result \n", +"// The energy of the electron in lowest state = 5.98 eV\n", +"// The energy of the electron in second state = 23.93 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.37: Lowest_energy_of_the_neutron_confined_to_the_nucleus.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.37:: Page-1.47 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m = 1.67e-027; // Electronic mass, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"l = 2.5e-010; // Length of one dimensional potential box, m\n", +"delta_x = 1e-014; // Uncertainty in position of neutron, m\n", +"// From uncertainty principle, \n", +"// delta_x*delta_p = h/(4*%pi), solving for delta_p\n", +"delta_p = h/(4*%pi*delta_x); // Uncertainty in momentum of neutron, kg-m/s\n", +"p = delta_p; // Momemtum of neutron in the box, kg-m/s\n", +"KE = p^2/(2*m); // Kinetic energy of neutron in the box, J\n", +"printf('\nThe lowest energy of the neutron confined to the nucleus = %4.2f MeV', KE/(e*1e+06));\n", +"// Result \n", +"// The lowest energy of the neutron confined to the nucleus = 0.05 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.38: X_ray_scattering.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.38: : Page-1.56 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m0 = 9.1e-031; // Electronic mass, kg\n", +"c = 3e+08; // Speed of light, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"phi = 45; // Scattering angle of X-rays, degrees\n", +"E = 75; // Incident energy of X-rays, keV\n", +"// As from Compton shift formula\n", +"// 1/E_prime - 1/E = 1/(m0*c^2)*(1-cosd(phi))\n", +"// Solving for E_prime\n", +"E_prime = 1/((1/(m0*c^2/(e*1e+03)))*(1-cosd(phi))+1/E); // Energy of scattered photon, keV\n", +"E_recoil = E - E_prime; // Energy of recoil electron, keV\n", +"printf('\nThe energy of scattered X-ray = %4.1f keV', E_prime);\n", +"printf('\nThe energy of recoil electron = %3.1f keV', E_recoil);\n", +"// Result \n", +"// The energy of scattered X-ray = 71.9 keV\n", +"// The energy of recoil electron = 3.1 keV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.39: Wavelength_of_scattered_Xray.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.39: : Page-1.57 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m0 = 9.1e-031; // Electronic mass, kg\n", +"c = 3e+08; // Speed of light, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"phi = 60; // Scattering angle of X-rays, degrees\n", +"E = 75; // Incident energy of X-rays, keV\n", +"// As from Compton shift formula\n", +"delta_L = h/(m0*c)*(1-cosd(phi)); // Change in photon wavelength, m\n", +"lambda = 0.198e-010; // Wavelength of incident photon, m\n", +"lambda_prime = (lambda+delta_L)/1e-010; // Wavelength of scattered X-ray, angstrom \n", +"printf('\nThe wavelength of scattered X-ray = %6.4f angstrom', lambda_prime);\n", +"// Result \n", +"// The wavelength of scattered X-ray = 0.2101 angstrom" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.3: de_Broglie_wavelength_of_an_accelerated_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.3: Page-1.5 (2009)\n", +"clc; clear;\n", +"V = 20e+03; // Accelerating voltage of electron, V\n", +"lambda = 12.25/sqrt(V); // de Broglie wavelength of the accelerated electron, m\n", +"printf('\nThe de Broglie wavelength of the electron = %6.4f angstrom', lambda);\n", +"\n", +"// Result \n", +"// The de Broglie wavelength of the electron = 0.0866 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.40: Wavelength_of_scattered_radiation_with_changed_angle_of_view.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.40:: Page-1.57 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m0 = 9.1e-031; // Electronic mass, kg\n", +"c = 3e+08; // Speed of light, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"phi = 180; // Scattering angle of X-rays, degrees\n", +"lambda = 1.78; // Wavelength of incident photon, m\n", +"lambda_prime = 1.798; // Wavelength of scattered X-ray, angstrom \n", +"// As from Compton shift formula\n", +"// lambda_prime - lambda = h/(m0*c)*(1-cosd(phi)), Change in photon wavelength, m\n", +"// Or we may write, lambda_prime - lambda = k*(1-cosd(phi))\n", +"// solving for k\n", +"k = (lambda_prime - lambda)/(1-cosd(phi)); // k = h/(m0*c) value, angstrom\n", +"// For phi = 60\n", +"phi = 60; // New angle of scattering, degrees\n", +"lambda_prime = lambda + k*(1-cosd(phi)); // Wavelength of scattered radiation at 60 degree angle, angstrom\n", +"printf('\nThe wavelength of scattered X-ray at %d degrees view = %6.4f angstrom', phi, lambda_prime);\n", +"// Recoil energy of electron\n", +"E = h*c*(1/lambda - 1/lambda_prime)*1e+010; // Recoil energy of electron, joule\n", +"printf('\nThe recoil energy of electron scattered through %d degrees = %4.1f eV', phi, E/e); \n", +"// Result \n", +"// The wavelength of scattered X-ray at 60 degrees view = 1.7845 angstrom\n", +"// The recoil energy of electron scattered through 60 degrees = 17.5 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.41: Compton_scattering_through_aluminium_foil.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.41:: Page-1.58 (2009)\n", +"clc; clear;\n", +"h = 6.6e-034; // Planck's constant, Js\n", +"m0 = 9.1e-031; // Electronic mass, kg\n", +"c = 3e+08; // Speed of light, m/s\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"phi = 90; // Scattering angle of X-rays, degrees\n", +"E = 510*1e+03*e; // Energy of incident photon, J\n", +"// As E = h*c/lambda, solving for lambda\n", +"lambda = h*c/E; // Wavelength of incident photon, m\n", +"// As from Compton shift formula\n", +"// lambda_prime - lambda = h/(m0*c)*(1-cosd(phi)), solving for lambda_prime\n", +"lambda_prime = lambda + h/(m0*c)*(1-cosd(phi)); // Wavelength of scattered X-ray, m \n", +"printf('\nThe wavelength of scattered X-ray as viewed at %d degrees = %4.2e m', phi, lambda_prime);\n", +"// Recoil energy of electron\n", +"E = h*c*(1/lambda - 1/lambda_prime); // Recoil energy of electron, joule\n", +"printf('\nThe recoil energy of electron scattered through %d degrees = %4.2e eV', phi, E/e);\n", +"// Direction of recoil electron\n", +"theta = atand(lambda*sind(phi)/(lambda_prime-lambda*cosd(phi))); // Direction of recoil electron, degrees\n", +"printf('\nThe direction of emission of recoil electron = %5.2f degrees', theta);\n", +" \n", +"// Result \n", +"// The wavelength of scattered X-ray as viewed at 90 degrees = 4.84e-12 m\n", +"// The recoil energy of electron scattered through 90 degrees = 2.55e+05 eV\n", +"// The direction of emission of recoil electron = 26.61 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.42: Energetic_electrons_in_the_Xray_tube.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.42: : Page-1.59 (2009)\n", +"clc; clear;\n", +"m = 9.1e-031; // Electronic mass, kg\n", +"c = 3e+08; // Speed of light, m/s\n", +"e = 1.6e-019; // Charge on the electron, C\n", +"V = 12.4e+03; // Potential diffeence applied across the X-ray tube, V\n", +"i = 2e-03; // Current through the X-ray tube, A\n", +"t = 1; // Time for which the electrons strike the target material, s\n", +"N = i*t/e; // Number of electrons striking the target per sec, per sec\n", +"v_max = sqrt(2*e*V/m); // Maximum speed of the electrons, m/s\n", +"printf('\nThe number of electrons striking the target per sec = %4.2e electrons/sec', N);\n", +"printf('\nThe maximum speed of the electrons when they strike = %3.1e m/s', v_max);\n", +" \n", +"// Result \n", +"// The number of electrons striking the target per sec = 1.25e+16 electrons/sec\n", +"// The maximum speed of the electrons when they strike = 6.6e+07 m/s" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.4: Energy_of_the_electron_from_de_Broglie_wavelength.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.4: Page-1.6 (2009)\n", +"clc; clear;\n", +"lambda = 5.2e-03; // de Broglie wavelength of the electron, m\n", +"m = 9.1e-031; // Mass of the electron, kg\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"// From de Broglie relation, lambda = h/sqrt(2*m*E), solving for E\n", +"E = h^2/(2*m*lambda^2*e); // Energy of the electron, eV\n", +"printf('\nThe energy of the electron from de Broglie wavelength = %5.3e eV', E);\n", +"\n", +"// Result \n", +"// The energy of the electron from de Broglie wavelength = 5.576e-014 eV \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.5: Velocity_and_de_Broglie_wavelength_of_a_neutron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.5: Page-1.6 (2009)\n", +"clc; clear;\n", +"m = 1.67e-027; // Mass of the neutron, kg\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"E = 1e+04*e; // Energy of the neutron, J\n", +"// As E = 1/2*m*v^2, solving for v\n", +"v = sqrt(2*E/m); // Velocity of the neutron, m/s\n", +"lambda = h/(m*v); // de Broglie wavelength of the neutron, m\n", +"printf('\nThe velocity of the neutron = %4.2e m/s', v);\n", +"printf('\nThe de Broglie wavelength of the neutron = %4.2e m', lambda);\n", +"\n", +"// Result \n", +"// The velocity of the neutron = 1.38e+006 m/s\n", +"// The de Broglie wavelength of the neutron = 2.87e-013 m \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.6: Wavelength_of_thermal_neutron_at_room_temperature.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.6: Page-1.6 (2009)\n", +"clc; clear;\n", +"m = 1.67e-027; // Mass of the neutron, kg\n", +"k = 1.38e-023; // Boltzmann constant, J/mol/K\n", +"T = 27+273; // Room temperature, K\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"v = sqrt(3*k*T/m); // Velocity of the neutron, m/s\n", +"lambda = h/(m*v); // de Broglie wavelength of the neutron, m\n", +"printf('\nThe de Broglie wavelength of the thermal neutrons = %4.2f angstrom', lambda/1e-010);\n", +"\n", +"// Result \n", +"// The de Broglie wavelength of the thermal neutrons = 1.45 angstrom \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.7: Angle_of_deviation_for_first_order_diffraction_maxima.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.7: Page-1.6 (2009)\n", +"clc; clear;\n", +"m = 9.1e-031; // Mass of the electron, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"E = 20e+03*e; // Energy of the electron, J\n", +"// As 1/2*m*v^2 = E, solving for v\n", +"v = sqrt(2*E/m); // Velocity of the electron, m/s\n", +"lambda = h/(m*v); // de Broglie wavelength of the electron, m\n", +"n = 1; // First order diffraction\n", +"d = 9.8e-011; // Atomic spacing for thin gold foil, m\n", +"// Using Bragg's equation, 2*d*sin(theta) = n*lambda and solving for theta\n", +"theta = asind(n*lambda/(2*d)); // Angle of deviation for first order diffraction maxima, degree\n", +"printf('\nThe angle of deviation for first order diffraction maxima = %4.2f degrees', theta);\n", +"\n", +"// Result \n", +"// The angle of deviation for first order diffraction maxima = 2.54 degrees \n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.8: de_Broglie_wavelength_of_a_moving_electron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.8: Page-1.7 (2009)\n", +"clc; clear;\n", +"m = 9.1e-031; // Mass of the electron, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"E = 5*e; // Energy of the electron, J\n", +"// As 1/2*m*v^2 = E, solving for v\n", +"v = sqrt(2*E/m); // Velocity of the electron, m/s\n", +"lambda = h/(m*v); // de Broglie wavelength of the electron, m\n", +"printf('\nThe de Broglie wavelength of the electron = %3.1f angstrom', lambda/1e-010);\n", +"\n", +"// Result \n", +"// The de Broglie wavelength of the electron = 5.5 angstrom\n", +"" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1.9: de_Broglie_wavelength_of_a_neutron_of_given_kinetic_energy.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.9: Page-1.7 (2009)\n", +"clc; clear;\n", +"m = 1.67e-027; // Mass of the neutron, kg\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"h = 6.626e-034; // Planck's constant, Js\n", +"E = 1*e; // Energy of the electron, J\n", +"lambda = h/sqrt(2*m*E); // de Broglie wavelength of the neutron, m\n", +"printf('\nThe de Broglie wavelength of the neutron = %4.2f angstrom', lambda/1e-010);\n", +"\n", +"// Result \n", +"// The de Broglie wavelength of the neutron = 0.29 angstrom \n", +"" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Physics_by_V_Yadav/2-Interference.ipynb b/Engineering_Physics_by_V_Yadav/2-Interference.ipynb new file mode 100644 index 0000000..4c57e85 --- /dev/null +++ b/Engineering_Physics_by_V_Yadav/2-Interference.ipynb @@ -0,0 +1,2191 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: Interference" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.10: Wavelength_of_light_in_a_biprism_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.10:: Page-2.12 (2009)\n", +"clc; clear;\n", +"D = 100; // Distance between slits and the screen, cm\n", +"d = 0.08; // Separation between the slits, cm\n", +"b = 2.121/25; // Fringe width of the interfernce pattern due to biprism, cm\n", +"lambda = b*d/D; // Wavelength of light in a biprism experiment, cm\n", +"printf('\nThe wavelength of light in a biprism experiment = %5.0f angstrom', lambda/1e-008);\n", +"// Result\n", +"// The wavelength of light in a biprism experiment = 6787 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.11: Fringe_width_at_a_certain_distance_from_biprism.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.11:: Page-2.13 (2009)\n", +"clc; clear;\n", +"alpha = %pi/180; // Acute angle of biprism, radian\n", +"mu = 1.5; // Refractive index of biprism\n", +"lambda = 5900e-008; // Wavelength of light used, cm\n", +"y1 = 10; // Distance of biprism from the source, cm\n", +"y2 = 100; // Distance of biprism from the screen, cm\n", +"D = y1 + y2; // Distance between slits and the screen, cm\n", +"d = 2*(mu-1)*alpha*y1; // Separation between the slits, cm\n", +"b = lambda*D/d; // Fringe width of the interfernce pattern due to biprism, cm\n", +"printf('\nThe fringe width at a distance of %d cm from biprism = %4.2e cm', y2, b);\n", +"// Result\n", +"// The fringe width at a distance of 100 cm from biprism = 3.72e-02 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.12: Distance_between_coherent_sources_in_biprism_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.12:: Page-2.13 (2009)\n", +"clc; clear;\n", +"lambda = 5893e-008; // Wavelength of light used, cm\n", +"y1 = 10; // Distance of biprism from the source, cm\n", +"y2 = 100; // Distance of biprism from the screen, cm\n", +"D = y1 + y2; // Distance between slits and the screen, cm\n", +"b = 3.5e-02; // Fringe width of the interfernce pattern due to biprism, cm\n", +"d = lambda*D/b; // Distance between coherent sources, cm\n", +"printf('\nThe distance between coherent sources = %5.3f cm', d);\n", +"// Result\n", +"// The distance between coherent sources = 0.185 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.13: Effect_of_slit_separation_on_fringe_width.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.13:: Page-2.13 (2009)\n", +"clc; clear;\n", +"b = 0.125; // Fringe width of the interfernce pattern due to biprism, cm\n", +"d = 1; // For simplicity assume distance between sources to be unity, cm\n", +"d_prime = 3/4*d; // New distance between sources, cm \n", +"// As b is proportional to 1/d, so\n", +"b_prime = b*d/d_prime; // New fringe width of the interfernce pattern due to biprism, cm\n", +"printf('\nThe new value of fringe width due to reduced slit separation = %5.3f cm', b_prime);\n", +"// Result\n", +"// The new value of fringe width due to reduced slit separation = 0.167 cm" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.14: Effect_of_slit_biprism_separation_on_fringe_width.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.14:: Page-2.13 (2009)\n", +"clc; clear;\n", +"b = 0.187; // Fringe width of the interfernce pattern due to biprism, cm\n", +"y1 = 1; // For simplicity assume distance between slit and biprism to be unity, cm\n", +"y1_prime = 1.25*y1; // New distance between slit and biprism, cm\n", +"// As d is directly proportional to y1 and b is directly proportional to d, so\n", +"// b is inversely proportional to y1\n", +"b_prime = b*y1/y1_prime; // New fringe width of the interfernce pattern due to biprism, cm\n", +"printf('\nThe new value of fringe width due to increased slit-biprism separation = %5.3f cm', b_prime);\n", +"// Result\n", +"// The new value of fringe width due to increased slit-biprism separation = 0.150 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.15: Distance_between_interference_bands.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.15:: Page-2.14 (2009)\n", +"clc; clear;\n", +"d1 = 5e-01; // First distance between images of the slit, cm\n", +"d2 = 2.25e-01; // Second distance between images of the slit, cm\n", +"lambda = 5896e-008; // Wavelength of the light used, cm\n", +"D = 120; // Distance between screen and the slits, cm\n", +"d = sqrt(d1*d2); // Geometric mean of distance between the two slits, cm\n", +"b = lambda*D/d; // Distance between interference bands, cm\n", +"printf('\nThe distance between interference bands = %5.3e cm', b);\n", +"// Result\n", +"// The distance between interference bands = 2.109e-02 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.16: Angle_of_vertex_of_Fresnel_biprism.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.16:: Page-2.14 (2009)\n", +"clc; clear;\n", +"mu = 1.5; // Refractive index of biprism\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"y1 = 25; // Distance of biprism from the source, cm\n", +"y2 = 150; // Distance of biprism from the screen, cm\n", +"D = y1 + y2; // Distance between slits and the screen, cm\n", +"b = 0.05; // Fringe width of the interfernce pattern due to biprism, cm\n", +"// As d = 2*(mu-1)*alpha*y1, solving for alpha\n", +"alpha = lambda*D/(b*2*(mu-1)*y1) // Angle of vertex of the biprism, radian\n", +"printf('\nThe angle of vertex of the biprism = %6.4f rad', alpha);\n", +"// Result\n", +"// The angle of vertex of the biprism = 0.0077 rad " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.17: Wavelength_of_light_used_in_biprism_experiment_to_illuminate_slits.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.17:: Page-2.15 (2009)\n", +"clc; clear;\n", +"theta = 178; // Vertex angle of biprism, degrees\n", +"alpha = (180-theta)/2*%pi/180; // Acute angle of biprism, radian\n", +"mu = 1.5; // Refractive index of biprism\n", +"y1 = 20; // Distance of biprism from the source, cm\n", +"y2 = 125; // Distance of biprism from the screen, cm\n", +"D = y1 + y2; // Distance between slits and the screen, cm\n", +"d = 2*(mu-1)*alpha*y1; // Separation between the slits, cm\n", +"b = 0.025; // Fringe width of the interfernce pattern due to biprism, cm\n", +"lambda = b*d/D; // Wavelength of light used, cm\n", +"printf('\nThe wavelength of light used to illuminate slits = %4d angstrom', lambda/1e-08);\n", +"// Result\n", +"// The wavelength of light used to illuminate slits = 6018 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.18: Vertex_angle_of_Fresnel_biprism.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.18:: Page-2.15 (2009)\n", +"clc; clear;\n", +"mu = 1.5; // Refractive index of biprism\n", +"lambda = 6600e-008; // Wavelength of light used, cm\n", +"y1 = 40; // Distance of biprism from the source, cm\n", +"y2 = 175; // Distance of biprism from the screen, cm\n", +"D = y1 + y2; // Distance between slits and the screen, cm\n", +"b = 0.04; // Fringe width of the interfernce pattern due to biprism, cm\n", +"// As d = 2*(mu-1)*alpha*y1, solving for alpha\n", +"alpha = lambda*D/(b*2*(mu-1)*y1) // Acute angle of the biprism, radian\n", +"theta = (%pi-2*alpha); // Vertex angle of the biprism, radian\n", +"printf('\nThe vertex angle of the biprism = %6.2f degrees', theta*180/%pi);\n", +"// Result\n", +"// The vertex angle of the biprism = 178.98 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.19: Order_of_visible_fringe_for_changed_wavelength_of_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.19: : Page-2.16 (2009)\n", +"clc; clear;\n", +"lambda1 = 7000e-008; // Original wavelength of light, cm\n", +"lambda2 = 5000e-008; // New wavelength of light, cm\n", +"n1 = 10; // Order of the fringes with original wavelength\n", +"// As x = n*lambda*D/d, so n*lambda = constant\n", +"// n1*lambda1 = n2*lambda2, solving for n2\n", +"n2 = n1*lambda1/lambda2; // Order of visible fringe for changed wavelength of light\n", +" \n", +"printf('\nThe order of visible fringe for changed wavelength of light = %2d', ceil(n2));\n", +"// Result\n", +"// The order of visible fringe for changed wavelength of light = 14 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1: Slit_separation_in_Double_Slit_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.1:: Page-2.9 (2009)\n", +"clc; clear;\n", +"lambda = 5893e-008; // Wavelength of light used, m\n", +"D = 200; // Distance of the source from the screen, m\n", +"b = 0.2; // Fringe separation, cm\n", +"d = lambda*D/b; // Separation between the slits, cm\n", +"\n", +"printf('\nThe separation between the slits = %3.1e cm', d);\n", +"\n", +"// Result \n", +"// The separation between the slits = 5.9e-002 cm" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.20: Angle_of_vertex_of_biprism.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex1.20:: Page-2.16 (2009)\n", +"clc; clear;\n", +"y1 = 40; // Distance between biprism from the slit, cm\n", +"D = 160; // Distance between slit and the screen, cm\n", +"mu = 1.52; // Refractive index of material of the prism\n", +"lambda = 5893e-008; // Wavelength of light used, cm\n", +"b = 0.01; // Fringe width, cm\n", +"// As b = lambda*D/d, solving for d\n", +"d = lambda*D/b; // Distance between virtual sources, cm\n", +"// But d = 2*y1*(mu-1)*alpha, solving for alpha\n", +"alpha = d/(2*y1*(mu-1))*180/%pi; // Angle of biprism, degrees\n", +"theta = 180-2*alpha; // Angle of vertex of biprism, degrees\n", +"printf('\nThe angle of vertex of biprism = %5.1f degree', theta);\n", +"// Result \n", +"// The angle of vertex of biprism = 177.4 degree " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.21: Separation_between_two_coherent_sources.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.21: : Page-2.16 (2009)\n", +"clc; clear;\n", +"lambda = 6000e-008; // Wavelength of light used, cm\n", +"D = 100; // Distance between slits and the screen, cm\n", +"b = 0.05; // Fringe width of the interfernce pattern due to biprism, cm\n", +"d = lambda*D/b; // Distance between coherent sources, cm\n", +"printf('\nThe distance between coherent sources = %3.1f mm', d/1e-01);\n", +"// Result\n", +"// The distance between coherent sources = 1.2 mm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.22: Refractive_index_of_the_glass_sheet.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.22:: Page-2.19 (2009)\n", +"clc; clear;\n", +"t = 3.2e-04; // Thickness of the glass sheet, cm\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"n = 5; // Order of interference fringes\n", +"// As path difference (mu - 1)*t = n*lambda\n", +"mu = n*lambda/t + 1; // Refractive indexof the glass sheet\n", +"\n", +"printf('\nThe refractive index of the glass sheet= %4.2f', mu);\n", +"\n", +"// Result \n", +"// The refractive indexof the glass sheet= 1.86 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.23: Refractive_index_of_material_of_sheet.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.23:: Page-2.19 (2009)\n", +"clc; clear;\n", +"t = 2.1e-03; // Thickness of the glass sheet, cm\n", +"lambda = 5400e-008; // Wavelength of light used, cm\n", +"n = 11; // Order of interference fringes\n", +"// As path difference, (mu - 1)*t = n*lambda\n", +"mu = n*lambda/t + 1; // Refractive index of the glass sheet\n", +"\n", +"printf('\nThe refractive index of the glass sheet = %4.2f', mu);\n", +"\n", +"// Result \n", +"// The refractive index of the glass sheet= 1.28 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.24: Wavelength_of_light_used_in_biprism_arrangement.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.24:: Page-2.19 (2009)\n", +"clc; clear;\n", +"t = 9.21e-05; // Thickness of the mica sheet, cm\n", +"mu = 1.5; // Refractive index of material of sheet\n", +"n = 1; // Order of interference fringes\n", +"// As path difference, (mu - 1)*t = n*lambda, solving for lambda\n", +"lambda = (mu - 1)*t/n; // Wavelength of light used, cm\n", +"\n", +"printf('\nThe wavelength of light used = %5.3e cm', lambda);\n", +"\n", +"// Result \n", +"// The wavelength of light used = 4.605e-005 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.25: Thickness_of_the_transparent_sheet.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.25:: Page-2.19 (2009)\n", +"clc; clear;\n", +"lambda = 5890e-008; // Wavelength of light used, cm\n", +"mu = 1.5; // Refractive index of material sheet\n", +"// As shift = 9*lambda*D/d = D/d*(mu - 1)*t, solving for t\n", +"t = 9*lambda/(mu - 1); // Thickness of the glass sheet, cm\n", +"printf('\nThe thickness of the glass sheet = %4.2e cm', t);\n", +"\n", +"// Result \n", +"// The thickness of the glass sheet = 1.06e-003 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.26: Thickness_of_the_transparent_sheet_from_fringe_shift.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.26:: Page-2.20 (2009)\n", +"clc; clear;\n", +"lambda = 5400e-008; // Wavelength of light used, cm\n", +"mu = 1.7; // Refractive index of material sheet convering the first slit\n", +"mu_prime = 1.5; // Refractive index of material sheet convering the seecond slit\n", +"// As shift, S = D/d*(mu - mu_prime)*t = b/lambda*(mu - mu_prime)*t, solving for t\n", +"t = 8*lambda/(mu-mu_prime) // Thickness of the glass sheet, cm\n", +"\n", +"printf('\nThe thickness of the glass sheet = %4.2e cm', t);\n", +"\n", +"// Result \n", +"// The thickness of the glass sheet = 2.16e-003 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.27: Refractive_index_of_thin_mica_sheet.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.27:: Page-2.20 (2009)\n", +"clc; clear;\n", +"t = 21.5e-05; // Thickness of the glass sheet, cm\n", +"lambda = 5890e-008; // Wavelength of light used, cm\n", +"n = 1; // Order of interference fringes\n", +"// As path difference, (mu - 1)*t = n*lambda\n", +"mu = n*lambda/t + 1; // Refractive indexof the glass sheet\n", +"\n", +"printf('\nThe refractive index of the glass sheet = %5.3f', mu);\n", +"\n", +"// Result \n", +"// The refractive index of the glass sheet = 1.274 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.28: Wavelength_of_light_used_in_double_slit_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.28:: Page-2.20 (2009)\n", +"clc; clear;\n", +"D = 1; // For simplicity assume distance between source and slits to be unity, unit\n", +"d = 1; // For simplicity assume slit separation to be unity, unit\n", +"t = 2.964e-06; // Thickness of the mica sheet, cm\n", +"mu = 1.5; // Refractive index of material of shee\n", +"L = poly(0, 'L');\n", +"// As b = b_prime or 2.25*D*L/d = D/d*(mu-1)*t, or we may write\n", +"L = roots(2.25*D*L/d-D/d*(mu-1)*t); // Wavelength of the light used, m\n", +"\n", +"printf('\nThe wavelength of the light used = %4.0f angstrom', L/1e-010);\n", +"\n", +"// Result \n", +"// The wavelength of the light used = 6587 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.29: Thickness_of_mica_sheet_from_central_fringe_shift.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.29:: Page-2.21 (2009)\n", +"clc; clear;\n", +"lambda = 5890e-008; // Wavelength of light used, cm\n", +"n = 5; // Order of interference fringes\n", +"mu = 1.5; // Refractive index of the mica sheet\n", +"// As path difference, (mu - 1)*t = n*lambda, solving for t\n", +"t = n*lambda/(mu-1); // Thickness of the mica sheet, cm\n", +"\n", +"printf('\nThe thickness of the mica sheet = %4.2e cm', t);\n", +"\n", +"// Result \n", +"// The thickness of the mica sheet = 5.89e-004 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2: Wavelength_of_light_in_Young_Double_Slit_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.2:: Page-2.10 (2009)\n", +"clc; clear;\n", +"d = 0.2; // Separation between the slits, cm\n", +"D = 100; // Distance of the source from the screen, m\n", +"b = 0.35e-01; // Fringe separation, cm\n", +"lambda = b*d/D; // Wavelength of light used, m\n", +"printf('\nThe wavelength of the light = %3.1e cm', lambda);\n", +"\n", +"// Result \n", +"// The wavelength of the light = 7.0e-005 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.30: Refractive_index_of_material_from_shifting_fringe_pattern.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.30:: Page-2.21 (2009)\n", +"clc; clear;\n", +"b = 1; // For simplicity assume fringe width to be unity, cm\n", +"S = 30*b; // Fringe shift, cm\n", +"lambda = 6600e-008; // Wavelength of light used, cm\n", +"t = 4.9e-003; // Thickness of the film, cm\n", +"// As S = b/lambda*(mu-1)*t, solving for mu\n", +"mu = S*lambda/t + 1; // Refractive index of material from shifting fringe pattern\n", +"\n", +"printf('\nThe refractive index of material from shifting fringe pattern = %3.1f', mu);\n", +"\n", +"// Result \n", +"// The refractive index of material from shifting fringe pattern = 1.4 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.31: EX2_31.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.31:: Page-2.22 (2009)\n", +"clc; clear;\n", +"mu1 = 1.55; // Refractive index of mica\n", +"mu2 = 1.52; // Refractive index of glass\n", +"t = 0.75e-003; // Thickness of the sheets, m\n", +"d = 0.25e-02; // Separation between the slits, m\n", +"lambda = 5896e-010; // Wavelength of light used, m\n", +"D = 1.5; // Distance between the source ans the slits, m\n", +"// Fringe width\n", +"b = lambda*D/d; // Fringe width, m\n", +"// Optical path difference\n", +"delta_x = (mu1-1)*t-(mu2-1)*t; // Optical path change, m\n", +"\n", +"printf('\nThe fringe width = %3.1e m', b);\n", +"printf('\nThe optical path change = %5.3e m', delta_x);\n", +"\n", +"// Result \n", +"// The fringe width = 3.5e-004 m\n", +"// The optical path change = 2.250e-005 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.32: Thickness_of_mica_sheet_from_Fresnel_biprism_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.32:: Page-2.22 (2009)\n", +"clc; clear;\n", +"b = 1; // For simplicity assume fringe width to be unity, cm\n", +"S = 3*b; // Fringe shift, cm\n", +"lambda = 5890e-008; // Wavelength of light used, cm\n", +"mu = 1.6; // Refractive index of the mica sheet\n", +"// As S = b/lambda*(mu-1)*t, solving for t\n", +"t = S*lambda/(mu-1); // Thickness of the mica sheet, cm\n", +"\n", +"printf('\nThe thickness of the mica sheet = %3.1e m', t/1e+02);\n", +"\n", +"// Result \n", +"// The thickness of the mica sheet = 2.9e-006 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.33: Smallest_thickness_of_glass_plate_for_a_fringe_of_minimum_intensity.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.33: : Page-2.26 (2009)\n", +"clc; clear;\n", +"mu = 1.5; // Refractive index of glass\n", +"lambda = 5100e-008; // Wavelength of light used, cm\n", +"i = 30; // Angle of incidence, degrees\n", +"n = 1; // Order of interference fringes\n", +"// From Snell's law, mu = sind(i)/sind(r), solving for r\n", +"r = asind(sind(i)/mu); // Angle of refraction, degrees\n", +"// For a dark fringe in reflection, 2*mu*t*cosd(r) = n*lambda, solving for t\n", +"t = n*lambda/(2*mu*cosd(r)); // Smallest thickness of glass plate for a fringe of minimum intensity, cm\n", +"printf('\nThe smallest thickness of glass plate for a fringe of minimum intensity = %4.2e cm', t);\n", +"\n", +"// Result \n", +"// The smallest thickness of glass plate for a fringe of minimum intensity = 1.80e-005 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.34: The_wavelength_reflected_strongly_from_the_soap_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.34:: Page-2.26 (2009)\n", +"clc; clear;\n", +"t = 3.1e-05; // Thickness of the soap film, cm\n", +"mu = 1.33; // Refractive index of the soap film\n", +"r = 0; // Angle of refraction of the light ray on the soap film, degrees\n", +"// For bright fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = (2*n+1)*lambda/2\n", +"lambda = zeros(3); \n", +"for n = 1:1:3\n", +" lambda(n) = 4*mu*t*cosd(r)/(2*(n-1)+1); // Wavelengths for n = 1, 2 and 3\n", +" if lambda(n) > 4000e-008 & lambda(n) < 7500e-008 then\n", +" lambda_reflected = lambda(n);\n", +" end\n", +"end\n", +"printf('\nThe wavelength reflected strongly from the soap film = %5.3e cm', lambda_reflected);\n", +"// Result\n", +"// The wavelength reflected strongly from the soap film = 5.497e-05 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.35: Order_of_interference_of_the_dark_band.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.35:: Page-2.27 (2009)\n", +"clc; clear;\n", +"t = 3.8e-05; // Thickness of the transparent film, cm\n", +"mu = 1.5; // Refractive index of the transparent film\n", +"i = 45; // Angle of incidence of the light ray on the transparent film, degrees\n", +"lambda = 5700e-008; // Wavelength of light, cm\n", +"// As mu = sind(i)/sind(r), solving for r\n", +"r = asind(sind(i)/mu);\n", +"// For dark fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = 2*n*lambda, solving for n\n", +"n = 2*mu*t*cosd(r)/lambda; // Order of interference of dark band\n", +"printf('\nThe order of interference of dark band = %d', ceil(n));\n", +"// Result\n", +"// The order of interference of dark band = 2velength reflected strongly from the soap film = 5.497e-05 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.36: Absent_wavelength_of_reflected_light_in_the_visible_spectrum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.36:: Page-2.27 (2009)\n", +"clc; clear;\n", +"t = 4.5e-05; // Thickness of the soap film, cm\n", +"mu = 1.33; // Refractive index of the soap film\n", +"i = 45; // Angle of incidence of the light ray on the soap film, degrees\n", +"// As mu = sind(i)/sind(r), solving for r\n", +"r = asind(sind(i)/mu);\n", +"// For dark fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = n*lambda, solving for lambda for different n's\n", +"lambda = zeros(4); \n", +"for n = 1:1:4\n", +" lambda(n) = 2*mu*t*cosd(r)/n; // Wavelengths for n = 1, 2, 3 and 4\n", +" if lambda(n) > 4000e-008 & lambda(n) < 7500e-008 then\n", +" lambda_absent = lambda(n);\n", +" end\n", +"end\n", +"printf('\nThe absent wavelength of reflected light in the visible spectrum = %4.2e', lambda_absent);\n", +"// Result\n", +"// The absent wavelength of reflected light in the visible spectrum = 5.07e-05 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.37: Minimum_thickness_of_the_plate_that_will_appear_dark_in_the_reflection_pattern.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.37:: Page-2.28 (2009)\n", +"clc; clear;\n", +"mu = 1.6; // Refractive index of the mica plate\n", +"r = 60; // Angle of refraction of the light ray on the mica plate, degrees\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"n = 1; // Order of interference for minimum thickness\n", +"// For dark fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = 2*n*lambda, solving for t\n", +"t = n*lambda/(2*mu*cosd(r)); // Minimum thickness of the plate that will appear dark in the reflection pattern\n", +"printf('\nThe minimum thickness of the plate that will appear dark in the reflection pattern = %4.2e cm', t);\n", +"// Result\n", +"// The minimum thickness of the plate that will appear dark in the reflection pattern = 3.44e-05 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.38: Thickness_of_the_thin_soap_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.38:: Page-2.28 (2009)\n", +"clc; clear;\n", +"mu = 1.33; // Refractive index of the thin soap film\n", +"lambda1 = 5500e-008; // Wavelength of the first dark fringe, cm\n", +"lambda2 = 5400e-008; // Wavelength of the consecutive dark fringe, cm\n", +"i = 30; // Angle of incidence of the light ray on the soap film, degrees\n", +"// For overlapping fringes, \n", +"// n*lambda1 = (n+1)*lambda2, solving for n\n", +"n = lambda2/(lambda1-lambda2); // Order of interference fringes\n", +"// As mu = sind(i)/sind(r), solving for r\n", +"r = asind(sind(i)/mu);\n", +"// For dark fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = 2*n*lambda1, solving for t\n", +"t = n*lambda1/(2*mu*cosd(r)); // Thickness of the thin soap film\n", +"printf('\nThe thickness of the thin soap film = %5.3e cm', t);\n", +"// Result\n", +"// The thickness of the thin soap film = 1.205e-03 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.39: Order_of_interference_for_which_light_is_strongly_reflected.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.39:: Page-2.29 (2009)\n", +"clc; clear;\n", +"t = 0.75e-06; // Thickness of the glass plate, m\n", +"mu = 1.5; // Refractive index of the glass plate\n", +"lambda1 = 4000e-010; // First wavelength of visible range, cm\n", +"lambda2 = 7000e-010; // Last wavelength of visible range, cm\n", +"r = 0; // Angle of refraction for normal incidence, degrees\n", +"n = zeros(2);\n", +"// For bright fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = (2*n+1)*lambda/2, solving for n\n", +"// For lambda1\n", +"n(1) = (4*mu*t*cosd(r)/lambda1-1)/2;\n", +"// For lambda2\n", +"n(2) = (4*mu*t*cosd(r)/lambda2-1)/2;\n", +"printf('\nFor n = %d and n = %d the light is strongly reflected.', n(1), ceil(n(2)));\n", +"// Result\n", +"// For n = 5 and n = 3 the light is strongly reflected. " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3: Ratio_of_maximum_intensity_to_minimum_intensity_of_interference_fringes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.3:: Page-2.10 (2009)\n", +"clc; clear;\n", +"I2 = 1; // For simplicity assume intensity from slit 2 to be unity, W/sq-m\n", +"I1 = I2*25; // Intensity from slit 1, W/sq-m\n", +"I_ratio = I1/I2; // Intensity ratio\n", +"a_ratio = sqrt(I_ratio); // Amplitude ratio\n", +"a2 = 1; // For simplicity assume amplitude from slit 2 to be unity, m\n", +"a1 = a_ratio*a2; // Amplitude from slit 1, m\n", +"I_max = (a1 + a2)^2; // Maximum intensity of wave during interference, W/sq-m\n", +"I_min = (a1 - a2)^2; // Minimum intensity of wave during interference, W/sq-m\n", +"cf = 4; // Common factor\n", +"printf('\nThe ratio of maximum intentisy to minimum intensity of interference fringes = %d/%d', I_max/cf, I_min/cf); \n", +"\n", +"// Result \n", +"// The ratio of maximum intentisy to minimum intensity of interference fringes = 9/4 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.40: Minimum_thickness_of_the_film_for_which_light_is_strongly_reflected.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.40:: Page-2.30 (2009)\n", +"clc; clear;\n", +"mu = 1.45; // Refractive index of the film\n", +"lambda = 5500e-010; // First wavelength of visible range, cm\n", +"r = 0; // Angle of refraction for normal incidence, degrees\n", +"n = 0; // Order of interference is zero for minimum thickness\n", +"// For bright fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = (2*n+1)*lambda/2, solving for t\n", +"t = (2*n+1)*lambda/(4*mu*cosd(r)); // Minimum thickness of the film for which light is strongly reflected\n", +"printf('\nThe minimum thickness of the film for which light is strongly reflected = %4.2e cm', t);\n", +"// Result\n", +"// The minimum thickness of the film for which light is strongly reflected = 9.48e-08 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.41: Thickness_of_the_soap_film_for_dark_fringe_in_reflected_pattern.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.41:: Page-2.30 (2009)\n", +"clc; clear;\n", +"mu = 5/4; // Refractive index of the film\n", +"lambda = 5890e-010; // Wavelength of visible light, cm\n", +"i = 45; // Angle of incidence, degrees\n", +"n = 1; // Order of interference is unity for minimum thickness in dark reflected pattern\n", +"// As mu = sind(i)/sind(r), solving for r\n", +"r = asind(sind(i)/mu);\n", +"// For dark fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = n*lambda, solving for t\n", +"t = n*lambda/(2*mu*cosd(r)); // Thickness of the soap film for dark fringe in reflected pattern\n", +"printf('\nThe thickness of the soap film for dark fringe in reflected pattern = %5.3e cm', t);\n", +"// Result\n", +"// The thickness of the soap film for dark fringe in reflected pattern = 2.857e-07 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.42: Wavelength_in_the_visible_range_which_is_intensified_in_the_reflected_beam.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.42:: Page-2.30 (2009)\n", +"clc; clear;\n", +"mu = 1.5; // Refractive index of the plate\n", +"t = 0.5e-006; // Thickness of the plate, m\n", +"r = 0; // Angle of refraction for normal incidence, degrees\n", +"// For bright fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = (2*n+1)*lambda/2, solving for lambda for different n's\n", +"lambda = zeros(4); \n", +"for n = 0:1:3\n", +" lambda(n+1) = 4*mu*t*cosd(r)/(2*n+1); // Wavelengths for n = 0, 1, 2 and 3\n", +" lambda_strong = lambda(n+1);\n", +" if lambda(n+1) >= 4000e-010 & lambda(n+1) <= 7500e-010 then\n", +" if lambda_strong > lambda(n+1) then // Search for the stronger wavelength\n", +" lambda_strong = lambda(n+1);\n", +" end\n", +" end\n", +"end\n", +"printf('\nFor n = %d, %4.0f angstrom will be reflected strongly', n, lambda_strong/1e-010);\n", +"// Result\n", +"// For n = 3, 4286 angstrom will be reflected strongly " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.43: Thickness_of_the_film_with_incident_white_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.43:: Page-2.31(2009)\n", +"clc; clear;\n", +"mu = 1.33; // Refractive index of the film\n", +"i = asind(0.8); // Angle of refraction for normal incidence, degrees\n", +"// As mu = sind(i)/sind(r), solving for r\n", +"r = asind(sind(i)/mu);\n", +"lambda1 = 6100e-010; // First wavelength of dark band, m\n", +"lambda2 = 6000e-010; // Second wavelength of dark band, m\n", +"// For consecutive overlapping wavelenghts\n", +"// n*lambda1 = (n+1)*lambda2, solving for n\n", +"n = lambda2/(lambda1-lambda2);\n", +"// For dark fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = n*lambda1, solving for t\n", +"t = n*lambda1/(2*mu*cosd(r)); // Thickness of the film with incident white light. m\n", +"printf('\nThickness of the film with incident white light = %3.1e m', t);\n", +"// Result\n", +"// Thickness of the film with incident white light = 1.7e-05 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.44: Thickness_of_the_film_with_parallel_beam_of_yellow_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.44:: Page-2.31(2009)\n", +"clc; clear;\n", +"mu = 1.5; // Refractive index of the film\n", +"i = 45; // Angle of incidence, degrees\n", +"// As mu = sind(i)/sind(r), solving for r\n", +"r = asind(sind(i)/mu);\n", +"lambda = 5500e-010; // Wavelength of parallel beam of light, m\n", +"n = 15; // Order of dark band\n", +"// For dark fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = n*lambda, solving for t\n", +"t = n*lambda/(2*mu*cosd(r)); // Thickness of the film with incident parallel beam of light. m\n", +"printf('\nThe thickness of the film with paralle beam of yellow light = %4.2e m', t);\n", +"// Result\n", +"// The thickness of the film with paralle beam of yellow light = 3.12e-06 m" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.46: Refractive_index_of_oil.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.46:: Page-2.33(2009)\n", +"clc; clear;\n", +"V = 0.58e-006; // Volume of oil, metre cube\n", +"A = 2.5; // Area of water surface, metre square\n", +"t = V/A; // Thickness of film, m\n", +"r = 0; // Angle of refraction for normal incidence, degrees\n", +"n = 1; // Order of interference for minimum thickness\n", +"lambda = 4700e-010; // Wavelength of light used, m\n", +"// For dark fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = n*lambda, solving for mu\n", +"mu = n*lambda/(2*t*cosd(r)); // Refractive index of oil\n", +"printf('\nThe refractive index of oil = %5.3f', mu);\n", +"// Result\n", +"// The refractive index of oil = 1.013 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.47: EX2_47.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.47:: Page-2.33(2009)\n", +"clc; clear;\n", +"mu = 1.46; // Refractive index of the soap film\n", +"lambda = 6000e-010; // Wavelength of light used, m\n", +"r = 0; // Angle of refraction for normal incidence, degrees\n", +"n = 0; // Order of interference for minimum thickness\n", +"// For bright fringe in reflected pattern,\n", +"// 2*mu*t*cosd(r) = (2*n+1)*lambda/2, solving for mu\n", +"t = (2*n+1)*lambda/(4*mu*cosd(r)); // Thickness of soap film, m\n", +"printf('\nThe thickness of soap film = %5.3e m', t);\n", +"// Result\n", +"// The thickness of soap film = 1.027e-07 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.48: Wavelength_of_light_falling_on_wedge_shaped_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.48: : Page-2.35(2009)\n", +"clc; clear;\n", +"mu = 1.4; // Refractive index of the film\n", +"alpha = 1.07e-004; // Acute angle of the wedge, radian\n", +"b = 0.2; // Fringe width, cm\n", +"// As b = lambda/(2*mu*alpha), solving for lambda\n", +"lambda = 2*mu*alpha*b; // Wavelength of light falling on wedge shaped film, m\n", +"printf('\nThe wavelength of light falling on wedge shaped film = %4d ansgtrom', lambda/1e-008);\n", +"// Result\n", +"// The wavelength of light falling on wedge shaped film = 5991 ansgtrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.49: Difference_between_the_thicknesses_of_the_films.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.49:: Page-2.35(2009)\n", +"clc; clear;\n", +"mu = 1.4; // Refractive index of the film\n", +"lambda = 5500e-008; // Wavelength of the light, cm\n", +"// As alpha = (delta_t)/x and x = 10*b; b = lambda/(2*mu*alpha), solving for dt\n", +"delta_t = 10*lambda/(2*mu); // Difference between the thicknesses of the films, cm\n", +"printf('\nDifference between the thicknesses of the films = %4.2e cm', delta_t);\n", +"// Result\n", +"// Difference between the thicknesses of the films = 1.96e-04 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4: Wavelength_of_light_from_monochromatic_coherent_sources.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.4:: Page-2.10 (2009)\n", +"clc; clear;\n", +"d = 0.02; // Separation between the slits, cm\n", +"D = 100; // Distance of the source from the screen, m\n", +"n = 6; // No. of bright fringe from the centre\n", +"x = 1.22; // Position of 6th bright fringe, cm\n", +"lambda = x*d/(n*D); // Wavelength of light used, m\n", +"printf('\nThe wavelength of the light from coherent sources = %5.3e cm', lambda);\n", +"\n", +"// Result \n", +"// The wavelength of the light from coherent sources = 4.067e-005 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.50: Angle_of_thin_wedge_shaped_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.50:: Page-2.36(2009)\n", +"clc; clear;\n", +"mu = 1.6; // Refractive index of the film\n", +"lambda = 5500e-008; // Wavelength of the light, cm\n", +"b = 0.1; // Fringe width, cm\n", +"// As b = lambda/(2*mu*alpha), solving for alpha\n", +"alpha = lambda/(2*mu*b); // Angle of thin wedge shaped film, radian\n", +"printf('\nAngle of thin wedge shaped film = %3.1e radian', alpha);\n", +"// Result\n", +"// Angle of thin wedge shaped film = 1.7e-04 radian " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.51: Wavelength_of_light_used_to_illuminate_a_wedge_shaped_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.51:: Page-2.36(2009)\n", +"clc; clear;\n", +"mu = 1.5; // Refractive index of the film\n", +"b = 0.20; // Fringe width, cm\n", +"theta = 25/(60*60)*%pi/180; // Angle of the wedge, radian\n", +"// As b = lambda/(2*mu*theta), solving for lambda\n", +"lambda = 2*mu*b*theta; // Wavelength of light used to illuminate a wedge shaped film, cm\n", +"printf('\nThe wavelength of light used to illuminate a wedge shaped film = %4d angstrom', lambda/1e-008);\n", +"// Result\n", +"// The wavelength of light used to illuminate a wedge shaped film = 7272 angstrom\n", +"// The answer is given wrong in the textbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.52: Thickness_of_the_wire_separating_two_glass_surfaces.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.52:: Page-2.36(2009)\n", +"clc; clear;\n", +"lambda = 5893e-010; // Wavelength of light used, m\n", +"mu = 1; // Refractive index of the glass\n", +"b = 1; // Assume fringe width to be unity, cm\n", +"// As b = l/20, solving for l\n", +"l = b*20; // Length of the film, m\n", +"// As b = lambda/(2*mu*theta) and theta = t/l, solving for t\n", +"t = lambda*l/(2*mu); // Thickness of the wire separating two glass surfaces, m\n", +"printf('\nThe thickness of the wire separating two glass surfaces = %4.2e m', t);\n", +"// Result\n", +"// The thickness of the wire separating two glass surfaces = 5.89e-06 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.53: Angle_of_the_wedge_shaped_air_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.53:: Page-2.37(2009)\n", +"clc; clear;\n", +"mu = 1; // Refractive index of the air film\n", +"b = 1.5/25; // Fringe width, cm\n", +"lambda = 5893e-008; // Wavelength of light used to illuminate a wedge shaped film, cm\n", +"// As b = lambda/(2*mu*theta), solving for theta\n", +"theta = lambda/(2*mu*b); // Angle of the wedge, radian\n", +"printf('\nThe angle of the wedge shaped air film = %5.3f degrees', theta*180/%pi);\n", +"// Result\n", +"// The angle of the wedge shaped air film = 0.028 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.54: Acute_angle_of_the_wedge_shaped_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.54:: Page-2.37(2009)\n", +"clc; clear;\n", +"mu = 1.45; // Refractive index of the film\n", +"b = 1/10; // Fringe width, cm\n", +"lambda = 6600e-008; // Wavelength of light used to illuminate a wedge shaped film, cm\n", +"// As b = lambda/(2*mu*theta), solving for theta\n", +"theta = lambda/(2*mu*b); // Angle of the wedge, radian\n", +"printf('\nThe acute angle of the wedge shaped film = %6.4f degrees', theta*180/%pi);\n", +"// Result\n", +"// The acute angle of the wedge shaped film = 0.0130 degrees" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.55: Diameter_of_nth_dark_ring_due_to_first_wavelength.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.55:: Page-2.46(2009)\n", +"clc; clear;\n", +"lambda1 = 6000e-008; // First visible wavelength, cm\n", +"lambda2 = 4500e-008; // Second visible wavelength, cm\n", +"R = 100; // Radius of curvature of the lens, cm\n", +"// As diameter of nth dark ring due to lambda1 is\n", +"// D_n^2 = 4*n*R*lambda1 and D_nplus1^ = 4*(n+1)*R*lambda2, so that D_n^2 = D_nplus1^2 gives\n", +"n = lambda2/(lambda1-lambda2); // Order of interference for dark fringes\n", +"D_n = sqrt(4*n*R*lambda1); // Diameter of nth dark ring due to lambda1 \n", +"printf('\nThe diameter of nth dark ring due to wavelength of %4d angstrom = %4.2f cm', lambda1/1e-008, D_n);\n", +"// Result\n", +"// The diameter of nth dark ring due to wavelength of 6000 angstrom = 0.27 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.56: Diameter_of_fifteenth_dark_ring.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.56:: Page-2.46(2009)\n", +"clc; clear;\n", +"R = 1; // For simplicity assume radius of curvature of the lens to be unity, cm\n", +"D_n = 0.251; // Diameter of 3rd dark ring, cm\n", +"D_nplusp = 0.548; // Diameter of 9th dark ring, cm\n", +"n = 3; // Order of 3rd Newton ring\n", +"p = 9 - n; // Order of 6th Newton ring from 3rd ring\n", +"// As D_nplusp^2 - D_n^2 = 4*p*R*lambda, solving for lambda\n", +"lambda = (D_nplusp^2 - D_n^2)/(4*p*R); // Wavelength of light used\n", +"D_15 = sqrt(D_n^2+4*(15-n)*lambda*R); // Diameter of 15th dark ring, cm\n", +"printf('\nThe diameter of 15th dark ring = %5.3f cm', D_15);\n", +"// Result\n", +"// The diameter of 15th dark ring = 0.733 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.57: Order_of_a_dark_ring_having_thrice_the_diameter_of_the_thirtieth_ring.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.57: : Page-2.47(2009)\n", +"clc; clear;\n", +"R = 1; // For simplicity assume radius of curvature of the lens to be unity, cm\n", +"n = 30; // Order of 3rd Newton ring\n", +"D_30 = 1; // Assume diameter of thirtieth ring to be unity, cm\n", +"// As D_30^2 = 4*n*R*lambda, solving for lambda\n", +"lambda = D_30^2/(4*n*R); // Wavelength of light used, cm\n", +"D_n = 3*D_30; // Diameter of nth dark ring having thrice the diameter of the thirtieth ring, cm\n", +"n = D_n^2/(4*R*lambda); // Order of a dark ring having thrice the diameter of the thirtieth ring\n", +"printf('\nThe order of the dark ring having thrice the diameter of the thirtieth ring = %3d', n);\n", +"// Result\n", +"// The order of the dark ring having thrice the diameter of the thirtieth ring = 270 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.58: Radius_of_curvature_of_lens_and_thickness_of_air_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.58:: Page-2.47(2009)\n", +"clc; clear;\n", +"n = 15; // Order of 15rd Newton ring\n", +"D_15 = 0.75; // Diameter of fifteenth dark ring, cm\n", +"lambda = 5890e-008; // Wavelength of light used, cm\n", +"// As D_15^2 = 4*15*R*lambda, solving for R\n", +"R = D_15^2/(4*15*lambda); // Radius of curvature of lens, cm\n", +"// For dark ring, 2*t = n*lambda, solving for t\n", +"t = n*lambda/2; // Thickness of air film, cm\n", +"printf('\nThe radius of curvature of lens = %5.1f cm', R);\n", +"printf('\nThe thickness of air film = %3.1e cm', t);\n", +"// Result\n", +"// The radius of curvature of lens = 159.2 cm\n", +"// The thickness of air film = 4.4e-004 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.59: Refractive_index_of_the_liquid.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.59:: Page-2.47(2009)\n", +"clc; clear;\n", +"D_15 = 1.62; // Diameter of 15th dark ring with air film, cm\n", +"D_15_prime = 1.47; // Diameter of 15th dark ring with liquid, cm\n", +"R = 1; // For simplicity assume radius of curvature to be unity, cm\n", +"n = 15; // Order of 15rd Newton ring\n", +"// As for ring with air film, D_15^2 = 4*15*R*lambda, solving for lambda\n", +"lambda = D_15^2/(4*15*R); // Wavelength of light used, cm\n", +"// As for ring with liquid, D_15_prime^2 = 4*15*R*lambda/mu, solving for mu\n", +"mu = 4*15*R*lambda/D_15_prime^2; // Refractive index of the liquid\n", +"printf('\nThe refractive index of the liquid = %4.2f', mu)\n", +"// Result\n", +"// The refractive index of the liquid = 1.21 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5: Separation_between_fourth_order_dark_fringes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.5:: Page-2.10 (2009)\n", +"clc; clear;\n", +"lambda1 = 5890e-008; // Wavelength of D1 line of sodium, cm\n", +"lambda2 = 5896e-008; // Wavelength of D2 line of sodium, cm\n", +"D = 120; // Distance between source and the screen, cm\n", +"d = 0.025; // Separation between the slits, cm\n", +"n = 4; // Order of dark fringe\n", +"x1 = (2*n+1)*lambda1*D/(2*d); // Position of 4th dark fringe due to D1 line, cm\n", +"x2 = (2*n+1)*lambda2*D/(2*d); // Position of 4th dark fringe due to D2 line, cm\n", +"delta_x = x2-x1; // Fringe separation, cm\n", +"printf('\nThe separation between fourth order dark fringes = %4.2e cm', x2-x1);\n", +"// Result\n", +"// The separation between fourth order dark fringes = 1.30e-03 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.60: Wavelength_of_light_used_in_Newton_rings_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.60:: Page-2.48(2009)\n", +"clc; clear;\n", +"D_10 = 0.48; // Diameter of 10th dark ring with air film, cm\n", +"D_3 = 0.291; // Diameter of 3rd dark ring with air film, cm\n", +"p = 7; // Order of the 10th ring next to the 3rd ring\n", +"R = 90; // Radius of curvature of the lens, cm\n", +"lambda = (D_10^2-D_3^2)/(4*p*R); // Wavelength of light used in Newton rings experiment\n", +"printf('\nThe wavelength of light used in Newton rings experiment = %4d angstrom', lambda/1e-008);\n", +"// Result\n", +"// The wavelength of light used in Newton rings experiment = 5782 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.61: Diameter_of_fifteenth_bright_ring.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.61:: Page-2.48(2009)\n", +"clc; clear;\n", +"R1 = 200; // Radius of curvature of the convex surface, cm\n", +"R2 = 250; // Radius of curvature of the concave surface, cm\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"n = 15; // Order of interfernce Newton ring\n", +"// As r_n^2*(1/R1-1/R2) = (2*n-1)*lambda/2, solving for r_n\n", +"r_n = sqrt((2*n-1)*lambda/(2*(1/R1-1/R2))); // Radius of nth ring, cm\n", +"D_15 = 2*r_n; // Daimeter of 15th bright ring, cm\n", +"printf('\nThe daimeter of 15th bright ring = %4.2f cm', D_15);\n", +"// Result\n", +"// The daimeter of 15th bright ring = 1.79 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.62: Wavelength_of_light_used_in_Newton_rings_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.62:: Page-2.49(2009)\n", +"clc; clear;\n", +"R = 80; // Radius of curvature of the convex surface, cm\n", +"D5 = 0.192; // Diameter of 5th dark ring, cm\n", +"D25 = 0.555; // Diameter of 25th dark ring, cm\n", +"n = 5; // Order of interfernce Newton ring\n", +"P = 25 - n;\n", +"lambda = (D25^2 - D5^2)/(4*P*R); // Wavelength of light used, cm\n", +"printf('\nThe wavelength of light used = %5.3e cm', lambda);\n", +"// Result\n", +"// The wavelength of light used = 4.237e-005 cm \n", +"// The expression for lambda is given wrong in the textbook but solved correctly" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.63: Diameter_of_fifteenth_dark_Newton_ring.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.63:: Page-2.49(2009)\n", +"clc; clear;\n", +"R1 = 4; // Radius of curvature of the convex surface, m\n", +"R2 = 5; // Radius of curvature of the concave surface, m\n", +"lambda = 6600e-010; // Wavelength of light used, cm\n", +"n = 15; // Order of Newton ring\n", +"// As D_n^2*(1/R1-1/R2) = 4*n*lambda, solving for D_n\n", +"D_15 = sqrt(4*n*lambda/(1/R1-1/R2)); // Diameter of 15th dark ring, cm\n", +"printf('\nThe diameter of %dth dark ring = %4.2e m', n, D_15);\n", +"// Result\n", +"// The diameter of 15th dark ring = 2.81e-002 m \n", +"// The answer is given wrong in the textbook (the square root is not solved)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.64: Diameter_of_fifteenth_dark_ring_due_to_first_wavelength.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.64:: Page-2.49(2009)\n", +"clc; clear;\n", +"lambda1 = 6000e-008; // First visible wavelength, cm\n", +"lambda2 = 4500e-008; // Second visible wavelength, cm\n", +"R = 120; // Radius of curvature of the lens, cm\n", +"// As diameter of nth dark ring due to lambda1 is\n", +"// D_n^2 = 4*n*R*lambda1 and D_nplus1^ = 4*(n+1)*R*lambda2, so that D_n^2 = D_nplus1^2 gives\n", +"n = lambda2/(lambda1-lambda2); // Order of interference for dark fringes\n", +"printf('\nThe value of n = %d', n);\n", +"n = 15; // Order of interference fringe\n", +"D_n = sqrt(4*n*R*lambda1); // Diameter of nth dark ring due to lambda1 \n", +"printf('\nThe diameter of 15th dark ring due to wavelength of %4d angstrom = %4.2f cm', lambda1/1e-008, D_n);\n", +"// Result\n", +"// The value of n = 3\n", +"// The diameter of 15th dark ring due to wavelength of 6000 angstrom = 0.66 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.65: Refractive_index_of_the_liquid_filled_into_container.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.65:: Page-2.49(2009)\n", +"clc; clear;\n", +"lambda = 5896e-008; // Wavelength of light used, cm\n", +"R = 100; // Radius of curvature of the lens, cm\n", +"D10 = 0.4; // Diametre of 10th dark ring, cm\n", +"n = 10; // Order of Newton ring\n", +"// As for a dark ring, 2*mu*t = n*lambda and 2*t = (D10/2)^2/R, solving for mu\n", +"mu = 4*n*lambda*R/D10^2; // Refractive index of the liquid filled into container\n", +"printf('\nThe refractive index of the liquid filled into container = %4.2f', mu);\n", +"// Result\n", +"// The refractive index of the liquid filled into container = 1.47 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.67: Refractive_index_of_the_liquid.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.67:: Page-2.50(2009)\n", +"clc; clear;\n", +"Dn = 1.8; // Diameter of 15th dark ring, cm\n", +"Dn_prime = 1.67; // Diameter of 15th dark ring with liquid, cm\n", +"mu = (Dn/Dn_prime)^2; // Refractive index of the liquid\n", +"printf('\nThe refractive index of the liquid = %4.2f', mu);\n", +"// Result\n", +"// The refractive index of the liquid = 1.16 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.68: Diameter_of_eighteenth_dark_ring.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.68:: Page-2.51(2009)\n", +"clc; clear;\n", +"R = 1; // For simplicity assume radius of curvature to be unity, cm\n", +"D8 = 0.45; // Diameter of 8th dark ring, cm\n", +"D15 = 0.81; // Diameter of 15th dark ring, cm\n", +"n = 8; // Order of 8th Newton ring\n", +"p = 7; // Order of 7th Newton ring after 8th ring\n", +"lambda = (D15^2-D8^2)/(4*p*R); // Wavelength of light used, cm\n", +"// As D18^2-D15^2 = 4*p*lambda*R\n", +"p = 3; // For 18th and 15th rings\n", +"D18 = sqrt(D15^2+4*p*lambda*R); // Diameter of 18th ring, cm\n", +"printf('\nThe diameter of 18th dark ring = %6.4f cm', D18);\n", +"// Result\n", +"// The diameter of 18th dark ring = 0.9222 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.69: EX2_69.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.69:: Page-2.51(2009)\n", +"clc; clear;\n", +"R = 100; // Radius of curvature of plano-convex lens, cm\n", +"D15 = 0.590; // Diameter of 15th dark ring, cm\n", +"D5 = 0.336; // Diameter of 5th dark ring, cm\n", +"p = 10; // Order of 10th Newton ring after 5th ring\n", +"lambda = (D15^2-D5^2)/(4*p*R); // Wavelength of light used, cm\n", +"printf('\nThe wavelength of light used = %4.0f ansgtrom', lambda/1e-008);\n", +"// Result\n", +"// The wavelength of light used = 5880 ansgtrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6: Distance_between_two_coherent_sources.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.6:: Page-2.11 (2009)\n", +"clc; clear;\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"Y1 = 10; // Distance of biprism from the source, cm\n", +"Y2 = 90; // Distance of biprism from the screen, cm\n", +"D = Y1 + Y2; // Distance between slits and the screen, cm\n", +"b = 8.526e-02; // Fringe width, cm\n", +"d = lambda*D/b; // Separation between the slits, cm\n", +"printf('\nThe distance between two coherent sources = %4.2e cm', d);\n", +"// Result\n", +"// The distance between two coherent sources = 6.45e-02 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.70: Wavelength_of_monochromatic_light_used_in_Michelson_Interferometer.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.70:: Page-2.57(2009)\n", +"clc; clear;\n", +"N = 250; // Number of fringes crossing the field of view\n", +"delta_x = 0.0595e-01; // Displacement in movable mirror, cm\n", +"// As N*lambda/2 = delta_x, solving for lambda\n", +"lambda = 2*delta_x/N; // Wavelength of light used, cm\n", +"printf('\nThe wavelength of monochromatic light used = %4.0f ansgtrom', lambda/1e-008);\n", +"// Result\n", +"// The wavelength of monochromatic light used = 4760 ansgtrom \n", +"// Answer is given wrong in the textbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.71: Number_of_fringes_that_passes_across_the_cross_wire_of_telescope.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.71:: Page-2.58(2009)\n", +"clc; clear;\n", +"delta_x = 0.02559e-01; // Displacement in movable mirror, cm\n", +"lambda = 5890e-008; // Wavelength of light used, cm\n", +"// As N*lambda/2 = delta_x, solving for N\n", +"N = 2*delta_x/lambda; // Number of fringes crossing the field of view\n", +"printf('\nThe number of fringes that passes across the cross wire of telescope = %2d', ceil(N));\n", +"// Result\n", +"// The number of fringes that passes across the cross wire of telescope = 87 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.72: Distance_between_two_successive_positions_of_movable_mirror.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.72:: Page-2.58(2009)\n", +"clc; clear;\n", +"lambda1 = 5890e-008; // Wavelength corresponding to the D1 line, cm\n", +"lambda2 = 5896e-008; // Wavelength corresponding to the D2 line, cm\n", +"delta_lambda = lambda2 - lambda1; // Difference in the wavelengths, cm\n", +"// As delta_lambda = lambda1*lambda2/(2*x), solving for x\n", +"x = lambda1*lambda2/(2*(lambda2-lambda1)); // Distance between two successive positions of movable mirror\n", +"printf('\nThe distance between two successive positions of movable mirror = %3.1e cm', x);\n", +"// Result\n", +"// The distance between two successive positions of movable mirror = 2.9e-002 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.73: Thickness_of_the_transparent_glass_film.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.73:: Page-2.58(2009)\n", +"clc; clear;\n", +"N = 550; // Number of fringes crossing the field of view\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"mu = 1.5; // Refractive index of the glass slab\n", +"// As 2*(mu-1)*t = N*lambda, solving for t\n", +"t = N*lambda/(2*(mu-1)); // Thickness of the transparent glass film\n", +"printf('\nThe distance between two successive positions of movable mirror = %3.1e cm', t);\n", +"// Result\n", +"// The distance between two successive positions of movable mirror = 3.0e-002 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7: Fringe_width_of_the_interference_pattern_due_to_biprism.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.7:: Page-2.11 (2009)\n", +"clc; clear;\n", +"alpha = %pi/180; // Acute angle of biprism, radian\n", +"mu = 1.5; // Refractive index of biprism\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"y1 = 5; // Distance of biprism from the source, cm\n", +"y2 = 75; // Distance of biprism from the screen, cm\n", +"D = y1 + y2; // Distance between slits and the screen, cm\n", +"d = 2*(mu-1)*alpha*y1; // Separation between the slits, cm\n", +"b = lambda*D/d; // Fringe width of the interfernce pattern due to biprism, cm\n", +"printf('\nThe fringe width of the interfernce pattern due to biprism = %4.2e cm', b);\n", +"// Result\n", +"// The fringe width of the interfernce pattern due to biprism = 5.04e-02 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.8: Angle_of_vertex_of_the_biprism.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.8:: Page-2.11 (2009)\n", +"clc; clear;\n", +"mu = 1.5; // Refractive index of biprism\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"y1 = 5; // Distance of biprism from the source, cm\n", +"y2 = 95; // Distance of biprism from the screen, cm\n", +"D = y1 + y2; // Distance between slits and the screen, cm\n", +"b = 0.025; // Fringe width of the interfernce pattern due to biprism, cm\n", +"// As d = 2*(mu-1)*alpha*y1, solving for alpha\n", +"alpha = lambda*D/(b*2*(mu-1)*y1) // Angle of vertex of the biprism, radian\n", +"printf('\nThe angle of vertex of the biprism = %3.1e rad', alpha);\n", +"// Result\n", +"// The angle of vertex of the biprism = 4.4e-02 rad " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.9: Number_of_interference_fringes_for_changed_wavelength.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex2.9:: Page-2.12 (2009)\n", +"clc; clear;\n", +"n1 = 69; // Number of interference fringes obtained with yellow wavelength\n", +"lambda1 = 5893e-008; // Wavelength of yellow light used, cm\n", +"lambda2 = 5461e-008; // Wavelength of green light used, cm\n", +"// As n*lambda = l*d/D = constant, therefore\n", +"n2 = n1*lambda1/lambda2; // Number of interference fringes for green wavelength\n", +"printf('\nThe number of interference fringes for changed wavelength = %2d', ceil(n2));\n", +"// Result\n", +"// The number of interference fringes for changed wavelength = 75 " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Physics_by_V_Yadav/3-Diffraction.ipynb b/Engineering_Physics_by_V_Yadav/3-Diffraction.ipynb new file mode 100644 index 0000000..4eb1e2e --- /dev/null +++ b/Engineering_Physics_by_V_Yadav/3-Diffraction.ipynb @@ -0,0 +1,1494 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 3: Diffraction" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.10: Slit_width_in_Fraunhoffer_single_slit_experiment.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.10:: Page-3.24 (2009)\n", +"clc; clear;\n", +"f = 250; // Focal length of the lens, cm\n", +"x = 0.8; // Half width of central maxima, cm\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"// As x = f*lambda/a, solving for a\n", +"a = f*lambda/x; // Slit width in Fraunhofer single slit experiment\n", +"\n", +"printf('\nThe slit width = %5.3f cm', a);\n", +"\n", +"// Result \n", +"// The slit width = 0.017 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.11: Half_angular_width_of_central_maxima.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.11:: Page-3.25 (2009)\n", +"clc; clear;\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"a = 8.5e-005; // Width of the slit, cm\n", +"n = 1; // Order of diffraction\n", +"// For a single slit Fraunhofer diffraction, a*sind(theta) = n*lambda, solving for theta\n", +"theta = asind(n*lambda/a); // Half angular width at central maximum in Fraunhoffer diffraction, degrees\n", +"\n", +"printf('\nThe half angular width at central maximum in Fraunhoffer diffraction = %4.1f degrees', theta);\n", +"\n", +"// Result \n", +"// The half angular width at central maximum in Fraunhoffer diffraction = 40.3 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.12: Wavelength_of_light_used_in_Fraunhoffer_diffraction_due_to_single_slit.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.12:: Page-3.25 (2009)\n", +"clc; clear;\n", +"a = 0.04; // Slit width, cm\n", +"x = 0.5; // Half width of central maximum, cm\n", +"f = 300; // Focal length of the lens, cm\n", +"// As x = lambda*f/a, solving for lambda\n", +"lambda = a*x/f; // Wavelength of light used in Fraunhoffer diffraction due to single slit, cm\n", +"\n", +"printf('\nThe wavelength of light used in Fraunhoffer diffraction due to a single slit = %4d angstrom', lambda/1e-008);\n", +"\n", +"// Result \n", +"// The wavelength of light used in Fraunhoffer diffraction due to a single slit = 6666 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.13: Width_of_central_maxima_from_position_of_first_secondary_minima.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.13:: Page-3.25 (2009)\n", +"clc; clear;\n", +"a = 0.045; // Slit width, cm\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"f = 250; // Focal length of the lens, cm\n", +"x = lambda*f/a; // Position of central maxima, cm\n", +"\n", +"printf('\nThe position of central maxima = %5.3f cm', x);\n", +"printf('\nThe width of central maxima from first minima = %5.3f cm', 2*x);\n", +"\n", +"// Result \n", +"// The position of central maxima = 0.306 cm\n", +"// The width of central maxima from first minima = 0.611 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.14: Wavelength_of_monochromatic_light_used_in_illuminating_a_slit.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.14:: Page-3.26 (2009)\n", +"clc; clear;\n", +"a = 0.025; // Slit width, cm\n", +"n = 2; // Order of diffraction\n", +"f = 400; // Focal length of the lens, cm\n", +"x = 2.1; // Position of central maxima, cm\n", +"// As theta = n*lambda/a and theta = x/f, solving for lambda\n", +"lambda = x*a/(n*f); // Wavelength of light used, cm\n", +"printf('\nThe wavelength of light used = %4d angstrom', lambda/1e-008);\n", +"\n", +"// Result \n", +"// The wavelength of light used = 6562 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.15: Distance_between_second_dark_and_next_bright_fringe_on_the_axes.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.15:: Page-3.26 (2009)\n", +"clc; clear;\n", +"a = 0.25; // Slit width, cm\n", +"lambda = 5890e-008; // Wavelength of light, cm\n", +"f = 80; // Focal length of the lens, cm\n", +"n = 2; // Order of diffraction\n", +"// As for minima, theta = n*lambda/a and theta = x/f, solving for x\n", +"x2 = 2*lambda*f/a; // Position of 2nd dark fringe, cm\n", +"// As for maxima, theta = (2*n+1)*lambda/(2*a) and theta = x/f, solving for x\n", +"x2_prime = 5*lambda*f/(2*a); // Position of 2nd bright fringe, cm\n", +"delta_x = x2_prime-x2; // Distance between 2nd dark and next bright, cm\n", +"printf('\nThe distance between 2nd dark and next bright fringe = %4.2e cm', delta_x);\n", +"\n", +"// Result \n", +"// The distance between 2nd dark and next bright fringe = 9.42e-003 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.16: Width_of_the_slit_from_first_order_diffractio.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.16:: Page-3.27 (2009)\n", +"clc; clear;\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"x = 3.9e-001; // Half width of central maximum, cm\n", +"f = 220; // Focal length of the lens, cm\n", +"n = 1; // Order for first order diffraction\n", +"// As a*sin(theta) = n*lambda, a*theta = n*lambda\n", +"// As theta = lambda/a and theta = x/f, solving for a\n", +"a = lambda*f/x; // Half angular width at central maximum, cm\n", +"\n", +"printf('\nThe width of the slit = %3.1e cm', a);\n", +"\n", +"// Result \n", +"// The width of the slit = 3.1e-002 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.18: Fraunhoffer_diffraction_due_to_double_slits.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.18:: Page-3.30 (2009)\n", +"clc; clear;\n", +"a = 0.019e-003; // Width of each slit, m\n", +"b = 2.0e-004; // Width of opacity between two slits, m\n", +"lambda = 5000e-010; // Wavelengh of light used, m\n", +"D = 0.6; // Distance between slit and the screen, m\n", +"// As angular separation, theta = x/D = lambda/(a+b), solving for x\n", +"x = D*lambda/(a+b); // Fringe spacing on the screen, m\n", +"// As half angular separation, theta1 = x1/D = lambda/(2*(a+b)), solving for x1\n", +"x1 = D*lambda/(2*(a+b)); // Distance between central maxima and first minima, m\n", +"\n", +"printf('\nThe fringe spacing on the screen = %4.2f mm', x/1e-003);\n", +"printf('\nThe distance between central maxima and first minima = %4.2f mm', x1/1e-003);\n", +"\n", +"// Result \n", +"// The fringe spacing on the screen = 1.37 mm\n", +"// The distance between central maxima and first minima = 0.68 mm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.19: Fringe_separation_in_Fraunhoffer_double_slit_diffraction_pattern.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.19:: Page-3.31 (2009)\n", +"clc; clear;\n", +"f = 150; // Distance between screen and slit, cm\n", +"a = 0.005; // Slit width, cm\n", +"b = 0.06; // Distance between slits, cm\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"// As half angular separation, theta1 = x1/f = lambda/(2*(a+b)), solving for x1\n", +"x1 = f*lambda/(2*(a+b)); // Distance between central maxima and first minima, cm\n", +"delta_theta = lambda/(2*(a+b)); // Angular separation between two consecutive minima, radians\n", +"printf('\nThe distance between central maxima and first minima = %4.2e cm', x1);\n", +"printf('\nThe angular separation between two consecutive minima = %3.1e radians', delta_theta);\n", +"\n", +"// Result \n", +"// The distance between central maxima and first minima = 6.35e-002 cm\n", +"// The angular separation between two consecutive minima = 4.2e-004 radians " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.1: Position_of_the_screen_so_that_light_is_focused_on_the_brightest_spot.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.1:: Page-3.9 (2009)\n", +"clc; clear;\n", +"lambda = 5890e-008; // Wavelength of light used, cm\n", +"r1 = 0.2; // Radius of first ring of zone plate, cm\n", +"n = 1; // Order of zone plate\n", +"f1 = r1^2/(n*lambda); // Position of the screen so that light is focused on the brightest spot, cm\n", +" \n", +"printf('\nThe position of the screen so that light is focused on the brightest spot = %3.1e cm', lambda);\n", +"\n", +"// Result \n", +"// The position of the screen so that light is focused on the brightest spot = 5.9e-005 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.20: Positions_of_first_secondary_maxima_and_minima_in_double_slit_diffraction.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.20:: Page-3.32 (2009)\n", +"clc; clear;\n", +"f = 120; // Distance between screen and slit, cm\n", +"a = 0.019; // Slit width, cm\n", +"b = 0.041; // Distance between slits, cm\n", +"lambda = 6500e-008; // Wavelength of light used, cm\n", +"// As theta1 = x1/f = lambda/(2*(a+b)), solving for x1\n", +"x1 = f*lambda/(2*(a+b)); // Position of first secondary minima, cm\n", +"// As theta2 = x2/f = lambda/(a+b), solving for x2\n", +"x2 = f*lambda/(a+b); // Position of first secondary maxima, cm\n", +"\n", +"printf('\nThe position of first secondary minima = %5.3f cm', x1);\n", +"printf('\nThe position of first secondary maxima = %4.2f cm', x2);\n", +"\n", +"// Result \n", +"// The position of first secondary minima = 0.065 cm\n", +"// The position of first secondary maxima = 0.13 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.21: Missing_orders_of_spectra_in_Fraunhoffer_double_slit_diffraction.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.21:: Page-3.34 (2009)\n", +"clc; clear;\n", +"a = 0.2; // Slit width, mm\n", +"b = 0.8; // Distance between slits, mm\n", +"p = [1 2 3 4]; // Orders of pth diffraction maxima\n", +"// As diffraction of pth diffraction maxima, a*sin(theta)=p*lambda --- (i)\n", +"// and that of nth diffraction maxima, (a+b)*sin(theta)=n*lambda --- (ii)\n", +"// Dividing (ii) by (i), we have\n", +"// (a+b)/a = n/p, solving for n\n", +"n = (a+b)/a*p; // Orders of nth diffraction maxima\n", +"\n", +"printf('\nThe missing orders of spectra in diffraction maxima, n = %d, %d, %d, %d,...', n(1), n(2), n(3), n(4));\n", +"\n", +"\n", +"// Result \n", +"// The missing orders of spectra in diffraction maxima, n = 5, 10, 15, 20,... " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.22: Angles_of_diffraction_for_the_principal_maxima_for_two_lines_of_sodium.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.22:: Page-3.45 (2009)\n", +"clc; clear;\n", +"lambda1 = 5890e-008; // Wavelength of D1 line of Na, cm\n", +"lambda2 = 5896e-008; // Wavelength of D2 line of Na, cm\n", +"N = 3000/0.5; // No. of lines per cm of grating, lines/cm\n", +"a_plus_b = 1/N; // Grating element, cm\n", +"n = 1; // Order of diffraction for principal maxima\n", +"// As (a+b)*sin(theta1) = n*lambda, solving for theta1\n", +"theta1 = asind(n*lambda1/(a_plus_b)); // Angle of diffraction for the principal maxima of D1 line, degrees\n", +"theta2 = asind(n*lambda2/(a_plus_b)); // Angle of diffraction for the principal maxima of D2 line, degrees\n", +"printf('\nThe angle of diffraction for the principal maxima of D1 line = %5.2f degrees', theta1);\n", +"printf('\nThe angle of diffraction for the principal maxima of D2 line = %5.2f degrees', theta2);\n", +"\n", +"// Result \n", +"// The angle of diffraction for the principal maxima of D1 line = 20.70 degrees\n", +"// The angle of diffraction for the principal maxima of D2 line = 20.72 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.23: Highest_order_spectrum_which_can_be_seen_in_monochromatic_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.23:: Page-3.45 (2009)\n", +"clc; clear;\n", +"lambda = 5500e-008; // Wavelength of light used, cm\n", +"N = 15000; // No. of lines per inch of grating, lines/inch\n", +"a_plus_b = 2.54/N; // Grating element, cm\n", +"n = 1; // Order of diffraction for principal maxima\n", +"// As (a+b)*sin(theta_n) = n*lambda and for maximum possible order of spectra sin(theta_n) = 1\n", +"// So (a+b) = n*lambda, solving for n\n", +"n = (a_plus_b)/lambda; // The highest order spectrum which can be seen in monochromatic light\n", +"\n", +"printf('\nThe highest order spectrum which can be seen in monochromatic light = %d', n);\n", +"\n", +"// Result \n", +"// The highest order spectrum which can be seen in monochromatic light = 3 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.24: Angle_of_separation_in_second_order_of_diffraction_spectrum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.24: : Page-3.46 (2009)\n", +"clc; clear;\n", +"lambda1 = 5890e-008; // Wavelength of D1 line, cm\n", +"lambda2 = 5896e-008; // Wavelength of D2 line, cm\n", +"N = 15000; // No. of lines per inch of grating, lines/inch\n", +"a_plus_b = 2.54/N; // Grating element, cm\n", +"n = 2; // Order of diffraction for secondary maxima\n", +"// As (a+b)*sin(theta_n) = n*lambda, solving for theta1 and theta2\n", +"theta1 = asind(n*lambda1/a_plus_b); // Direction of secondary maxima with lambda1, degrees\n", +"theta2 = asind(n*lambda2/a_plus_b); // Direction of secondary maxima with lambda2, degrees\n", +"\n", +"printf('\nThe angle of separation in second order diffraction spectrum = %3.1f degrees', theta2-theta1);\n", +"\n", +"// Result \n", +"// The angle of separation in second order diffraction spectrum = 0.1 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.25: Separation_of_two_lines_in_first_order_spectrum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.25:: Page-3.46 (2009)\n", +"clc; clear;\n", +"lambda1 = 5500e-008; // First wavelength, cm\n", +"lambda2 = 3700e-008; // Second wavelength, cm\n", +"N = 15000; // No. of lines per inch of grating, lines/inch\n", +"a_plus_b = 2.54/N; // Grating element, cm\n", +"f = 120; // Focal length of the lens, cm\n", +"n = 1; // Order of diffraction for principal maxima\n", +"// As (a+b)*sin(theta_n) = n*lambda, solving for theta1 and theta2\n", +"theta1 = asind(n*lambda1/a_plus_b); // Direction of principal maxima with lambda1, degrees\n", +"theta2 = asind(n*lambda2/a_plus_b); // Direction of principal maxima with lambda2, degrees\n", +"// As tand(theta) = x/f, solving for x1 - x2 = dx\n", +"dx = f*(tand(theta1)-tand(theta2)); // Linear separation of two lines in first order spectrum, cm\n", +"\n", +"printf('\nThe linear separation of two lines in first order spectrum = %5.2f cm', dx);\n", +"\n", +"// Result \n", +"// The linear separation of two lines in first order spectrum = 14.34 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.26: Difference_in_the_deviation_in_the_first_and_third_order_spectra.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.26:: Page-3.47 (2009)\n", +"clc; clear;\n", +"lambda = 5000e-008; // Wavelength of light used, cm\n", +"N = 5000; // No. of lines per cm of grating, lines/cm\n", +"a_plus_b = 1/N; // Grating element, cm\n", +"n = 1; // Order of diffraction for first order spectra\n", +"// As (a+b)*sin(theta_n) = n*lambda, solving for theta for first and third orders\n", +"theta1 = asind(n*lambda/a_plus_b); // Direction of principal maxima with lambda1, degrees\n", +"n = 3; // Order of diffraction for third order spectra\n", +"theta3 = asind(n*lambda/a_plus_b); // Direction of principal maxima with lambda2, degrees\n", +"delta_theta = theta3 - theta1; // Angular separation in the first and third order spectra, \n", +"\n", +"printf('\nThe difference in the deviation in the first and third order spectra = %4.1f degrees', delta_theta);\n", +"\n", +"// Result \n", +"// The difference in the deviation in the first and third order spectra = 34.1 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.27: Order_of_diffraction_for_the_given_grating_element_and_wavelength_of_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.27:: Page-3.48 (2009)\n", +"clc; clear;\n", +"lambda = 6500e-008; // Wavelength of light used, cm\n", +"N = 10000; // No. of lines per cm of grating, lines/cm\n", +"a_plus_b = 1/N; // Grating element, cm\n", +"theta_n = 90; // Direction for maximum possible orders, degrees\n", +"// As (a+b)*sin(theta_n) = n*lambda, solving for theta for n\n", +"n = a_plus_b*sind(theta_n)/lambda; // Order of diffraction for \n", +"\n", +"printf('\nThe order of diffraction for the given grating element and wavelength of light = %d', n);\n", +"\n", +"// Result \n", +"// The order of diffraction for the given grating element and wavelength of light = 1 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.28: Number_of_lines_ruled_on_the_grating_surface.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.28:: Page-3.48 (2009)\n", +"clc; clear;\n", +"lambda1 = 6500e-008; // Wavelength of first line, cm\n", +"lambda2 = 4500e-008; // Wavelength of scecond line, cm\n", +"theta1 = 18; // Direction of lower order, degrees\n", +"theta2 = 18; // Direction of higher order, degrees\n", +"// As (a+b)*sin(theta1) = n*lambda1 and (a+b)*sin(theta2) = (n+1)*lambda2, solving for n\n", +"n = lambda2/(lambda1 - lambda2); // Order of diffraction for first wavelength\n", +"// As a_plus_b = n*lambda1/sind(theta1), solving for a_plus_b\n", +"a_plus_b = ceil(n)*lambda1/sind(theta1); // Grating element, cm\n", +"N = 1/a_plus_b; // No. of lines on the grating surface, lines/cm\n", +"\n", +"printf('\nThe number of lines ruled on the grating surface = %4d lines/cm', N);\n", +"\n", +"// Result \n", +"// The number of lines ruled on the grating surface = 1584 lines/cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.29: Angles_at_which_first_and_second_order_maxima_are_observed.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.29:: Page-3.48 (2009)\n", +"clc; clear;\n", +"lambda = 6328e-008; // Wavelength of He-Laser, cm\n", +"a_plus_b = 1/6000; // Grating element, cm\n", +"n = 1; // First order of diffraction for given wavelength\n", +"// As (a+b)*sin(theta1) = n*lambda, solving for theta1\n", +"theta1 = asind(n*lambda/a_plus_b); // Angle at which first order maximum is observed, degrees\n", +"n = 2; // second order of diffraction for given wavelength\n", +"theta2 = asind(n*lambda/a_plus_b); // Angle at which second order maximum is observed, degrees\n", +"\n", +"printf('\nThe angle at which first order maximum is observed = %4.1f degrees', theta1);\n", +"printf('\nThe angle at which second order maximum is observed = %4.1f degrees', theta2);\n", +"\n", +"// Result \n", +"// The angle at which first order maximum is observed = 22.3 degrees\n", +"// The angle at which second order maximum is observed = 49.4 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.2: Zone_plate_with_a_point_source_of_light_on_the_axis.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.2:: Page-3.9 (2009)\n", +"clc; clear;\n", +"v1 = 36; // Position of the strongest image from the zone plate, cm\n", +"v2 = 9; // Position of the next image from the zone plate, cm\n", +"lambda = 5890e-008; // Wavelength of light used, cm\n", +"r1 = 1; // For simplicity assume radius of first ring of zone plate to be unity, cm\n", +"n = 1; // Order of zone plate\n", +"// As 1/v1-1/u = n*lambda/r1^2 = 1/3*(1/v2-1/u), solving for u\n", +"u = 2/(3/36-1/9); // Distance of the zone plate from source, cm\n", +"// As 1/v-1/u = n*lambda/r1^2, solving for r1\n", +"r1 = sqrt(lambda/(1/v1-1/abs(u))); // Radius of first zone, cm\n", +"f1 = r1^2/(n*lambda); // Principal focal length, cm\n", +"\n", +"printf('\nThe distance of the zone plate from source = %2d cm', u);\n", +"printf('\nThe radius of first zone = %3.1e cm', r1);\n", +"printf('\nThe principal focal length = %4.1f cm', f1);\n", +"\n", +"// Result \n", +"// The distance of the zone plate from source = -72 cm\n", +"// The radius of first zone = 6.5e-002 cm\n", +"// The principal focal length = 72.0 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.30: Least_width_of_plane_transmission_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.30:: Page-3.49 (2009)\n", +"clc; clear;\n", +"lambda1 = 5890e-008; // Wavelength of D1 line of Na, cm\n", +"lambda2 = 5896e-008; // Wavelength of D2 line of Na, cm\n", +"d_lambda = lambda2-lambda1; // Linear separation of two lines just seen as separate, cm\n", +"P = 500; // Number of lines per cm on grating, lines/cm\n", +"n = 2; // Order of diffraction\n", +"// As resolving power of grating, lambda/d_lambda = n*N, solving for N\n", +"N = lambda1/(d_lambda*n); // No. of lines required per cm on grating, lines/cm\n", +"w = N/P; // Least width of grating, cm\n", +"\n", +"printf('\nThe least width of plane transmission grating = %5.3f cm', w);\n", +"\n", +"// Result \n", +"// The least width of plane transmission grating = 0.982 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.31: Minimum_grating_width_required_to_resolve_two_wavelengths.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.31:: Page-3.49 (2009)\n", +"clc; clear;\n", +"theta1 = 18; // Direction at which first spectral line appears, degrees\n", +"theta2 = 18+5/(60*60); // Direction at which second spectral line appears, degrees\n", +"d_theta = (theta2-theta1)*%pi/180; // Angular separation of two spectral lines, radians\n", +"d_lambda = 50e-010; // Linear separation of two spectral lines just seen as separate, cm\n", +"DP = d_theta/d_lambda; // Dispersive power of grating\n", +"n = 1; // Order of diffraction\n", +"// As dispersive power of grating d_theta/d_lambda = DP = n/((a_plus_b)*cosd(theta1)), solving for a_plus_b\n", +"a_plus_b = n/(DP*cosd(theta1)); // Grating element, cm\n", +"// But a_plus_b*sind(theta1)=n*lambda1, solving for lambda1\n", +"lambda1 = a_plus_b*sind(theta1)/n; // Wavelength of first spectral line, cm\n", +"lambda2 = lambda1+d_lambda/1e-002; // Wavelength of second spectral line, cm\n", +"// As resolving power of grating, lambda/d_lambda = n*N, solving for N\n", +"N = lambda1/(d_lambda*n); // No. of lines required per cm on grating\n", +"w = N*a_plus_b; // Minimum grating width required to resolve two wavelengths, cm\n", +"\n", +"printf('\nThe wavelength of first spectral line = %4.0f angstrom', lambda1/1e-008);\n", +"printf('\nThe wavelength of second spectral line = %4.0f angstrom', lambda2/1e-008);\n", +"printf('\nThe minimum grating width required to resolve two wavelengths = %3.1f cm', w);\n", +"\n", +"// Result \n", +"// The wavelength of first spectral line = 6702 angstrom\n", +"// The wavelength of second spectral line = 6752 angstrom\n", +"// The minimum grating width required to resolve two wavelengths = 2.9 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.32: Angle_of_diffraction_for_maxima_in_first_order.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.32:: Page-3.50 (2009)\n", +"clc; clear;\n", +"// Function to convert theta into degree-minute\n", +"function[degre, minute]=deg_2_degminsec(theta)\n", +" degre = floor(theta);\n", +" minute = (theta-floor(theta))*60;\n", +"endfunction\n", +"\n", +"N = 15000; // No. of lines on the grating per inch, lines/inch\n", +"a_plus_b = 2.54/N; // Grating element, cm\n", +"lambda = 6000e-008; // Wavelength of light used, cm\n", +"n = 1; // Order of diffraction spectra\n", +"// But a_plus_b*sind(theta)=n*lambda, solving for theta\n", +"theta = asind(n*lambda/a_plus_b); // Direction in which first order spectra is seen, degrees\n", +"[deg, mint] = deg_2_degminsec(theta);\n", +"printf('\nThe angle of diffraction for maxima in first order = %2d degrees %2d min', deg, mint);\n", +"\n", +"// Result \n", +"// The angle of diffraction for maxima in first order = 20 degrees 45 min " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.33: Wavelength_of_light_used_in_obtaining_second_order_diffraction_maximum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.33:: Page-3.50 (2009)\n", +"clc; clear;\n", +"N = 12000; // No. of lines on the grating per inch, lines/inch\n", +"a_plus_b = 2.54/N; // Grating element, cm\n", +"n = 2; // Order of diffraction spectra\n", +"theta = 39; // Angle of diffraction for maxima in second order, degrees\n", +"// But a_plus_b*sind(theta)=n*lambda, solving for lambda\n", +"lambda = a_plus_b*sind(theta)/n; // Wavelength of light used, cm\n", +"\n", +"printf('\nThe wavelength of light used in obtaining second order diffraction maximum = %4d angstrom', lambda/1e-008);\n", +"\n", +"// Result \n", +"// The wavelength of light used in obtaining second order diffraction maximum = 6660 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.34: Number_of_visible_orders_using_diffraction_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.34:: Page-3.51 (2009)\n", +"clc; clear;\n", +"lambda = 5890e-008; // Wavelength of light used, cm\n", +"N = 6000; // No. of lines on the grating per inch, lines/inch\n", +"a_plus_b = 2.54/N; // Grating element, cm\n", +"theta_max = 90; // Direction of maxima for maximum possible orders\n", +"// But a_plus_b*sind(theta_max)=n*lambda, solving for n\n", +"n = a_plus_b*sind(theta_max)/lambda; // Number of visible orders\n", +"\n", +"printf('\nThe number of visible orders using diffraction grating = %d', n);\n", +"\n", +"// Result \n", +"// The number of visible orders using diffraction grating = 7 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.35: Distance_between_two_wavelengths_seen_as_separate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.35:: Page-3.51 (2009)\n", +"clc; clear;\n", +"lambda = 5500e-008; // Mean of two wavelengths, cm\n", +"theta = 35; // Angle of diffraction for maxima in second order\n", +"d_theta = 0.15; // Angular separation between two neighbouring wavelengths, radians\n", +"d_lambda = lambda*cotd(theta)*d_theta; // Distance between two wavelengths seen as separate, cm\n", +"\n", +"printf('\nThe distance between two wavelengths seen as separate = %d angstrom', d_lambda/1e-008);\n", +"\n", +"// Result \n", +"// The distance between two wavelengths seen as separate = 1178 angstrom " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.36: Number_of_lines_per_cm_on_grating_surface.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.36:: Page-3.51 (2009)\n", +"clc; clear;\n", +"lambda1 = 5500e-008; // First wavelength of light, cm\n", +"lambda2 = 4500e-008; // Second wavelength of light, cm\n", +"theta = 45; // Angle of diffraction for lower order, degrees\n", +"n = lambda2/(lambda1-lambda2); // Lower order of diffraction\n", +"// But a_plus_b*sind(theta)=n*lambda, solving for a_plus_b\n", +"a_plus_b = floor(n)*lambda1/sind(theta); // Grating element, cm\n", +"N = 1/a_plus_b; // No. of lines per cm on grating surface, lines/cm\n", +"\n", +"printf('\nThe number of lines per cm on grating surface = %4d lines/cm', ceil(N));\n", +"\n", +"// Result \n", +"// The number of lines per cm on grating surface = 3215 lines/cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.37: Total_number_of_lines_on_grating_surface.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.37:: Page-3.52 (2009)\n", +"clc; clear;\n", +"lambda = 6500e-008; // Wavelength of light used, cm\n", +"theta = 19.5; // Angle of diffraction for maxima in first order, degrees\n", +"l = 3.5; // Length of the grating, cm\n", +"n = 1; // Order of diffraction\n", +"// But a_plus_b*sind(theta)=n*lambda, solving for a_plus_b\n", +"a_plus_b = n*lambda/sind(theta); // Grating element, cm\n", +"N = 1/a_plus_b; // No. of lines per cm on grating surface, lines/cm\n", +"N_total = l*N; // Total number of lines on grating surface\n", +"\n", +"printf('\nThe total number of lines on grating surface = %5d', N_total);\n", +"\n", +"// Result \n", +"// The total number of lines on grating surface = 17974 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.38: Angular_separation_between_the_sodium_D1_and_D2_lines.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code EX3.38:: Page-3.52 (2009)\n", +"clc;clear;\n", +"function [mint, secnd]=degmin(theta)\n", +" mint = (theta-floor(theta))*60;\n", +" secnd = (mint-floor(mint))*60\n", +"endfunction\n", +"lambda_D1 = 5890e-008; // Wavelength of sodium D1 line, cm\n", +"lambda_D2 = 5896e-008; // Wavelength of sodium D2 line, cm\n", +"n = 2; // Order of diffraction\n", +"N = 6500; // Number of lines per cm on grating, lines/cm\n", +"a_plus_b = 1/6500; // Grating element, cm\n", +"// As a_plus_b*sin(theta1)=n*lambda1, solving for theta1\n", +"theta1 = asind(n*lambda_D1/a_plus_b);\n", +"// As a_plus_b*sin(theta2)=n*lambda2, solving for theta1\n", +"theta2 = asind(n*lambda_D2/a_plus_b);\n", +"d_theta = theta2-theta1; // Angular separation between the sodium D1 and D2 lines, degrees\n", +"[mint, secnd] = degmin(d_theta); // Call deg_2_degmin function\n", +"printf('\nThe angular separation between the sodium D1 and D2 lines = %d minutes %d seconds', mint, secnd);\n", +"// Result\n", +"// The angular separation between the sodium D1 and D2 lines = 4 minutes 10 seconds \n", +"// Since theta1 and theta2 are rounded off in the textbook, therefore the answer is mismatching." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.39: Minimum_number_of_lines_in_a_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code EX3.39:: Page-3.55 (2009)\n", +"clc;clear;\n", +"lambda1 = 5890e-008; // Wavelength of sodium D1 line, cm\n", +"lambda2 = 5896e-008; // Wavelength of sodium D2 line, cm\n", +"d_lambda = lambda2-lambda1; // Difference in the wavelength of two lines, cm\n", +"n = 2; // Order of diffraction\n", +"// As lambda/d_lambda = n*N, solving for N\n", +"N = lambda1/(d_lambda*n); // Minimum number of lines in a grating\n", +"printf('\nThe minimum number of lines in a grating = %3d lines', N);\n", +"// Result\n", +"// The minimum number of lines in a grating = 490 lines " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.3: Position_of_the_first_image_in_a_zone_plate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.3:: Page-3.10 (2009)\n", +"clc; clear;\n", +"lambda = 5500e-010; // Wavelength of light used, cm\n", +"u = -4; // Distance of the zone plate from source, cm\n", +"D = 3.7e-003; // Diameter of central zone of zone plate, cm\n", +"r = D/2; // Radius of central zone of zone plate, cm\n", +"n = 1; // Order of zone plate\n", +"f1 = r^2/(n*lambda); // Principal focal length, cm\n", +"v1 = 36; // Position of the strongest image from the zone plate, cm\n", +"v2 = 9; // Position of the next image from the zone plate, cm\n", +"// As 1/v - 1/u = 1/f, solving for v\n", +"v = 1/(1/f1+1/u); // Position of the first image in a zone plate, cm\n", +"\n", +"printf('\nThe position of the first image in a zone plate = %2d cm', floor(v));\n", +"\n", +"// Result \n", +"// The position of the first image in a zone plate = -12 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.40: Linear_separation_of_two_points_on_the_moon.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code EX3.40:: Page-3.56 (2009)\n", +"clc;clear;\n", +"lambda = 5500e-008; // Wavelength of most sensitive color to an eye, cm\n", +"a = 400; // Aperture of the telescope, cm\n", +"D = 3.8e+010; // Distance of the moon from the earth, cm\n", +"d_theta = 1.22*lambda/a; // Limit of resolution of telescope, radians\n", +"// As d_theta = x/D, solving for x\n", +"x = d_theta*D; // Linear separation of two points on the moon, cm\n", +"printf('\nThe linear separation of two points on the moon = %5.2f m', x/1e+002);\n", +"// Result\n", +"// The linear separation of two points on the moon = 63.74 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.41: Minimum_required_number_of_lines_on_the_plane_transmission_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code EX3.41:: Page-3.56 (2009)\n", +"clc;clear;\n", +"lambda1 = 5890e-008; // Wavelength of sodium D1 line, cm\n", +"lambda2 = 5896e-008; // Wavelength of sodium D2 line, cm\n", +"d_lambda = lambda2-lambda1; // Wavelength difference, cm\n", +"n = 2; // Order of diffraction\n", +"// As lambda/d_lambda = n*N, solving for N\n", +"N = 1/n*(lambda1+lambda2)/(2*d_lambda); // Minimum required number of lines on the plane transmission grating\n", +"printf('\nThe minimum required number of lines on the plane transmission grating = %3d', N);\n", +"// Result\n", +"// The minimum required number of lines on the plane transmission grating = 491 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.42: EX3_42.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code EX3.42:: Page-3.57 (2009)\n", +"clc;clear;\n", +"lambda1 = 5890e-008; // Wavelength of sodium D1 line, cm\n", +"lambda2 = 5896e-008; // Wavelength of sodium D2 line, cm\n", +"d_lambda = lambda2-lambda1; // Wavelength difference, cm\n", +"w = 2.5; // Width of the grating, cm\n", +"n = 2; // Order of diffraction\n", +"// As lambda/d_lambda = n*N, solving for N\n", +"N = 1/n*(lambda1+lambda2)/(2*d_lambda); // Minimum required number of lines on the plane transmission grating\n", +"printf('\nThe number of lines on the plane transmission grating to just resolve the sodium lines = %3d', N/w);\n", +"// Result\n", +"// The number of lines on the plane transmission grating to just resolve the sodium lines = 196 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.43: Minimum_width_of_the_grating_to_resolve_the_sodium_lines_in_third_order.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code EX3.43:: Page-3.57 (2009)\n", +"clc;clear;\n", +"lambda1 = 5890e-008; // Wavelength of sodium D1 line, cm\n", +"lambda2 = 5896e-008; // Wavelength of sodium D2 line, cm\n", +"d_lambda = lambda2-lambda1; // Wavelength difference, cm\n", +"n = 3; // Order of diffraction\n", +"P = 2500; // Number of lines per unit length of grating\n", +"// As lambda/d_lambda = n*N, solving for N\n", +"N = 1/n*(lambda1+lambda2)/(2*d_lambda); // Total lines on the grating \n", +"w = N/P; // Minimum width of the grating, cm\n", +"printf('\nThe minimum width of the grating to resolve the sodium lines in third order = %5.3f cm', w);\n", +"// Result\n", +"// The minimum width of the grating to resolve the sodium lines in third order = 0.131 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.44: Dispersive_power_and_diffraction_angle_for_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code EX3.44:: Page-3.57 (2009)\n", +"clc;clear;\n", +"w = 2; // Width of the grating, cm\n", +"P = 4500; // Total number of lines on the grating\n", +"a_plus_b = w/P; // Grating element, cm\n", +"lambda1 = 5890e-008; // Wavelength of sodium D1 line, cm\n", +"lambda2 = 5896e-008; // Wavelength of sodium D2 line, cm\n", +"lambda = (lambda1+lambda2)/2; // Mean wavelength of light used, cm\n", +"d_lambda=lambda2-lambda1; // Difference in wavelengths of D-lines of sodium, cm\n", +"n = 2; // Order of diffraction\n", +"// As a_plus_b*sind(theta)=n*lambda, solving for theta\n", +"theta = asind(n*lambda/a_plus_b); // Angle of diffraction, degrees\n", +"DP = n/(a_plus_b*cosd(theta)); // Dispersive power of grating\n", +"d_theta = DP*d_lambda*180/%pi; // Angular separation between D-lines, degrees\n", +"RP = lambda/d_lambda; // Required resolving power of grating for sodium lines\n", +"N = 2.54/a_plus_b; // No. of lines per cm on grating, lines/cm\n", +"RP_cal = n*N; // Calculated resolving power of grating \n", +"printf('\nThe angle of diffraction for maxima in second order = %6.4f degrees', d_theta);\n", +"printf('\nAs %5.3e > %3d, D-lines can be resolved.', RP_cal, RP);\n", +"// Result\n", +"// The angle of diffraction for maxima in second order = 0.0160 degrees\n", +"// As 1.143e+04 > 982, D-lines can be resolved. " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.45: Distance_between_centres_of_images_of_the_two_stars.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code EX3.45:: Page-3.58 (2009)\n", +"clc;clear;\n", +"lambda = 5500e-010; // Wavelength of light used, m\n", +"a = 0.01; // Diameter of objective of telescope, m\n", +"f = 3.0; // Focal length of tlescope objective, m \n", +"// For telescope, the limit of resolution, \n", +"// theta = x/f = 1.22*lambda/a, solving for x\n", +"x = 1.22*lambda/a*f; // Distance between centres of imgaes of the two stars\n", +"printf('\nThe distance between centres of imgaes of the two stars = %4.2e m', x);\n", +"// Result\n", +"// The distance between centres of imgaes of the two stars = 2.01e-04 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.46: Aperture_of_the_objective_of_the_microscope.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code EX3.46:: Page-3.59 (2009)\n", +"clc;clear;\n", +"lambda = 5461e-008; // Wavelength of light used, cm\n", +"d = 4e-005; // Separation distance between two self-luminous objects, cm\n", +"NA = 1.22*lambda/(2*d); // Numerical aperture of microscope, cm\n", +"printf('\nThe numerical aperture of the objective of the microscopes = %6.4f cm', NA);\n", +"// Result\n", +"// The numerical aperture of the objective of the microscopes = 0.8328 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.4: Principal_focal_length_of_zone_plate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.4:: Page-3.11 (2009)\n", +"clc; clear;\n", +"lambda = 1; // For simplicity assume wavelength of light used to be unity, unit\n", +"R = 150; // Radius of curvature of the curved surface, cm\n", +"r1 = sqrt(lambda*R); // For Newton's ring, cm\n", +"f1 = r1^2/lambda; // Principal focal length of zone plate, cm\n", +"\n", +"printf('\nThe principal focal length of zone plate = %3d cm', f1);\n", +"\n", +"// Result \n", +"// The principal focal length of zone plate = 150 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.5: Half_angular_width_at_central_maximum_in_Fraunhoffer_diffraction.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.5:: Page-3.22 (2009)\n", +"clc; clear;\n", +"lambda = 5000e-008; // Wavelength of light used, cm\n", +"a = 15e-005; // Width of the slit, cm\n", +"n = 1; // Order of diffraction\n", +"// For a single slit Fraunhofer diffraction, a*sin(theta) = n*lambda, solving for theta\n", +"theta = asin(n*lambda/a); // Half angular width at central maximum in Fraunhoffer diffraction, radian\n", +"\n", +"printf('\nThe half angular width at central maximum in Fraunhoffer diffraction = %5.3f rad', theta);\n", +"\n", +"// Result \n", +"// The half angular width at central maximum in Fraunhoffer diffraction= 0.340 rad " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.6: Width_of_the_slit.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.6:: Page-3.23 (2009)\n", +"clc; clear;\n", +"lambda = 5000e-010; // Wavelength of light used, cm\n", +"n = 1; // Order of diffraction\n", +"x = 5e-003; // Position of first minima on either sides of central maximum, m\n", +"D = 2.5; // Distance of screen from the narrow slir, m\n", +"sin_theta = x/sqrt(x^2+D^2); // Sine of angle theta, rad\n", +"// For a single slit Fraunhofer diffraction, a*sin(theta) = n*lambda, solving for a\n", +"a = n*lambda/sin_theta; // Width of the slit, m\n", +"\n", +"printf('\nThe Width of the slit = %3.1e m', a);\n", +"\n", +"// Result \n", +"// The Width of the slit = 2.5e-004 m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.7: Angular_width_of_central_maximum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.7:: Page-3.23 (2009)\n", +"clc; clear;\n", +"lambda = 6000e-010; // Wavelength of light used, m\n", +"a = 15e-007; // Width of the slit, m\n", +"// For a single slit Fraunhofer diffraction, a*sind(theta) = n*lambda, solving for theta\n", +"theta = asind(lambda/a); // Half angular width of central maximum, degrees\n", +"\n", +"printf('\nThe angular width of central maximum = %2d degrees', 2*ceil(theta));\n", +"\n", +"// Result \n", +"// The angular width of central maximum = 48 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.8: Distance_between_first_minima_and_the_next_minima_from_the_axis.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.8:: Page-3.23 (2009)\n", +"clc; clear;\n", +"lambda = 5000e-010; // Wavelength of light used, m\n", +"a = 0.7e-002; // Width of the slit, m\n", +"f = 0.5; // Focal length of the lens, m\n", +"n = 1; // Order of diffraction\n", +"// For minima, a*sind(theta_n) = n*lambda\n", +"// Also theta_n = n*lambda/a = x1/f, solving for x1\n", +"x1 = f*n*lambda/a; // Position of first minima, cm\n", +"// For secondary maxima, a*sind(theta_n) = (2*n+1)*lambda/2\n", +"// Also theta_n = 3*lambda/(2*a) = x2/f, solving for x2\n", +"n = 1; // Order of diffraction for first secondary minima\n", +"x2 = 3*f*lambda/(2*a); // Position of first secondary maxima, cm\n", +"\n", +"printf('\nThe distance between first minima and the next minima from the axis = %4.2e cm', x2-x1);\n", +"\n", +"// Result \n", +"// The distance between first minima and the next minima from the axis = 1.79e-005 cm " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3.9: Width_of_central_maxima_in_diffraction_pattern.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex3.9:: Page-3.24 (2009)\n", +"clc; clear;\n", +"lambda = 6600e-008; // Wavelength of light used, cm\n", +"a = 0.018; // Width of the slit, cm\n", +"f = 200; // Focal length of the lens, cm\n", +"n = 1; // Order for first order diffraction\n", +"// As a*sin(theta) = n*lambda, a*theta = n*lambda\n", +"// As theta = lambda/a and theta = x/f, solving for x\n", +"x = lambda*f/a; // Half angular width at central maximum, cm\n", +"\n", +"printf('\nThe width of central maximum = %3.1f cm', 2*x);\n", +"\n", +"// Result \n", +"// The width of central maximum = 1.5 cm " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Physics_by_V_Yadav/4-Polarization.ipynb b/Engineering_Physics_by_V_Yadav/4-Polarization.ipynb new file mode 100644 index 0000000..69cf5ed --- /dev/null +++ b/Engineering_Physics_by_V_Yadav/4-Polarization.ipynb @@ -0,0 +1,850 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 4: Polarization" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.10: Thickness_of_quarter_wave_plate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.10:: Page-4.23 (2009)\n", +"clc; clear;\n", +"mu_o = 1.658; // Refractive index of ordinary wave\n", +"mu_e = 1.486; // Refractive index of extraordinary wave\n", +"lambda = 5893e-008; // Wavelength of light used, m\n", +"// As (mu_o - mu_e)*t = lambda/4, solving for t\n", +"t = lambda/(4*(mu_o - mu_e)); // Thickness of quarter-wave plate, cm\n", +"\n", +"printf('\nThe thickness of quarter-wave plate = %3.1e cm', t);\n", +"\n", +"// Result \n", +"// The thickness of quarter-wave plate = 8.6e-005 cm \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.11: Least_thickness_of_plate_for_which_emergent_beam_is_plane_polarised.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.11:: Page-4.23 (2009)\n", +"clc; clear;\n", +"mu_o = 1.5442; // Refractive index of ordinary wave\n", +"mu_e = 1.5533; // Refractive index of extraordinary wave\n", +"lambda = 5000e-008; // Wavelength of light used, m\n", +"// As (mu_o - mu_e)*t = lambda/4, solving for t\n", +"t = lambda/(4*(mu_e - mu_o)); // Least thickness of plate for which emergent beam is plane polarised, cm\n", +"\n", +"printf('\nThe least thickness of plate for which emergent beam is plane polarised = %4.2e cm', t);\n", +"\n", +"// Result \n", +"// The least thickness of plate for which emergent beam is plane polarised = 1.37e-003 cm \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.12: Difference_in_refractive_indices_of_rays.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.12:: Page-4.23 (2009)\n", +"clc; clear;\n", +"lambda = 5893e-008; // Wavelength of light used, m\n", +"t = 0.005; // Thickness of the crystal, cm\n", +"// As for quarter wave plate, mu_diff*t = (mu_o - mu_e)*t = lambda/4, solving for mu_diff\n", +"mu_diff = lambda/(4*t); // The difference in refractive indices of rays, cm\n", +"printf('\nThe least thickness of plate for which emergent beam is plane polarised = %4.2e cm', mu_diff);\n", +"\n", +"// Result \n", +"// The least thickness of plate for which emergent beam is plane polarised = 2.95e-003 cm \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.13: The_thickness_of_a_half_wave_plate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.13:: Page-4.24 (2009)\n", +"clc; clear;\n", +"mu_o = 1.54; // Refractive index of ordinary wave\n", +"mu_e = 1.45; // Refractive index of extraordinary wave\n", +"lambda = 5500e-008; // Wavelength of light used, m\n", +"// As for a half wave plate, (mu_o - mu_e)*t = lambda/4, solving for t\n", +"t = lambda/(2*(mu_o - mu_e)); // The thickness of a half wave plate for wavelength, cm\n", +"\n", +"printf('\nThe thickness of a half wave plate for wavelength = %4.2e cm', t);\n", +"\n", +"// Result \n", +"// The thickness of a half wave plate for wavelength = 3.06e-004 cm \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.14: The_thickness_of_a_quarter_wave_plate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.14:: Page-4.24 (2009)\n", +"clc; clear;\n", +"mu_o = 1.55; // Refractive index of ordinary wave\n", +"mu_e = 1.52; // Refractive index of extraordinary wave\n", +"lambda = 5500e-008; // Wavelength of light used, m\n", +"// As for a half wave plate, (mu_o - mu_e)*t = lambda/4, solving for t\n", +"t = lambda/(4*(mu_o - mu_e)); // The thickness of a quarter wave plate for wavelength, cm\n", +"\n", +"printf('\nThe thickness of a quarter wave plate for wavelength = %4.2e cm', t);\n", +"\n", +"// Result \n", +"// The thickness of a quarter wave plate for wavelength = 4.58e-004 cm \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.15: The_thickness_of_a_half_wave_plate_quartz.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.15:: Page-4.24 (2009)\n", +"clc; clear;\n", +"mu_o = 1.51; // Refractive index of ordinary wave\n", +"mu_e = 1.55; // Refractive index of extraordinary wave\n", +"lambda = 6000e-008; // Wavelength of light used, m\n", +"// As for a half wave plate, (mu_o - mu_e)*t = lambda/4, solving for t\n", +"t = lambda/(2*(mu_e - mu_o)); // The thickness of a quarter wave plate for wavelength, cm\n", +"\n", +"printf('\nThe thickness of a half wave plate quartz = %4.2e cm', t);\n", +"\n", +"// Result \n", +"// The thickness of a half wave plate quartz = 7.50e-004 cm \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.16: Difference_between_refractive_indices.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.16:: Page-4.24 (2009)\n", +"clc; clear;\n", +"lambda = 5890e-008; // Wavelength of light used, m\n", +"t = 7.5e-004; // Thickness of the crystal, cm\n", +"// As for quarter wave plate, mu_diff*t = (mu_e - mu_o)*t = lambda/4, solving for mu_diff\n", +"mu_diff = lambda/(4*t); // The difference in refractive indices of rays, cm\n", +"printf('\nThe difference between refractive indices = %6.4f cm', mu_diff);\n", +"\n", +"// Result \n", +"// The difference between refractive indices = 0.0196 cm \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.17: Specific_rotation_of_superposition.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.17:: Page-4.34 (2009)\n", +"clc; clear;\n", +"theta = 15.2; // Angle through which plane of polarization is rotated, degrees\n", +"c = 0.2; // Concentration of sugar, g/cc\n", +"l = 25; // Length of sugar, cm\n", +"S = 10*theta/(l*c); // Specific rotation of superposition, degrees\n", +"\n", +"printf('\nThe specific rotation of superposition = %4.1f cm', S);\n", +"\n", +"// Result \n", +"// The specific rotation of superposition = 30.4 cm \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.18: Strength_of_sugar_solution.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.18: : Page-4.34 (2009)\n", +"clc; clear;\n", +"theta = 15.2; // Angle through which plane of polarization is rotated, degrees\n", +"S = 65; // Specific rotation of sugar solution, degrees\n", +"l = 15; // Length of sugar, cm\n", +"// As S = 10*theta/(l*c), solving for c\n", +"c = 10*theta/(l*S); // Concentration of sugar, g/cc\n", +"\n", +"printf('\nThe strength of sugar solution = %4.2f g/cc', c);\n", +"\n", +"// Result \n", +"// The strength of sugar solution = 0.16 g/cc \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.19: Quantity_of_sugar_contained_in_the_tube_in_the_form_of_solution.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.19:: Page-4.34 (2009)\n", +"clc; clear;\n", +"theta = 15; // Angle through which plane of polarization is rotated, degrees\n", +"S = 69; // Specific rotation of sugar solution, degrees\n", +"l = 10; // Length of sugar, cm\n", +"V = 50; // Volume of the tube, cc\n", +"// As S = 10*theta/(l*c), solving for c\n", +"c = 10*theta/(l*S); // Concentration of sugar, g/cc\n", +"M = c*V; // Mass of sugar in solution, g\n", +"\n", +"printf('\nThe quantity of sugar contained in the tube in the form of solution = %5.2f g', M);\n", +"\n", +"// Result \n", +"// The quantity of sugar contained in the tube in the form of solution = 10.87 g \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.1: Refractive_index_of_the_material.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.1:: Page-4.5 (2009)\n", +"clc; clear;\n", +"ip = 60; // Polarizing angle, degrees\n", +"mu = tand(ip); // Refractive index of the material from Brewster's law \n", +"printf('\nThe refractive index of the material = %5.3f', mu);\n", +"\n", +"// Result \n", +"// The refractive index of the material = 1.732 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.20: Specific_rotation_of_sugar_solution_from_the_given_data.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.20:: Page-4.35 (2009)\n", +"clc; clear;\n", +"theta = 8; // Angle through which plane of polarization is rotated, degrees\n", +"M = 10; // Amount of sugar, g\n", +"l = 14; // Length of the tube, cm\n", +"V = 44; // Volume of sugar solution, cc\n", +"c = M/V; // Concentration of sugar, g/cc\n", +"S = 10*theta/(l*c); // Specific rotation of sugar solution from the given data, degrees\n", +"\n", +"printf('\nThe specific rotation of sugar solution from the given data = %4.1f degrees', S);\n", +"\n", +"// Result \n", +"// The specific rotation of sugar solution from the given data = 25.1 degrees \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.21: Angle_of_rotation_of_the_plane_of_polarization.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.21:: Page-4.35 (2009)\n", +"clc; clear;\n", +"m = 15; // Amount of sugar, g\n", +"S = 66; // Specific rotation of sugar solution from the given data, degrees\n", +"l = 20; // Length of the tube, cm\n", +"V = 100; // Volume of sugar solution, cc\n", +"c = m/V; // Concentration of sugar, g/cc\n", +"// As S = 10*theta/(l*c), solving for theta\n", +"theta = S*l*c/10; // Angle of rotation of the plane of polarization, degrees\n", +"\n", +"printf('\nThe angle of rotation of the plane of polarization = %4.1f degrees', theta);\n", +"\n", +"// Result \n", +"// The angle of rotation of the plane of polarization = 19.8 degrees \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.22: Angle_of_rotation_of_the_optically_active_solution.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.22: : Page-4.35 (2009)\n", +"clc; clear;\n", +"l = 5; // Length of the tube, dm\n", +"m = 50; // Amount of sugar, g\n", +"S = 50; // Specific rotation of sugar solution, degrees\n", +"V = 150; // Volume of sugar solution, cc\n", +"c = m/V; // Concentration of sugar, g/cc\n", +"// As S = theta/(l*c), solving for theta\n", +"theta = S*l*c; // Angle of rotation of the optically active solution\n", +"\n", +"printf('\nThe angle of rotation of the optically active solution = %4.1f degrees', theta);\n", +"\n", +"// Result \n", +"// The angle of rotation of the optically active solution = 83.3 degrees \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.23: Angle_of_rotation_in_a_tube_of_new_length.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.23:: Page-4.35 (2009)\n", +"clc; clear;\n", +"l = 3; // Length of the tube, dm\n", +"theta = 17.0; // Angle of rotation of the plane of polarization, degrees\n", +"c = 1.0; // For simplicity assume concentration of solution to be unity, g/cc\n", +"l_prime = 2.5; // New length of the tube, dm\n", +"c_prime = 1.25*c; // Concentration of solution with 25 cm length of tube, g/cc\n", +"theta_prime = theta*l_prime*c_prime/(l*c); // Angle of rotation in a tube of new length\n", +"\n", +"\n", +"printf('\nThe angle of rotation in a tube of new length of %3.1f cm = %4.1f degrees', l_prime, theta_prime);\n", +"\n", +"// Result \n", +"// The angle of rotation in a tube of new length of 2.5 cm = 17.7 degrees \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.24: Mass_of_sugar_in_the_solution_contained_in_the_tube.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.24:: Page-4.36 (2009)\n", +"clc; clear;\n", +"l = 17; // Length of the tube, cm\n", +"V = 37; // Volume of sugar solution, cc\n", +"theta = 15; // Angle of rotation of the plane of polarization, degrees\n", +"S = 68; // Specific rotation of sugar solution, degrees\n", +"// As S = 10*theta/(l*c), solving for c\n", +"c = 10*theta/(l*S); // Concentration of sugar solution, g/cc\n", +"m = c*V; // Mass of sugar in the solution contained in the tube, g\n", +"\n", +"printf('\nThe mass of sugar in the solution contained in the tube = %3.1f g', m);\n", +"\n", +"// Result \n", +"// The mass of sugar in the solution contained in the tube = 4.8 g \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.25: Percentage_purity_of_the_sugar_sample.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.25:: Page-4.36 (2009)\n", +"clc; clear;\n", +"m = 80; // Mass of sugar in the solution, g\n", +"theta = 9.9; // Angle of rotation of the plane of polarization, degrees\n", +"l = 20; // Length of the tube, cm\n", +"S_pure = 66; // Specific rotation of pure sugar solution, degrees per dm per (g/cc)\n", +"c = 0.08; // Concentration of sugar solution, g/cc\n", +"S = 10*theta/(l*c); // calculated specific rotation of sugar solution, degrees per dm per (g/cc)\n", +"percent_purity = S/S_pure*100; // Percentage purity of sugar sample, percent\n", +"\n", +"printf('\nThe percentage purity of the sugar sample = %5.2f percent', percent_purity);\n", +"\n", +"// Result \n", +"// The percentage purity of the sugar sample = 93.75 percent \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.26: Angle_of_rotation_produced_by_the_polarimeter_plate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.26:: Page-4.42 (2009)\n", +"clc; clear;\n", +"lambda = 6600e-010; // Wavelength of circularly polarized light, cm\n", +"mu_R = 1.53914; // Refractive index of right-handed circularly polarized light\n", +"mu_L = 1.53920; // Refractive index of left-handed circularly polarized light\n", +"t = 0.0005; // Thickness of polarimeter plate, m\n", +"theta = %pi/lambda*(mu_L-mu_R)*t; // Angle of rotation produced by the polarimeter plate, radian\n", +"\n", +"printf('\nThe angle of rotation produced by the polarimeter plate = %4.2f degrees', theta*180/%pi);\n", +"\n", +"// Result \n", +"// The angle of rotation produced by the polarimeter plate = 8.18 degrees \n", +"\n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.2: Polarization_by_reflection.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.2:: Page-4.6 (2009)\n", +"clc; clear;\n", +"ip = 57; // Polarizing angle, degrees\n", +"mu = tand(ip); // Refractive index of the material from Brewster's law \n", +"printf('\nThe refractive index of the material = %4.2f', mu);\n", +"\n", +"// Result \n", +"// The refractive index of the material = 1.54 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.3: Angle_of_refraction_of_the_ray.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.3:: Page-4.6 (2009)\n", +"clc; clear;\n", +"mu = 1.53; // Refractive index of the material from Brewster's law \n", +"// As mu = tand(ip), solving for ip\n", +"ip = atand(mu); // Polarizing angle, degrees\n", +"// But mu = sind(ip)/sind(r), solving for r\n", +"r = asind(sind(ip)/mu); // Angle of refraction, degrees\n", +"\n", +"printf('\nThe angle of refraction of the ray = %4.1f degrees', r);\n", +"\n", +"// Result \n", +"// The angle of refraction of the ray = 33.2 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.4: Angle_of_minimum_deviation_for_green_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.4:: Page-4.6 (2009)\n", +"clc; clear;\n", +"ip = 60; // Polarizing angle, degrees\n", +"A = 60; // Angle of equilateral prism, degrees\n", +"mu = tand(ip); // Refractive index of the material from Brewster's law \n", +"// For angle of minimum deviation in prism, delta_m, refractive index\n", +"// mu = sind((A+delta_m)/2)/sind(A/2), solving for delta_m\n", +"delta_m = 2*asind(mu*sind(A/2))-A; // Angle of minimum deviation, degrees\n", +"\n", +"printf('\nThe angle of minimum deviation for green light = %2d degrees', ceil(delta_m));\n", +"\n", +"// Result \n", +"// The angle of minimum deviation for green light = 60 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.5: Polarizing_angles_of_the_materials_for_given_refractive_indices.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.5:: Page-4.7 (2009)\n", +"clc; clear;\n", +"mu = [1.33 1.65 1.55]; // Refractive indices of the material\n", +"// As mu = tand(ip), solving for ip\n", +"ip = atand(mu); // Brewster's law gives polarizing angle, degrees\n", +"for i =1:1:3 \n", +"printf('\nmu = %4.2f, ip = %4.1f degrees', mu(i), ip(i));\n", +"end\n", +"\n", +"// Result \n", +"// mu = 1.33, ip = 53.1 degrees\n", +"// mu = 1.65, ip = 58.8 degrees\n", +"// mu = 1.55, ip = 57.2 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.6: Angle_of_rotation_of_analyser.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.6:: Page-4.8 (2009)\n", +"clc; clear;\n", +"E0 = 1; // For simplicity assume maximum intensity through polarizer and analyser to be unity, unit\n", +"E = 1/6*E0; // One-sixth of the maximum intensity, unit\n", +"// From Malus law, E = E0*cosd(theta)^2, solving for theta\n", +"theta = acosd(sqrt(E)); // Angle through which analyser should be rotated, degrees\n", +"printf('\nThe angle of rotation of analyser = %4.1f degrees', theta);\n", +"\n", +"// Result \n", +"// The angle of rotation of analyser = 65.9 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.7: Angles_of_rotation_of_analyser_for_given_transmitted_light_intensities.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.7:: Page-4.8 (2009)\n", +"clc; clear;\n", +"E0 = 1; // For simplicity assume maximum intensity through polarizer and analyser to be unity, unit\n", +"light_fraction = [0.25 0.45 0.65 0.75 0.0];\n", +"for i = 1:1:5\n", +"E = light_fraction(i)*E0; // Light fraction of the maximum intensity, unit\n", +"// From Malus law, E = E0*cosd(theta)^2, solving for theta\n", +"theta = acosd(sqrt(E)); // Angle through which analyser should be rotated, degrees\n", +"printf('\nE = %4.2fE0, theta = %4.1f degrees', light_fraction(i), theta);\n", +"end\n", +"\n", +"// Result \n", +"// E = 0.25E0, theta = 60.0 degrees\n", +"// E = 0.45E0, theta = 47.9 degrees\n", +"// E = 0.65E0, theta = 36.3 degrees\n", +"// E = 0.75E0, theta = 30.0 degrees\n", +"// E = 0.00E0, theta = 90.0 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.8: Angle_of_minimum_deviation_for_green_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.8:: Page-4.9 (2009)\n", +"clc; clear;\n", +"ip = 60; // Polarizing angle, degrees\n", +"mu = tand(ip); // Brewster's law giving refractive index\n", +"A = 60; // Angle of prism, degrees\n", +"d = (mu - 1)*A; // Angle of minimum deviation for green light, degrees\n", +"\n", +"printf('\nThe angle of minimum deviation for green light = %5.2f degrees', d);\n", +"\n", +"// Result \n", +"// The angle of minimum deviation for green light = 43.92 degrees \n", +" " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4.9: Ratio_of_ordinary_to_extraordinary_ray_intensities.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex4.9:: Page-4.9 (2009)\n", +"clc; clear;\n", +"theta = 30; // Angle which the plane of vibration makes with the incident beam, degrees\n", +"// As intensity of ordinary and extraordinary ray are\n", +"// E_E = A^2*cosd(theta)^2 and E_O = A^2*sind(theta)^2, solving for E_E/E_O\n", +"EE_ratio_EO = cotd(30)^2; // Ratio of ordinary and extraordinary ray intensities \n", +"\n", +"printf('\nThe ratio of ordinary to extraordinary ray intensities = %d', EE_ratio_EO);\n", +"\n", +"// Result \n", +"// The ratio of ordinary to extraordinary ray intensities = 3 \n", +" " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Physics_by_V_Yadav/5-Nuclear_Physics.ipynb b/Engineering_Physics_by_V_Yadav/5-Nuclear_Physics.ipynb new file mode 100644 index 0000000..ebbdce8 --- /dev/null +++ b/Engineering_Physics_by_V_Yadav/5-Nuclear_Physics.ipynb @@ -0,0 +1,263 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5: Nuclear Physics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.1: Mass_defect_of_He.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.1 :: Page-5.2 (2009)\n", +"clc;clear;\n", +"m_p = 1.007826; // Mass of a proton, amu\n", +"m_n = 1.008665; // Mass of a neutron, amu\n", +"M_He = 4.002604; // Measured mass of He nucleuc, amu\n", +"delta_m = 2*m_p+2*m_n - M_He; // Mass defect of He, amu\n", +"printf('\nThe mass defect of He = %f amu', delta_m);\n", +"\n", +"// Result\n", +"// The mass defect of He = 0.030378 amu " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.3: Maximum_energy_of_proton_in_a_cyclotron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.3 :: Page-5.16 (2009)\n", +"clc;clear;\n", +"B = 0.70; // Magnetic field of cyclotron, weber/metre square\n", +"q = 1.6e-019; // Charge of the proton, C\n", +"R = 3; // Radius of Dee's, m\n", +"m = 1.67e-027; // Mass of the proton, kg\n", +"E_max = B^2*q^2*R^2/(2*m); // Maximum energy of the proton in the cyclotron, joule\n", +"printf('\nThe maximum energy of the proton in the cyclotron = %4.2e MeV', E_max/1.6e-013);\n", +"\n", +"// Result\n", +"// The maximum energy of the proton in the cyclotron = 2.11e+02 MeV \n", +"// The unit has been given wrong in the textbook. It should be MeV instead of eV" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.4: Energy_of_an_electron_in_a_betatron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.4 :: Page-5.20 (2009)\n", +"clc;clear;\n", +"f = 1e+06; // Frequency of revolution of electron, Hz\n", +"rate_phi_B = 25; // Rate of change of magnetic flux, wb/s\n", +"E = f*rate_phi_B; // Energy of 'f' revolutios, eV\n", +"printf('\nThe energy of the electron in Betatron after %g revolutions = %3.1e eV', f, E);\n", +"\n", +"// Result\n", +"// The energy of the electron in Betatron after 1e+06 revolutions = 2.5e+07 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.5: Final_energy_gained_by_electrons_in_a_betatron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.5 :: Page-5.20 (2009)\n", +"clc;clear;\n", +"e = 1.6e-019; // Charge on an electron, C\n", +"D = 2.0; // Diameter of the stable orbit in betatron, m\n", +"R = D/2; // Radius of the stable orbit in betatron, m\n", +"B = 0.5; // Magnetic field of betatron, wb/metre square\n", +"c = 3e+08; // final speed of electron in betatron, m/s\n", +"E = B*e*R*c; // Final energy gained by electrons in a betatron, eV\n", +"printf('\nThe final energy gained by electrons in the betatron = %3.1e eV', E/e);\n", +"\n", +"// Result\n", +"// The final energy gained by electrons in the betatron = 1.5e+08 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.6: Energy_produced_in_fission_of_U235.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.6 :: Page-5.27 (2009)\n", +"clc;clear;\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"A = 235; // Atomic weight of uranium, gm/mol\n", +"N_A = 6.023e+026; // No. of atoms present in 235 kg of uranium\n", +"N = N_A/(A*1000); // No. of nuceli of uranium per gram\n", +"E = N*200; // Energy produced by 1 g of U-235, MeV\n", +"printf('\nThe energy produced by 1 g of U-235 = %3.1e joule', E*e*1e+06);\n", +"\n", +"// Result\n", +"// The energy produced by 1 g of U-235 = 8.2e+10 joule " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.7: Power_output_of_nuclear_reactor.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.7 :: Page-5.32 (2009)\n", +"clc;clear;\n", +"A = 235; // Atomic weight of uranium, gm/mol\n", +"N_A = 6.023e+026; // No. of atoms present in 235 kg of uranium-235\n", +"N = N_A*5/A; // No. of nuceli of uranium in 5 kg of U-235\n", +"E = N*200; // Energy released in the fission of 5 kg of U-235, MeV\n", +"t = 24*3600; // Time taken to consume 5 kg of U-235, sec\n", +"P = E/t; // Total power output of the nuclear reactor, MeV per second\n", +"printf('\nThe total power output of the nuclear reactor = %4.2e MeV per second', P);\n", +"\n", +"// Result\n", +"// The total power output of the nuclear reactor = 2.97e+22 MeV per second " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.8: Average_current_in_the_GM_counter_circuit.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.8 :: Page-5.34 (2009)\n", +"clc;clear;\n", +"e = 1.6e-019; // Electronic charge, C\n", +"f = 450; // Count rate of GM counter, counts/min\n", +"N = f*1e+08; // Total number of electrons collected per min\n", +"Q = N*e; // Charge collected per min, C\n", +"I = Q/60; // Averge current in the GM counter, A\n", +"printf('\nThe averge current in the GM counter= %3.1e A', I);\n", +"\n", +"// Result\n", +"// The averge current in the GM counter= 1.2e-10 A " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5.9: Energy_needed_to_remove_a_neutron_from_Ca_nucleus.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex5.9 :: Page-5.39 (2009)\n", +"clc;clear;\n", +"m_Ca_41 = 40.962278; // Mass of one Ca-41 nuclei, amu\n", +"m_Ca_42 = 41.958618; // Mass of one Ca-41 nuclei, amu\n", +"m_n = 1.008665; // Mass of a neutron, amu\n", +"delta_m = m_Ca_42 - (m_Ca_41 + m_n); // Difference in the mass of Ca-42 and Ca_41 nuclei, amu\n", +"E = delta_m*(931.49); // Binding energy of the missing neutron, MeV\n", +"printf('\nThe energy needed to remove a neutron from Ca-42 nucleus = %5.2f MeV', abs(E));\n", +"\n", +"// Result\n", +"// The energy needed to remove a neutron from Ca-42 nucleus = 11.48 MeV " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Physics_by_V_Yadav/6-Semiconductors_and_Nano_Physics.ipynb b/Engineering_Physics_by_V_Yadav/6-Semiconductors_and_Nano_Physics.ipynb new file mode 100644 index 0000000..69ccd09 --- /dev/null +++ b/Engineering_Physics_by_V_Yadav/6-Semiconductors_and_Nano_Physics.ipynb @@ -0,0 +1,92 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6: Semiconductors and Nano Physics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.1: Resistivity_of_intrinsic_semiconductor_at_300_K.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.1:: Page-6.19 (2009)\n", +"clc; clear;\n", +"T = 300; // Temperature of pure semiconductor, K\n", +"n_i = 2.5e+019; // Intrinsic carrier density, per metre square\n", +"e = 1.6e-019; // Charge on an electron, C\n", +"mu_e = 0.39; // Mobility of electrons, Sq.m/V/s\n", +"mu_h = 0.19; // Mobility of holes, Sq.m/V/s\n", +"sigma_i = e*n_i*(mu_e+mu_h); // Conductivity of intrinsic semiconductor at 300 K, mho/m\n", +"rho_i = 1/sigma_i; // Resistivity of intrinsic semiconductor at 300 K, ohm-m\n", +"\n", +"printf('\nThe resistivity of intrinsic semiconductor at 300 K = %4.2f ohm-m', rho_i);\n", +"\n", +"// Result \n", +"// The resistivity of intrinsic semiconductor at 300 K = 0.43 ohm-m " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6.2: Velocity_of_electron_at_Fermi_level.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex6.2: : Page-6.19 (2009)\n", +"clc; clear;\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"E_F = 2.0*e; // Fermi level of Po, J\n", +"m = 9.1e-031; // Mass of an electron, kg\n", +"// As E_F = 1/2*m*v^2, solving for v\n", +"v = sqrt(2*E_F/m); // Velocity of electron at Fermi level, m/s \n", +"printf('\nThe Velocity of electron at Fermi level = %4.2e m/s', v);\n", +"\n", +"// Result \n", +"// The Velocity of electron at Fermi level = 8.39e+05 m/s " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Physics_by_V_Yadav/7-Fiber_Optics.ipynb b/Engineering_Physics_by_V_Yadav/7-Fiber_Optics.ipynb new file mode 100644 index 0000000..af2877e --- /dev/null +++ b/Engineering_Physics_by_V_Yadav/7-Fiber_Optics.ipynb @@ -0,0 +1,372 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 7: Fiber Optics" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.10: Radius_of_core_for_single_mode_operation_in_step_index_fibre.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.10:: Page-7.14 (2009)\n", +"clc; clear;\n", +"n1 = 1.480; // Refractive index of core material\n", +"n2 = 1.47; // Refractive index of cladding material\n", +"lambda = 850e-006; // Wavelength of light used, m\n", +"NA = sqrt(n1^2-n2^2); // Numerical aperture of the step index fibre\n", +"theta0 = asind(NA); // Maximum acceptance angle for the fibre, degrees\n", +"M_N = 1; // Number of modes in step index cable\n", +"// As number of modes, M_N = 1/2*V^2, solving for V\n", +"V = sqrt(2*M_N); // V-number for the fibre\n", +"// As V = 2*%pi*a/lambda*NA, solving for a\n", +"a = V*lambda/(2*%pi*NA); // Radius of core for single mode operation in step index fibre, m\n", +"printf('\nThe radius of core for single mode operation in step index fibre = %3.1e', a);\n", +"// Result \n", +"// The radius of core for single mode operation in step index fibre = 1.1e-03 \n", +"// The ansswer is quoted wrong in the textbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.11: Signal_attenuation_in_optical_fibre.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.11: : Page-7.16 (2009)\n", +"clc; clear;\n", +"Pi = 1.5; // Input power to the optical fibre, mW\n", +"Po = 0.5; // Output power to the optical fibre, mW\n", +"L = 0.12; // Length of the optical fibre, km\n", +"alpha_dB = 10/L*log10(Pi/Po); // Signal attenuation in optical fibre, dB/km\n", +"\n", +"printf('\nThe signal attenuation in optical fibre = %4.1f dB/km', alpha_dB);\n", +"\n", +"// Result \n", +"// The signal attenuation in optical fibre = 39.8 dB/km " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.1: Critical_angle_and_acceptance_angle_in_an_optical_fibre.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.1:: Page-7.7 (2009)\n", +"clc; clear;\n", +"n1 = 1.6; // Refractive index of core material of fibre\n", +"n2 = 1.3; // Refractive index of cladding material of fibre\n", +"phi_C = asind(n2/n1); // Critical angle of optical fibre, degrees\n", +"theta_Q = asind(sqrt(n1^2-n2^2)); // Acceptance angle of optical fibre, degrees\n", +"\n", +"printf('\nThe critical angle of optical fibre = %4.1f degrees', phi_C);\n", +"printf('\nThe angle of acceptance cone = %5.1f degrees', 2*theta_Q);\n", +"\n", +"// Result \n", +"// The critical angle of optical fibre = 54.3 degrees\n", +"// The angle of acceptance cone = 137.7 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.2: Critical_angle_acceptance_angle_and_numerical_aperture_in_an_optical_fibre.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.2:: Page-7.8 (2009)\n", +"clc; clear;\n", +"n1 = 1.50; // Refractive index of core material of fibre\n", +"n2 = 1.47; // Refractive index of cladding material of fibre\n", +"phi_C = asind(n2/n1); // Critical angle of optical fibre, degrees\n", +"NA = sqrt(n1^2-n2^2); // Numerical aperture for the fibre \n", +"theta_Q = asind(sqrt(n1^2-n2^2)); // Acceptance angle of optical fibre, degrees\n", +"\n", +"printf('\nThe critical angle of optical fibre = %4.1f degrees', phi_C);\n", +"printf('\nThe numerical aperture for the fibre = %5.3f', NA);\n", +"printf('\nThe angle of acceptance cone = %5.1f degrees', theta_Q);\n", +"\n", +"// Result \n", +"// The critical angle of optical fibre = 78.5 degrees\n", +"// The numerical aperture for the fibre = 0.298\n", +"// The angle of acceptance cone = 17.4 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.3: Parameters_of_an_optical_fibre_using_relative_refractive_index_difference.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.3:: Page-7.8 (2009)\n", +"clc; clear;\n", +"n1 = 1.46; // Refractive index of the core material\n", +"delta = 0.01; // Relative refractive index difference\n", +"NA = n1*sqrt(2*delta); // Numerical aperture for the fibre \n", +"theta_Q = %pi*NA^2; // Solid acceptance angle of optical fibre for small angles, radians\n", +"// As relative refractive index, delta = 1-n2/n1, solving for n2\n", +"n2 = n1*(1-delta); // Refractive index of cladding\n", +"phi_C = asind(n2/n1); // Critical angle of optical fibre, degrees\n", +"\n", +"printf('\nThe numerical aperture for the fibre = %4.2f', NA);\n", +"printf('\nThe solid acceptance angle of the optical fibre = %4.2f radians', theta_Q);\n", +"printf('\nThe critical angle of optical fibre = %4.1f degrees', phi_C);\n", +"\n", +"// Result \n", +"// The numerical aperture for the fibre = 0.21\n", +"// The solid acceptance angle of the optical fibre = 0.13 radians\n", +"// The critical angle of optical fibre = 81.9 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.4: Refractive_index_of_cladding.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.4:: Page-7.9 (2009)\n", +"clc; clear;\n", +"n1 = 1.54; // Refractive index of the core material\n", +"NA = 0.45; // Numerical aperture for the fibre \n", +"n2 = sqrt(n1^2-NA^2); // Refractive index of cladding\n", +"\n", +"printf('\nThe refractive index of cladding = %4.2f', n2);\n", +"\n", +"// Result \n", +"// The refractive index of cladding = 1.47 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.5: Numerical_aperture_for_an_optical_fibre.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.5:: Page-7.9 (2009)\n", +"clc; clear;\n", +"n1 = 1.544; // Refractive index of the core material\n", +"n2 = 1.412; // Refractive index of cladding\n", +"NA = sqrt(n1^2-n2^2); // Numerical aperture for the fibre \n", +"\n", +"printf('\nThe numerical aperture for an optical fibre = %4.2f', NA);\n", +"\n", +"// Result \n", +"// The numerical aperture for an optical fibre = 0.62 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.6: Refractive_index_of_the_cladding.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.6:: Page-7.9 (2009)\n", +"clc; clear;\n", +"n1 = 1.544; // Refractive index of the core material\n", +"theta0 = 35; // Acceptance angel for an optical fibre, degrees\n", +"// As theta0 = asind(sqrt(n1^2-n2^2)), solving for n2\n", +"n2 = sqrt(n1^2-sind(theta0)^2); // Refractive index of cladding\n", +"\n", +"printf('\nThe refractive index of the cladding = %4.2f', n2);\n", +"\n", +"// Result \n", +"// The refractive index of the cladding = 1.43 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.7: EX7_7.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.7:: Page-7.10 (2009)\n", +"clc; clear;\n", +"NA = 0.4; // Numerical aperture of the optical fibre\n", +"n0 = 1; // Refractive index of fibre in air\n", +"theta_a = asind(NA/n0); // Acceptance angle for meridional rays, degrees\n", +"theta = 100; // Direction through which the skew rays are bent at each reflection, degrees\n", +"r = theta/2; // Angle of reflection, degrees\n", +"theta_as = asind(NA/(cosd(r)*n0)); // Acceptance angle for skew rays, degrees\n", +"\n", +"printf('\nAcceptance angle for meridional rays = %4.1f degrees', theta_a);\n", +"printf('\nAcceptance angle for skew rays = %4.1f degrees', theta_as);\n", +"\n", +"// Result \n", +"// Acceptance angle for meridional rays = 23.6 degrees\n", +"// Acceptance angle for skew rays = 38.5 degrees " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.8: Normalized_frequency_for_V_number_for_the_fibre.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.8: : Page-7.13 (2009)\n", +"clc; clear;\n", +"NA = 0.16; // Numerical aperture of the step index fibre\n", +"n1 = 1.50; // Refractive index of the core material\n", +"d = 65e-006; // Diameter of the core, m\n", +"lambda = 0.9e-006; // Wavelength of transmitted light, m\n", +"V = %pi*d/lambda*NA; // V-number for the optical fibre\n", +"\n", +"printf('\nThe V-number for the optical fibre = %5.2f', V);\n", +"\n", +"// Result \n", +"// The V-number for the optical fibre = 36.30 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7.9: Number_of_modes_in_the_step_index_fibre.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex7.9:: Page-7.13 (2009)\n", +"clc; clear;\n", +"NA = 0.28; // Numerical aperture of the step index fibre\n", +"d = 55e-006; // Diameter of the core, m\n", +"lambda = 0.9e-006; // Wavelength of transmitted light, m\n", +"M_N = (2.22*d*(NA)/lambda)^2; // Number of modes in the step index fibre\n", +"\n", +"printf('\nThe number of modes in the step index fibre = %4d degrees', M_N);\n", +"\n", +"// Result \n", +"// The number of modes in the step index fibre = 1442 degrees " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} diff --git a/Engineering_Physics_by_V_Yadav/8-Laser.ipynb b/Engineering_Physics_by_V_Yadav/8-Laser.ipynb new file mode 100644 index 0000000..cb04ca1 --- /dev/null +++ b/Engineering_Physics_by_V_Yadav/8-Laser.ipynb @@ -0,0 +1,184 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 8: Laser" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.1: EX8_1.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.1:: Page-8.8 (2009)\n", +"clc; clear;\n", +"lambda = 31235; // Wavelength of prominent emission of laser, aangstrom\n", +"E = 12400/lambda; // Energy difference between the two levels, eV\n", +"\n", +"printf('\nThe difference between upper and lower energy levels for the most prominent wavelength = %5.3f eV', E);\n", +"\n", +"// Result \n", +"// The difference between upper and lower energy levels for the most prominent wavelength = 0.397 eV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.2: Frequency_and_wavelength_of_carbon_dioxide_laser.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.2:: Page-8.8 (2009)\n", +"clc; clear;\n", +"E = 0.121; // Energy difference between the two levels, eV\n", +"lambda = 12400/E; // Wavelength of the radiation, angstrom\n", +"f = 3e+08/(lambda*1e-010); // Frequency of the radiation, Hz\n", +"\n", +"printf('\nThe wavelength of the radiation = %8.1f angstrom', lambda);\n", +"printf('\nThe frequency of the radiation = %4.2e Hz', f);\n", +"\n", +"// Result \n", +"// The wavelength of the radiation = 102479.3 angstrom\n", +"// The frequency of the radiation = 2.93e+13 Hz " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.3: Energy_of_one_emitted_photon_and_total_energy_available_per_laser_pulse.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.3:: Page-8.8 (2009)\n", +"clc; clear;\n", +"lambda = 7000; // Wavelength of the Ruby laser, angstrom\n", +"e = 1.6e-019; // Energy equivalent of 1 eV, J/eV\n", +"N = 2.8e+019; // Total number of photons\n", +"E = 12400/lambda; // Energy of one emitted photon, eV\n", +"E_p = E*e*N; // Total energy available per laser pulse, joule\n", +"\n", +"printf('\nThe energy of one emitted photon = %4.2e J', E*e);\n", +"printf('\nThe total energy available per laser pulse = %4.2f joule', E_p);\n", +"\n", +"// Result \n", +"// The energy of one emitted photon = 2.83e-19 J\n", +"// The total energy available per laser pulse = 7.94 joule " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.4: Relative_population_of_levels_in_Ruby_laser.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.4:: Page-8.9 (2009)\n", +"clc; clear;\n", +"lambda = 7000; // Wavelength of the emitted light, angstrom\n", +"k = 8.6e-005; // Boltzmann constant, eV/K\n", +"dE = 12400/lambda; // Energy difference of the levels, eV\n", +"T = [300 500]; // Temperatures of first and second states, K\n", +"for i = 1:1:2\n", +" N2_ratio_N1 = exp(-(dE/(k*T(i)))); // Relative population\n", +" printf('\nThe relative population at %d K = %3.1e', T(i), N2_ratio_N1);\n", +"end\n", +"\n", +"// Result \n", +"// The relative population at 300 K = 1.5e-30\n", +"// The relative population at 500 K = 1.3e-18 \n", +"// The answer is given wrong in the textbook for first part." + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8.5: Population_of_two_states_in_He_Ne_laser.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab Code Ex8.5:: Page-8.9 (2009)\n", +"clc; clear;\n", +"lambda = 7000; // Wavelength of the emitted light, angstrom\n", +"k = 8.6e-005; // Boltzmann constant, eV/K\n", +"dE = 12400/lambda; // Energy difference of the levels, eV\n", +"T = 27+273; // Temperatures of the state, K\n", +"N2_ratio_N1 = exp(-(dE/(k*T))); // Relative population\n", +"printf('\nThe relative population of two states in He-Ne laser at %d K = %3.1e', T, N2_ratio_N1);\n", +"\n", +"\n", +"// Result \n", +"// The relative population of two states in He-Ne laser at 300 K = 1.5e-30 \n", +"// The answer is given wrong in the textbook" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |