{
"cells": [
 {
		   "cell_type": "markdown",
	   "metadata": {},
	   "source": [
       "# Chapter 3: Vibration Waves and Light"
	   ]
	},
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_02: Frequency_of_particle_executing_SHM.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.a.2: Page-132 (2008)\n",
"clc; clear;\n",
"m = 10;    // Mass of the particle, g\n",
"x = poly(0, 'x');\n",
"V = 50*x^2 + 100;    // Potential field surrounding the particle, erg/g\n",
"U = m*V;    // Potential energy of the particle field system, erg\n",
"F = -derivat(U);    // Force acting on the particle, dyne\n",
"// As F = -m*a = -m*omega^2*x = -m*(2%pi*f)^2*x, solving for f\n",
"f = sqrt(eval(pol2str(-pdiv(F,x)/m)))/(2*%pi);    // Frequency of oscillations of the particle executing SHM, Hz\n",
"printf('\nThe frequency of oscillations of the particle executing SHM = %4.2f Hz', f);\n",
"\n",
"// Result\n",
"// The frequency of oscillations of the particle executing SHM = 1.59 Hz "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_03: A_body_executing_SHM.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.a.3:Page-133 (2008)\n",
"clc; clear;\n",
"v1 = 80;    // Velocity of the body at 3 cm displacement, cm/s\n",
"v2 = 60;    // Velocity of the body at 4 cm displacement, cm/s\n",
"x1 = 3;    // Displacement of the body at velocity of 80 cm/s\n",
"x2 = 4;    // Displacement of the body at velocity of 60 cm/s\n",
"// As v = omega*sqrt(a^2 - x^2), solving for a\n",
"a = poly(0, 'a');\n",
"a = roots(v1^2*(a^2-16) - v2^2*(a^2 - 9));\n",
"omega = v1/sqrt(a(1)^2 - x1^2);    // Angular ferquency of the oscillations, rad/s\n",
"x = a(1);    // Maximum displacement, cm\n",
"// As x = a*sin(omega*t), solving for t\n",
"t_ex = asin(x/a(1))/omega;    // Time taken to reach the +ve extremity, s\n",
"d = a(1) - 2.5;    // Distance of the point from the mean position, cm\n",
"t = asin(d/a(1))/omega;    // Time taken to travel from mean position to positive extremity, s\n",
"printf('\nThe time taken to travel from 2.5 cm from +ve extremity = %5.3f s', t_ex - t);    \n",
"\n",
"// Result\n",
"// The time taken to travel from 2.5 cm from +ve extremity = 0.052 s "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_04: Time_period_of_a_body_oscillating_in_the_tunnel_across_the_earth.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.a.4: Page-134 (2008)\n",
"clc; clear;\n",
"R = 6.4e+006;    // Radius of the earth, m\n",
"g = 10;    // Acceleration due to gravity, m/sec-square\n",
"T = 2*%pi*sqrt(R/g);    // Time period of oscillations of the body, s\n",
"printf('\nThe time period of oscillations of the body = %4.1f min', T/60);\n",
"\n",
"// Result\n",
"// The time period of oscillations of the body = 83.8 min "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_05: Resultant_amplitude_and_phase_angle_relative_to_the_first_SHM.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.a.5: Page-135 (2008)\n",
"clc; clear;\n",
"phi1 = 0;    // Phase of the first SHM, degree\n",
"phi2 = 60;    // Phase of the second SHM, degree\n",
"phi3 = 90;    // Phase of the third SHM, degree\n",
"a1 = 1.0;    // Amplitude of the first SHM, cm\n",
"a2 = 1.5;    // Amplitude of the second SHM, cm\n",
"a3 = 2.0;    // Amplitude of the third SHM, cm\n",
"A = sqrt((a1 + a2*cosd(phi2)+a3*cosd(phi3))^2 + (a2*sind(phi2)+a3*sind(phi3))^2);    // Resultant amplitude relative to the first SHM, cm\n",
"phi = atand((a2*sind(phi2)+a3*sind(phi3))/(a1 + a2*cosd(phi2)+a3*cosd(phi3)));    // Resultant phase angle relative to the first SHM, degree\n",
"printf('\nThe resultant amplitude and phase angle relative to the first SHM = %4.2f cm and %2d degrees respectively', A, phi);\n",
"\n",
"// Result\n",
"// The resultant amplitude and phase angle relative to the first SHM are 3.73 cm and 62 degrees respectively"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_07: Two_SHMs_acting_in_the_same_direction.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.a.7:Page-136 (2008)\n",
"clc; clear;\n",
"phi1 = 0;    // Phase of the first SHM, degree\n",
"phi2 = 45;    // Phase of the second SHM, degree\n",
"a1 = 0.005;    // Amplitude of the first SHM, m\n",
"a2 = 0.002;    // Amplitude of the second SHM, m\n",
"A = sqrt((a1 + a2*cosd(phi2))^2 + (a2*sind(phi2))^2);    // Resultant amplitude relative to the first SHM, m\n",
"phi = atand(a2*sind(phi2)/(a1 + a2*cosd(phi2)));    // Resultant phase angle relative to the first SHM, degree\n",
"printf('\nThe amplitude of the resultant displacement and phase angle relative to the first SHM are %7.5f m and %5.2f degrees respectively', A, phi);\n",
"\n",
"// Result\n",
"// The amplitude of the resultant displacement and phase angle relative to the first SHM are 0.00657 m and 12.43 degrees respectively  "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_11: A_spring_disc_system_undergoing_damped_oscillation.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.b.1: Page-138 (2008)\n",
"clc; clear;\n",
"m = 100;    // Mass of the horizontal disc, g\n",
"t = 60;    // Time during which the amplitude reduces to half of its undamped value, s\n",
"f = 10;    // Frequency of oscillations of the system, Hz\n",
"omega_prime = 2*%pi*f;    // Angular frequency of the oscillations, rad/s\n",
"A0 = 1;    // Assume the amplitude of undamped oscillations to be unity, cm\n",
"// As A = A0*exp(-k*t), solving for k\n",
"A = A0/2;    // Amplitude of damped oscillations after 1 min, cm\n",
"k = log(A0/A)/t;    // Resisting force per unit mass per unit velocity, nepers/sec\n",
"r = 2*k*m;    // Resistive force constant, sec/cm\n",
"tau = 1/k;    // Relaxation time, sec\n",
"Q = m*omega_prime/r;    // Quality factor\n",
"s = m*(omega_prime^2 + k^2);    // Force constant of the spring, dynes/Sq.cm\n",
"printf('\nThe resistive force constant = %4.2f dyne-sec/cm', r);\n",
"printf('\nThe relaxation time of the system = %4.2f sec', tau);\n",
"printf('\nThe quality factor, Q = %4.2f', Q);\n",
"printf('\nThe force constant of the spring = %4.2e dyne/Sq.cm', s);\n",
"\n",
"// Result\n",
"// The resistive force constant = 2.31 dyne-sec/cm\n",
"// The relaxation time of the system = 86.56 sec\n",
"// The quality factor, Q = 2719.42\n",
"// The force constant of the spring = 3.95e+005 dyne/Sq.cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_12: A_mass_executing_damped_oscillations_in_one_dimension.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.b.2: Page-139 (2008)\n",
"clc; clear;\n",
"function m = check_motion_type(k, omega0)\n",
"    if k > omega0 then\n",
"        m = 'aperiodic';\n",
"    else if  k == omega0 then\n",
"            m = 'criticallydamped';\n",
"        else if  k < omega0 then\n",
"                m = 'oscillatory';\n",
"            end\n",
"        end\n",
"    end\n",
"endfunction\n",
"m = 10;    // Mass of the body, g\n",
"s = 10;    // Restoring force, dyne/cm\n",
"r = 2;    // Resistive force constant, dyne.sec/cm\n",
"k = r/(2*m);    // Resisting force, nepers/sec\n",
"// As omega0^2 = s/m, solving for omega0\n",
"omega0 = sqrt(s/m);    // Angular frequency, rad/s\n",
"motion = check_motion_type(k, omega0);    // Check for the type of motion\n",
"r_new = 2*sqrt(m*s);    // Resistive force constant, dyne-sec/cm\n",
"m = r^2/(4*s);    // Mass for which the given forces makes the motion critically damped, g\n",
"printf('\nThe motion is %s in nature', motion);\n",
"printf('\nThe resistive force constant = %d dyne-sec/cm', r_new);\n",
"printf('\nThe mass for which the given forces makes the motion critically damped = %3.1f g', m);\n",
"\n",
"// Result\n",
"// The motion is oscillatory in nature\n",
"// The resistive force constant = 20 dyne-sec/cm\n",
"// The mass for which the given forces makes the motion critically damped = 0.1 g "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_14: A_mass_executing_damped_oscillations_in_one_dimension.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.b.4: Page-140 (2008)\n",
"clc; clear;\n",
"m = 1;    // Mass of the suspended body, kg\n",
"s = 25;    // Stifness constant of the spring, N/m\n",
"r = poly(0, 'r');\n",
"// As f0/f_prime = 2/sqrt(3), solving for r\n",
"r = roots(4*(s/m-r^2/(4*m^2))-3*s/m);    // Damping factor, kg/sec\n",
"printf('\nThe damping factor of damped oscillations = %d kg/sec', r(1));\n",
"\n",
"// Result\n",
"// The damping factor of damped oscillations = 5 kg/sec "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_15: Resisting_force_for_critically_damped_motion.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"\n",
"// Scilab Code Ex3a.b.5: Page-141 (2008)\n",
"clc; clear;\n",
"function m = check_motion_type(k, omega0)\n",
"    if k > omega0 then\n",
"        m = 'aperiodic';\n",
"    else if  k == omega0 then\n",
"            m = 'criticallydamped';\n",
"        else if  k < omega0 then\n",
"                m = 'oscillatory';\n",
"            end\n",
"        end\n",
"    end\n",
"endfunction\n",
"m = 10;    // Mass of the oscillating body, g\n",
"r = 2;    // Resisting force, dyne-sec/cm\n",
"s = 5;    // Restoring force, dyne/cm\n",
"k = r/(2*m);    // Resisting force, nepers/sec\n",
"// As omega0^2 = s/m, solving for omega0\n",
"omega0 = sqrt(s/m);    // Angular frequency, rad/s\n",
"motion = check_motion_type(k, omega0);    // Check for the type of motion\n",
"r = 2*sqrt(m*s);    // Resistive force constant for critical damping, dyne-sec/cm\n",
"printf('\nThe motion is %s in nature', motion);\n",
"printf('\nThe resistive force constant for critical damping = %4.1f dyne-sec/cm', r);\n",
"\n",
"// Result\n",
"// The motion is oscillatory in nature\n",
"// The resistive force constant for critical damping = 14.1 dyne-sec/cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_16: Damped_oscillatory_motio.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.b.6: Page-141 (2008)\n",
"clc; clear;\n",
"m = 0.1;    // Mass of the oscillating body, kg\n",
"t = 50;    // Time during which the energy of system decays to 1/e of its undamped value, s\n",
"s = 10;    // Spring constant, N/m\n",
"E0 = 1;    // Assume the energy of undamped oscillations to be unity, erg\n",
"// As E = E0*exp(-k*t) and E/E0 = 1/e,  solving for k\n",
"E = E0/%e;    // Energy of damped oscillations after 50 sec, erg\n",
"k = log(E0/E)/t;    // Resisting force per unit mass per unit velocity, nepers/sec\n",
"p = m*k;    // A resistive force constant, N-s/m\n",
"omega0 = sqrt(s/m);    // Angular frequency in the absence of damping, rad/sec\n",
"omega_prime = sqrt(omega0^2 - k^2/4);    // Angular frequency when damping takes place, rad/sec\n",
"Q = omega_prime/k;    // Quality factor\n",
"printf('\nThe resistive force constant, p = %1.0e N-s/m', p);\n",
"printf('\nThe quality factor, Q = %d', ceil(Q));\n",
"\n",
"// Result\n",
"// The resistive force constant, p = 2e-003 N-s/m\n",
"// The quality factor, Q = 500 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_17: Damped_simple_harmonic_motion.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.b.7: Page-142 (2008)\n",
"clc; clear;\n",
"t = 10;    // Time during which the amplitude reduces to 1/10th of its undamped value, s\n",
"f = 200;    // Frequency of oscillations of the system, Hz\n",
"omega0 = 2*%pi*f;    // Angular frequency of the oscillations, rad/s\n",
"A0 = 1;    // Assume the amplitude of undamped oscillations to be unity, cm\n",
"// As A = A0*exp(-k*t), solving for k\n",
"A = A0/10;    // Amplitude of damped oscillations after 10 sec, cm\n",
"k = log(A0/A)/t;    // Resisting force per unit mass per unit velocity, nepers/sec\n",
"tau = 1/(2*k);    // Relaxation time, sec\n",
"Q = omega0*tau;   // Quality factor\n",
"E0 = 1;    // Assume energy of undamped oscillations to be unity, erg\n",
"E = E0/10;    // Energy of damped oscillations after t sec, erg\n",
"// As E = E0*exp(-2*k*t), solving for t\n",
"t = 1/(2*k)*log(E0/E);    // Time during which the energy falls to 1/10 of its initial value, sec\n",
"printf('\nThe relaxation time = %4.2f sec', tau);\n",
"printf('\nThe quality factor, Q = %d', Q);\n",
"printf('\nThe time during which the energy falls to 1/10 of its initial value = %d sec', t);\n",
"printf('\nThe damping constant, k = %4.2f', k);\n",
"\n",
"// Result\n",
"// The relaxation time = 2.17 sec\n",
"// The quality factor, Q = 2728\n",
"// The time during which the energy falls to 1/10 of its initial value = 5 sec\n",
"// The damping constant, k = 0.23 \n",
"// The answer for Q is given wrongly in the textbook"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_21: Characteristics_of_progressive_waves.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.c.1: Page-143 (2008)\n",
"clc; clear;\n",
"// Comparing with the standard progressive wave equation, we have\n",
"a = 0.5;    // Amplitude of the wave, m\n",
"lambda = 2*%pi/12.56;    // Wavelength of the wave, m\n",
"v = 314/12.56;    // Wave velocity, m/s\n",
"nu = v/lambda;    // Frequency of the wave, Hz\n",
"printf('\nThe amplitude of the wave = %3.1f m', a);\n",
"printf('\nThe wavelength of the wave = %3.1f m', lambda);\n",
"printf('\nThe velocity of the wave = %d m/s', v);\n",
"printf('\nThe frequency of the wave = %d Hz', ceil(nu));\n",
"\n",
"// Result\n",
"// The amplitude of the wave = 0.5 m\n",
"// The wavelength of the wave = 0.5 m\n",
"// The velocity of the wave = 25 m/s\n",
"// The frequency of the wave = 50 Hz "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_22: A_simple_harmonic_wave_travelling_along_X_axis.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.c.2: Page-144 (2008)\n",
"clc; clear;\n",
"// Comparing with the standard progressive wave equation, we have\n",
"a = 5;    // Amplitude of the wave, m\n",
"nu = 0.2;    // Frequency of the wave, Hz\n",
"lambda = 1/0.5;    // Wavelength of the wave, m\n",
"v = nu*lambda;    // Wave velocity, m/s\n",
"printf('\nThe amplitude of the wave = %3.1f m', a);\n",
"printf('\nThe wavelength of the wave = %3.1f m', lambda);\n",
"printf('\nThe velocity of the wave = %3.1f m/s', v);\n",
"printf('\nThe frequency of the wave = %3.1f Hz', nu);\n",
"\n",
"// Result\n",
"// The amplitude of the wave = 5.0 m\n",
"// The wavelength of the wave = 2.0 m\n",
"// The velocity of the wave = 0.4 m/s\n",
"// The frequency of the wave = 0.2 Hz   "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.a_23: Travelling_wave_characteristics_and_phase_difference.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3a.c.3: Page-144 (2008)\n",
"clc; clear;\n",
"// Comparing with the standard progressive wave equation, we have\n",
"a = 8;    // Amplitude of the wave, cm\n",
"nu = 4/2;    // Frequency of the wave, Hz\n",
"lambda = 2/0.02;    // Wavelength of the wave, cm\n",
"v = nu*lambda;    // Wave velocity, cm/s\n",
"delta_x = 20;    // Path difference between two particles, cm\n",
"delta_phi = delta_x*2*%pi/lambda*180/%pi;    // Phase difference between two particles, degree\n",
"printf('\nThe amplitude of the wave = %3.1f cm', a);\n",
"printf('\nThe wavelength of the wave = %3.1f cm', lambda);\n",
"printf('\nThe velocity of the wave = %3.1f cm/s', v);\n",
"printf('\nThe frequency of the wave = %d Hz', nu);\n",
"printf('\nThe phase difference between two particles = %d degree', delta_phi);\n",
"\n",
"// Result\n",
"// The amplitude of the wave = 8.0 cm\n",
"// The wavelength of the wave = 100.0 cm\n",
"// The velocity of the wave = 200.0 cm/s\n",
"// The frequency of the wave = 2 Hz\n",
"// The phase difference between two particles = 72 degree "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.b_101: Brewster_angle_and_angle_of_refraction_for_glass.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3b.1: Page-163 (2008)\n",
"clc; clear;\n",
"mu = 1.5;    // Refractive indexof glass\n",
"i_p = atand(mu);    // Angle of polarization from Brewster's law, degree\n",
"r = 90 - i_p;    // Angale of refraction, degree\n",
"printf('\nThe Brewster angle for glass = %4.1f degree', i_p);\n",
"printf('\nThe angle of refraction for glass = %4.1f degree', r);\n",
"\n",
"// Result\n",
"// The Brewster angle for glass = 56.3 degree\n",
"// The angle of refraction for glass = 33.7 degree "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.b_102: Polarizing_angles_for_various_pair_of_media.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3b.2: Page-163 (2008)\n",
"clc; clear;\n",
"// Function to convert degree to degree-minute\n",
"function [d,m]= deg2deg_min(deg)\n",
"    d = int(deg);\n",
"    m = (deg - d)*60;\n",
"endfunction\n",
"mu_air = 1;    // Refractive index fo air\n",
"mu_glass = 1.54;    // Refractive index of glass\n",
"mu_water = 1.33;    // Refractive index of water\n",
"// Air to glass incidence\n",
"i_p = atand(mu_glass/mu_air);    // Angle of polarization for air to glass incidence, degree\n",
"printf('\nFor air to glass, i_p = %d degree', i_p);\n",
"// glass to air incidence\n",
"i_p = atand(mu_air/mu_glass);    // Angle of polarization for glass to air incidence, degree\n",
"printf('\nFor glass to air, i_p = %d degree', ceil(i_p));\n",
"// Water to glass incidence\n",
"i_p = atand(mu_glass/mu_water);    // Angle of polarization for water to glass incidence, degree\n",
"[d,m] = deg2deg_min(i_p);    // Call function to convert to deg-min\n",
"printf('\nFor water to glass, i_p = %d degree %d min', d, m);\n",
"// Glass to water incidence\n",
"i_p = atand(mu_water/mu_glass);    // Angle of polarization for glass to water incidence, degree\n",
"[d,m] = deg2deg_min(i_p);    // Call function to convert to deg-min\n",
"printf('\nFor glass to water, i_p = %d degree %d min', d, m);\n",
"// Air to water incidence\n",
"i_p = atand(mu_water/mu_air);    // Angle of polarization for air to water incidence, degree\n",
"[d,m] = deg2deg_min(i_p);    // Call function to convert to deg-min\n",
"printf('\nFor air to water, i_p = %d degree %d min', d, m);\n",
"// Water to air incidence\n",
"i_p = atand(mu_air/mu_water);    // Angle of polarization for water to airincidence, degree\n",
"[d,m] = deg2deg_min(i_p);    // Call function to convert to deg-min\n",
"printf('\nFor water to air, i_p = %d degree %d min', d, m);\n",
"\n",
"// Result\n",
"// For air to glass, i_p = 57 degree\n",
"// For glass to air, i_p = 33 degree\n",
"// For water to glass, i_p = 49 degree 11 min\n",
"// For glass to water, i_p = 40 degree 48 min\n",
"// For air to water, i_p = 53 degree 3 min\n",
"// For water to air, i_p = 36 degree 56 min "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.b_103: Polarizing_angle_for_glass.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3b.3: Page-163 (2008)\n",
"clc; clear;\n",
"C = 40;    // Critical angle for glass to air\n",
"mu = 1/sind(C);    // Refractive index of glass w.r.t. air\n",
"i_p = atand(mu);    // Polarizing angle for glass, degree\n",
"printf('\nThe polarizing angle for glass = %4.1f degree', i_p);\n",
"\n",
"// Result\n",
"// The polarizing angle for glass = 57.3 degree "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.b_104: Polarization_by_reflection.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3b.4: Page-164 (2008)\n",
"clc; clear;\n",
"i = 60;    // Angle of incidence, degree\n",
"i_p = i;    // Angle of polarization, degree\n",
"mu = tand(i_p);    // Refractive index of the medium\n",
"r = 90 - i;    // Angle of refraction, degree\n",
"printf('\nThe refractive index of transparent medium = %5.3f', mu);\n",
"printf('\nThe angle of refraction, r = %d degree', r);\n",
"printf('\nThe reflected and transmitted components are at right angles to each other.');\n",
"\n",
"// Result\n",
"// The refractive index of transparent medium = 1.732\n",
"// The angle of refraction, r = 30 degree\n",
"// The reflected and transmitted components are at right angles to each other."
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.b_105: Intensity_ratio_of_two_beams_through_analyser.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3b.5: Page-164 (2008)\n",
"clc; clear;\n",
"theta_A = 30;    // Angle between principal sections of polariser and  analyser for beam A, degree\n",
"theta_B = 60;    // Angle between principal sections of polariser and  analyser for beam B, degree\n",
"// As I_A*cosd(theta_A)^2 = I_B*cosd(theta_B)^2, solving for I ratio\n",
"I_ratio = cosd(theta_B)^2/cosd(theta_A)^2;    // The intensity ratio of the two beams\n",
"printf('\nThe intensity ratio of the two beams = %4.2f', I_ratio);\n",
"\n",
"// Result\n",
"// The intensity ratio of the two beams = 0.33"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.b_106: Percentage_reduction_in_the_intensity_of_the_inident_light.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3b.6: Page-165 (2008)\n",
"clc; clear;\n",
"theta = [30 45 60 90];    // Angles between principal sections of polariser and analyser, degree\n",
"for i = 1:1:4\n",
"    P_red = (1-cosd(theta(i))^2)*100;    // Percentage reduction in intensity of incident light\n",
"    printf('\nFor theta = %d degree, percentage reduction = %1.0f percent', theta(i), P_red);\n",
"end\n",
"\n",
"// Result\n",
"// For theta = 30 degree, percentage reduction = 25 percent\n",
"// For theta = 45 degree, percentage reduction = 50 percent\n",
"// For theta = 60 degree, percentage reduction = 75 percent\n",
"// For theta = 90 degree, percentage reduction = 100 percent "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.b_107: Angle_of_rotation_of_polaroid_to_reduce_the_intensity.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3b.7: Page-165 (2008)\n",
"clc; clear;\n",
"// For half reduction in intensity\n",
"I_ratio = 1/2;    // Intensity ratio\n",
"theta = acosd(sqrt(I_ratio));    // Angle of rotation of polaroid, degree\n",
"printf('\nFor half reduction in intensity, the angle of rotation = %d degree', theta);\n",
"// For one-fourth reduction in intensity\n",
"I_ratio = 1/4;    // Intensity ratio\n",
"theta = acosd(sqrt(I_ratio));    // Angle of rotation of polaroid, degree\n",
"printf('\nFor one-fourth reduction in intensity, the angle of rotation = %d degree', theta);\n",
"\n",
"// Result\n",
"// For half reduction in intensity, the angle of rotation = 45 degree\n",
"// For one-fourth reduction in intensity, the angle of rotation = 60 degree "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_202: Ratio_of_maximum_to_minimum_intensity_in_the_interference_fringe_system.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.2: Page-184 (2008)\n",
"clc; clear;\n",
"I2 = 1;    // Assume intensity of light beam from the second source to be unity\n",
"I1 = 81*I2;    // Intensity of light beam from the first source\n",
"a = sqrt(I1);    // Width of the first slit, mm\n",
"b = sqrt(I2);    // Width of the second slit, mm\n",
"I_max = (1+a/b)^2;    // Maximum intensity in the fringe pattern\n",
"I_min = (1-a/b)^2;    // Minimum intensity in the fringe pattern\n",
"fact = gcd([I_max,I_min]); // Find l.c.m. of I_max and I_min\n",
"printf('\nThe ratio of maximum to minimum intensity in the fringe system, I_max:I_min = %d:%d', I_max/4, I_min/4);\n",
"\n",
"// Result\n",
"// The ratio of maximum to minimum intensity in the fringe system, I_max:I_min = 25:16 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_203: Wavelength_of_light_from_interference_of_fringes.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.3: Page-184 (2008)\n",
"clc; clear;\n",
"d = 0.1;    // Separation between the two slits, cm\n",
"D = 100;    // Distance between the source and the slit, cm\n",
"bita = 0.05;    // Fringe width, cm\n",
"lambda = bita*d/D;    // Wavelength of light, cm\n",
"printf('\nThe wavelength of light used = %4d angstrom', lambda/1e-008);\n",
"\n",
"// Result\n",
"// The wavelength of light used = 5000 angstrom "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_204: Fringe_width_from_interference_pattern.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.4: Page-184 (2008)\n",
"clc; clear;\n",
"d = 0.3;    // Separation between the two slits, cm\n",
"D = 60;    // Distance between the source and the slit, cm\n",
"lambda = 59e-006;    // Wavelength of light, cm\n",
"bita = lambda*D/d;    // Fringe width, cm\n",
"printf('\nThe fringe width = %4.2e cm', bita);\n",
"\n",
"// Result\n",
"// The fringe width = 1.18e-002 cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_205: Distance_between_the_two_coherent_sources.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.5: Page-185 (2008)\n",
"clc; clear;\n",
"D = 80;    // Distance between the source and the slit, cm\n",
"lambda = 5890e-008;    // Wavelength of light, cm\n",
"bita = 9.424e-002;    // Fringe width, cm\n",
"d = lambda*D/bita;    // Separation between the two slits, cm\n",
"printf('\nThe distance between the two coherent sources = %4.2f cm', d);\n",
"\n",
"// Result\n",
"// The distance between the two coherent sources = 0.05 cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_206: Distance_between_consecutive_interference_bands.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.6: Page-185 (2008)\n",
"clc; clear;\n",
"D = 100;    // Distance between the source and the slit, cm\n",
"lambda = 5893e-008;    // Wavelength of light, cm\n",
"d1 = 4.05e-001;    // Distance between the images of the two slits in one position, cm\n",
"d2 = 2.90e-001;    // Distance between the images of the two slits in second position, cm\n",
"d = sqrt(d1*d2);   // Separation between the two slits, cm\n",
"bita = lambda*D/d;    // Fringe width, cm\n",
"printf('\nThe distance between consecutive interference bands = %6.4f cm', bita);\n",
"\n",
"// Result\n",
"// The distance between consecutive interference bands = 0.0172 cm"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_207: Wavelength_of_the_light_used_in_biprism_experiment.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.7: Page-185 (2008)\n",
"clc; clear;\n",
"D = 1.2;    // Distance between the source and the slit, m\n",
"d = 7.5e-004;   // Separation between the two slits, cm\n",
"n = 20;    // Number of fringes crossed in the field of view\n",
"bita = 1.888e-002/n;    // Fringe width, cm\n",
"lambda = bita*d/D;    // Wavelength of light, cm\n",
"printf('\nThe wavelength of the light used in biprism experiment = %4d angstrom', lambda/1e-010);\n",
"\n",
"// Result\n",
"// The wavelength of the light used in biprism experiment = 5900 angstrom "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_208: Number_of_fringes_obtained_with_the_given_wavelength.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.8: Page-186 (2008)\n",
"clc; clear;\n",
"lambda1 = 5893;    // First wavelength of light, angstrom\n",
"lambda2 = 4358;    // Second wavelength of light, angstrom\n",
"n = 40;    // Number of fringes obtained with first wavelength\n",
"// As bita1/bita2 = lambda1/lambda2, so\n",
"x = n*lambda1/lambda2;    // Number of fringes obtained with the seocond wavelength\n",
"printf('\nThe number of fringes obtained with the given wavelength = %d', x);\n",
"\n",
"// Result\n",
"// The number of fringes obtained with the given wavelength = 54 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_209: Wavelength_of_light_from_biprism_interference_pattern.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.9: Page-186 (2008)\n",
"clc; clear;\n",
"D = 100;    // Distance between the source and the slit, cm\n",
"bita = 0.0135;    // Fringe width, cm\n",
"alpha = %pi/360;    // Angle of refracting face with the base of biprism, radian\n",
"mu = 1.5;    // Refractive index of the material of biprism\n",
"x = 50;    // Distance between slit and the biprism, cm\n",
"d = 2*(mu-1)*x*alpha;   // Separation between the two virtual slits, cm\n",
"lambda = bita*d/D;    // Wavelength of light, cm\n",
"printf('\nThe wavelength of light from biprism interference pattern = %4d angstrom', lambda/1e-008);\n",
"\n",
"// Result\n",
"// The wavelength of light from biprism interference pattern = 5890 angstrom "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_210: Fringe_width_observed_at_one_metre_distance_from_biprism.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.10: Page-187 (2008)\n",
"clc; clear;\n",
"mu = 1.5;    // Refractive index of the material of biprism\n",
"alpha = %pi/180;    // Base angle of biprism, radian\n",
"D = 110;    // Distance between the source and the slit, cm\n",
"x = 10;    // Distance between slit and the biprism, cm\n",
"d = 2*(mu-1)*x*alpha;   // Separation between the two virtual slits, cm\n",
"lambda = 5900e-008;    // Wavelength of light, cm\n",
"bita = lambda*D/d;    // Fringe width, cm\n",
"printf('\nThe fringe width observed at one metre distance from biprism = %6.4f cm', bita);\n",
"\n",
"// Result\n",
"// The fringe width observed at one metre distance from biprism = 0.0372 cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_211: Wavelength_of_light_in_Newton_ring_experiment.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.11: Page-187 (2008)\n",
"clc; clear;\n",
"D_n = 0.42;    // Diameter of nth ring, cm\n",
"D_mplusn = 0.7;    // Diameter of (m+n)th ring, cm\n",
"m = 14;    // Difference between (m+n)th and nth rings\n",
"R = 100;    // Radius of curvature of the plano-convex lens, m\n",
"lambda = (D_mplusn^2 - D_n^2)/(4*m*R);    // Wavelength of the light, cm\n",
"printf('\nThe wavelength of the light used = %4d angstrom', lambda/1e-008);\n",
"\n",
"// Result\n",
"// The wavelength of the light used = 5600 angstrom "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_212: Radius_of_plano_convex_lens.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.12: Page-187 (2008)\n",
"clc; clear;\n",
"D5 = 0.336;    // Diameter of 5th ring, cm\n",
"D10plus5 = 0.590;    // Diameter of (10+5)th ring, cm\n",
"m = 10;    // Difference between (10+5)th and 5th rings\n",
"lambda = 5890e-008;    // Wavelength of the light, cm\n",
"R = (D10plus5^2 - D5^2)/(4*m*lambda);    // Radius of curvature of the plano-convex lens, m\n",
"printf('\nThe radius of plano convex lens = %5.2f cm', R);\n",
"\n",
"// Result\n",
"// The radius of plano convex lens = 99.83 cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_213: Wavelenght_of_light_used_in_obtaining_Newton_rings.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.13: Page-187 (2008)\n",
"clc; clear;\n",
"D3 = 0.181;    // Diameter of 3rd ring, cm\n",
"D23 = 0.501;    // Diameter of 23rd ring, cm\n",
"m = 23-3;    // Difference between (m+n)th and nth rings\n",
"R = 50;    // Radius of curvature of the plano-convex lens, m\n",
"lambda = (D23^2 - D3^2)/(4*m*R);    // Wavelength of the light, cm\n",
"printf('\nThe wavelength of the light used = %4d angstrom', lambda/1e-008);\n",
"\n",
"// Result\n",
"// The wavelength of the light used = 5456 angstrom"
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_214: Diameter_of_the_20th_dark_ring.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.14: Page-188 (2008)\n",
"clc; clear;\n",
"D4 = 0.4;    // Diameter of 4th ring, cm\n",
"D12 = 0.7;    // Diameter of 12th ring, cm\n",
"m = 12-4;    // Difference between (m+n)th and nth rings\n",
"lambda_R = (D12^2 - D4^2)/(4*m);    // Wavelength-Radius product, Sq.cm\n",
"D20 = sqrt(80*lambda_R);    // Diameter of the 20th dark ring, cm\n",
"printf('\nThe diameter of the 20th dark ring = %5.3f cm', D20);\n",
"\n",
"// Result\n",
"// The diameter of the 20th dark ring = 0.908 cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_215: Radius_of_curvature_of_the_lens_and_the_thickness_of_the_air_film.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.15: Page-188 (2008)\n",
"clc; clear;\n",
"D10 = 0.50;    // Diameter of 10th ring, cm\n",
"n = 10;    // Number of dark fringe\n",
"lambda = 6250e-008;    // Wavelength of light used, cm\n",
"R = D10^2/(4*n*lambda);    // Radius of curvature of the lens, cm\n",
"t = D10^2/(8*R);    // Thickness of the air film, cm\n",
"printf('\nThe radius of curvature of the lens = %3d cm', R);\n",
"printf('\nThe thickness of the air film = %9.7f cm', t);\n",
"\n",
"// Result\n",
"// The radius of curvature of the lens = 100 cm\n",
"// The thickness of the air film = 0.0003125 cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_216: Newton_rings_observed_in_reflected_light.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.16: Page-188 (2008)\n",
"clc; clear;\n",
"D10 = 5e-003;    // Diameter of 10th ring, cm\n",
"n = 10;    // Number of dark fringe\n",
"lambda = 5.9e-007;    // Wavelength of reflected light, m\n",
"R = D10^2/(4*n*lambda);    // Radius of curvature of the lens, cm\n",
"t = D10^2/(8*R);    // Thickness of the air film, cm\n",
"printf('\nThe radius of curvature of the lens = %5.3f m', R);\n",
"printf('\nThe thickness of the air film = %4.2e m', t);\n",
"\n",
"// Result\n",
"// The radius of curvature of the lens = 1.059 m\n",
"// The thickness of the air film = 2.95e-006 m  "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.c_217: Smallest_thickness_of_the_glass_film_in_which_it_appears_dark.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3c.17: Page-189 (2008)\n",
"clc; clear;\n",
"lambda = 5893e-010;    // Wavelength of light used, m\n",
"mu = 1.5;    // Refractive index of glass film\n",
"r = 60;    // Angle of reflection in the film, degree\n",
"t = lambda/(2*mu*cosd(r));    // Smallest thickness of the \n",
"printf('\nThe smallest thickness of the glass film when it appears dark = %6.1f angstrom', t/1e-010);\n",
"\n",
"// Result\n",
"// The smallest thickness of the glass film when it appears dark = 3928.7 angstrom "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_301: Wavelength_of_light_used_in_diffraction_due_to_narrow_slit.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.1: Page-205 (2008)\n",
"clc; clear;\n",
"D = 200;    // Distance between the source and the slit, cm\n",
"a = 0.02;    // Slit width, cm\n",
"x = 0.5;    // Position of first minimum, cm\n",
"n = 1;    // Order of diffraction\n",
"lambda = a*x/(D*n);    // 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 = 5000 angstrom "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_302: Separation_between_the_second_minima_on_either_side_of_the_central_maximum.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.2: Page-205 (2008)\n",
"clc; clear;\n",
"f = 20;    // Focal length of the lens, cm\n",
"a = 0.06;    // Slit width, cm\n",
"n = 2;    // Order of diffraction\n",
"lambda = 6e-005;    // Wavelength of light used, cm\n",
"x = 2*lambda*f/a;    // Separation between the second minima on either side of the central maximum, cm\n",
"printf('\nThe separation between the second minimum an central maximum = %4.2f cm', x);\n",
"\n",
"// Result\n",
"// The separation between the second minimum an central maximum = 0.04 cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_303: Distance_of_the_first_dark_band_from_the_axis.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.3: Page-206 (2008)\n",
"clc; clear;\n",
"n = 1;    // Order of diffraction\n",
"f = 40;    // Focal length of the lens, cm\n",
"a = 0.03;    // Slit width, cm\n",
"lambda = 5890e-008;    // Wavelength of the light used, cm\n",
"// As a*sind(theta) = n*lambda, solving for theta\n",
"theta = asin(n*lambda/a);    // The angle of diffraction corresponding to the first minimum, radian\n",
"x = f*theta;    // The distance of the first dark band from the axis, cm  \n",
"printf('\nThe distance of the first dark band from the axis = %6.4f cm', x);\n",
"\n",
"// Result\n",
"// The distance of the first dark band from the axis = 0.0785 cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_304: Angle_of_diffraction_for_the_principal_maxima.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.4: Page-206 (2008)\n",
"clc; clear;\n",
"lambda1 = 5890e-008;    // Wavelength of D1 line of sodium lamp, cm\n",
"lambda2 = 5896e-008;    // Wavelength of D2 line of sodium lamp, cm\n",
"d_lambda = lambda2 - lambda1;    // Wavelength difference, cm\n",
"w = 0.5;    // Width of the grating, cm\n",
"N = 2500;    // Total number of grating lines\n",
"N_prime = N/w;    // Number of lines per cm, lines/cm\n",
"a_plus_b = 1/N_prime;    // Grating element, cm\n",
"n = 1;    // Order of diffraction\n",
"// Case 1\n",
"theta = asind(n*lambda1/a_plus_b);    // Angle of diffraction for D1 line, degree\n",
"// Case 2\n",
"theta_prime = asind(n*lambda2/a_plus_b);    // Angle of diffraction for D2 line, degree\n",
"printf('\nThe angle of diffraction for D1 and D2 lines of sodium are %5.2f dgree and %5.2f degree respectively.', theta, theta_prime);\n",
"// From the condition for just resolution, lambda/d_lambda = n*N, solving for N\n",
"N_min = lambda1/(d_lambda*n);    // Minimum number of lines required on the grating\n",
"if N_min < N then\n",
"    printf('\nThe two lines are well resolved.');\n",
"else\n",
"    printf('\nThe two lines are not resolved.');\n",
"end\n",
"\n",
"// Result\n",
"// The angle of diffraction for D1 and D2 lines of sodium are 17.13 dgree and 17.15 degree respectively.\n",
"// The two lines are well resolved. "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_305: Wavelength_of_the_spectral_line.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.5: Page-207 (2008)\n",
"clc; clear;\n",
"N = 4250;    // Number of lines per cm of grating, lines/cm\n",
"a_plus_b = 1/N;    // Grating element, cm\n",
"n = 2;    // Order of diffraction\n",
"theta = 30;    // Angle of diffraction, degree\n",
"lambda = sind(theta)*a_plus_b/n;    // Wavelength of spectral line from diffraction condition, cm\n",
"printf('\nThe wavelength of spectral line from diffraction condition = %4d angstrom', lambda/1e-008);\n",
"\n",
"// Result\n",
"// The wavelength of spectral line from diffraction condition = 5882 angstrom "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_306: Number_of_lines_in_one_centimeter_of_the_grating_surface.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.6: Page-207 (2008)\n",
"clc; clear;\n",
"n = 2;    // Order of diffraction\n",
"lambda = 5e-005;    // Wavelength of light, cm\n",
"theta = 30;    // Angle of diffraction, degree\n",
"N = sind(theta)/(n*lambda);    // Number of lines per cm of grating, lines/cm\n",
"printf('\nThe number of lines per cm of grating = %4d per cm', ceil(N));\n",
"\n",
"// Result\n",
"// The number of lines per cm of grating = 5000 per cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_307: Highest_order_spectrum_obtainable_with_the_given_diffraction_grating.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.7: Page-208 (2008)\n",
"clc; clear;\n",
"N = 5000;    // Number of lines per cm ruled on grating, lines/cm\n",
"lambda = 6e-005;    // Wavelength of light, m\n",
"a_plus_b = 1/N;    // Grating element, m\n",
"theta = 90;    // Maximum angle of diffraction, degree\n",
"n = a_plus_b*sind(theta)/lambda;    // Order of diffraction\n",
"printf('\nIn highest order spectrum obtainable with the given diffraction grating = %4.2f', n);\n",
"\n",
"// Result\n",
"// In highest order spectrum obtainable with the given diffraction grating = 3.33 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_308: Invisible_third_and_higher_order_principal_maxima_in_a_diffraction_grating.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.8: Page-208 (2008)\n",
"clc; clear;\n",
"lambda = 5.5e-007;    // Wavelength of light, m\n",
"a_plus_b = 1.5e-006;    // Grating element, m\n",
"theta = 90;    // Maximum angle of diffraction, degree\n",
"n = a_plus_b*sind(theta)/lambda;    // Order of diffraction\n",
"printf('\nIn this diffraction grating only %dnd order will be visible while %drd and higher orders are not possible.', n, n+1);\n",
"\n",
"// Result\n",
"// In this diffraction grating only 2nd order will be visible while 3rd and higher orders are not possible. "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_309: Number_of_lines_per_cm_on_the_grating.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.9: Page-208 (2008)\n",
"clc; clear;\n",
"theta = 30;    // Maximum angle of diffraction, degree\n",
"lambda1 = 5400e-010;    // Wavelength of light giving certain diffraction order, m\n",
"lambda2 = 4050e-010;    // Wavelength of light giving higher diffraction order, m\n",
"n = poly(0, 'n');\n",
"n = roots(lambda1*n-(n+1)*lambda2);    // Order of diffraction for first wavelength\n",
"a_plus_b = n*lambda1/sind(theta);    // Grating element, m\n",
"N = 1/a_plus_b;    // Number of lines per cm ruled on grating, lines/cm\n",
"printf('\nThe number of lines per cm on the diffraction grating = %d lines per cm', N/100);\n",
"\n",
"// Result\n",
"// The number of lines per cm on the diffraction grating = 3086 lines per cm "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_310: Minimum_number_of_lines_on_the_diffraction_grating.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.10: Page-209 (2008)\n",
"clc; clear;\n",
"lambda = 5890e-008;    // Wavelength of light, cm\n",
"n = 1;    // Order of diffraction\n",
"d_lambda = 6e-008;    // Difference in wavelengths of D1 and D2 lines, cm\n",
"N = lambda/(n*d_lambda);    // Number of lines on grating\n",
"printf('\nThe minimum number of lines on the diffraction grating = %d', ceil(N));\n",
"\n",
"// Result\n",
"// The minimum number of lines on the diffraction grating = 982 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_311: Design_of_a_plane_transmission_diffraction_grating.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.11: Page-209 (2008)\n",
"clc; clear;\n",
"lambda = 6000e-008;    // Wavelength of light, cm\n",
"n = 2;    // Order of diffraction\n",
"d_lambda = 6e-008;    // Difference in wavelengths of D1 and D2 lines, cm\n",
"N = lambda/(n*d_lambda);    // Number of lines on grating\n",
"printf('\nThe minimum number of lines in the required diffraction grating = %d', N);\n",
"\n",
"// Result\n",
"// The minimum number of lines in the required diffraction grating = 500 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_312: EX3_d_312.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.12: Page-209 (2008)\n",
"clc; clear;\n",
"lambda = 5890e-008;    // Wavelength of light, cm\n",
"n = 2;    // Order of diffraction\n",
"d_lambda = 6e-008;    // Difference in wavelengths of D1 and D2 lines, cm\n",
"w = 2.5;    // Width of the grating, cm\n",
"N = lambda/(n*d_lambda);    // Number of lines on grating\n",
"printf('\nThe minimum number of lines per cm in the diffraction grating = %5.1f', N/w);\n",
"\n",
"// Result\n",
"// The minimum number of lines per cm in the diffraction grating = 196.3 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_313: Maximum_resolving_power_of_a_plane_transmission_grating.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.13: Page-210 (2008)\n",
"clc; clear;\n",
"lambda = 5000e-008;    // Wavelength of light, cm\n",
"theta = 90;    // Angle of diffraction for the maximum resolving power, degree\n",
"N = 40000;    // Number of lines on grating\n",
"a_plus_b = 12.5e-005;    // Grating element, cm\n",
"n = 2;    // Order of diffraction\n",
"n_max = N*a_plus_b*sind(theta)/lambda;    // Maximum resolving power\n",
"printf('\nThe maximum resolving power = %d', n_max);\n",
"\n",
"// Result\n",
"// The maximum resolving power = 100000 "
   ]
   }
,
{
		   "cell_type": "markdown",
		   "metadata": {},
		   "source": [
			"## Example 3.d_314: Maximum_number_of_lines_of_a_grating.sce"
		   ]
		  },
  {
"cell_type": "code",
	   "execution_count": null,
	   "metadata": {
	    "collapsed": true
	   },
	   "outputs": [],
"source": [
"// Scilab Code Ex3d.14: Page-209 (2008)\n",
"clc; clear;\n",
"lambda = 5890e-008;    // Wavelength of light, cm\n",
"n = 3;    // Order of diffraction\n",
"d_lambda = 6e-008;    // Difference in wavelengths of D1 and D2 lines, cm\n",
"N = lambda/(n*d_lambda);    // Maximum number of lines of a grating\n",
"printf('\nThe maximum number of lines of the grating = %d', N);\n",
"\n",
"// Result\n",
"// The maximum number of lines of the grating = 327 "
   ]
   }
],
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			{
			 "text": "MetaKernel Magics",
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