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diff --git a/Engineering_Physics_by_H_K_Malik/2-DIFFRACTION.ipynb b/Engineering_Physics_by_H_K_Malik/2-DIFFRACTION.ipynb new file mode 100644 index 0000000..c15fe0d --- /dev/null +++ b/Engineering_Physics_by_H_K_Malik/2-DIFFRACTION.ipynb @@ -0,0 +1,1314 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2: DIFFRACTION" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.10: Calculation_of_No_of_zone_of_Fresnel.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 4e-7 // wavelength of light in meter\n", +"u = 0.2 // distance of object from zone plate in meter\n", +"v = 0.2 // distance of brightest image from from zone plate in meter \n", +"r = 0.01 // radius in meter\n", +"// Sample Problem 10 on page no. 2.41\n", +"printf('\n # PROBLEM 10 # \n')\n", +"f = (u * v) / (u + v) // calculation for focal length\n", +"n = (r^2) / (f * lambda) // calculation for no. of zone of Fresnel\n", +"printf('\n Standard formula used \n f = (u * v) / (u + v). \n n = (r^2) / (f * lambda).\n ')\n", +"printf('\n No. of zone of Fresnel = %f',n)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.11: Calculation_of_Distance_of_first_image_from_zone_plate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.893e-7 // wavelength of light in meter\n", +"d = 2.3e-3 // diameter of the central zone of zone plate in meter\n", +"u = 6 // distance between point source from zone plate in meter\n", +"// Sample Problem 11 on page no. 2.42\n", +"printf('\n # PROBLEM 11 # \n')\n", +"n = 1 // for central zone\n", +"f = (d^2) / (4 * lambda * n) // calculation for focal length\n", +"disp(f)\n", +"v = (f * u) / (u - f) // calculation for distance of first image from zone plate\n", +"printf('\n Standard formula used \n f = (d^2) / (4 * lambda * n). \n v = (f * u) / (u - f). \n ')\n", +"printf('\n Distance of first image from zone plate = %f meter ',v)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.12: Calculation_of_Principal_focal_length_of_zone_plate.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"R = 2 // radius of curvature in meter\n", +"// Sample Problem 12 on page no. 2.42\n", +"printf('\n # PROBLEM 12 # \n')\n", +"f = R // calculation for principal focal length of zone plate\n", +"printf('\n Standard formula used \n f = r^2 / lambda. \n r = sqrt(lambda*R). \n ')\n", +"printf('\n Principal focal length of zone plate = %f meter ',f)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.13: Calculation_of_Angular_spread_of_the_central_maxima.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.89e-7 // wavelength of light in meter\n", +"b = 1e-3 // slit-width in meter\n", +"// Sample Problem 13 on page no. 2.42\n", +"printf('\n # PROBLEM 13 # \n')\n", +"m = 1 // for first minima\n", +"theta = asin((m * lambda) / b) // calculation for angular spread of the central maxima in radian\n", +"theta_ = theta * (180 / %pi) // calculation for angular spread of the central maxima in degree\n", +"printf('\n Standard formula used \n theta = asin((m * lambda) / b).\n')\n", +"printf('\n Angular spread of the central maxima = %f degree ',2 * theta_)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.14: Calculation_of_Wavelength_of_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"d = 1.2 // distance of screen from slit in meter\n", +"x = 3.7e-3 // distance between first maxima to central maxima in meter\n", +"b = 2e-4 // slit-width in meter\n", +"// Sample Problem 14 on page no. 2.43\n", +"printf('\n # PROBLEM 14 # \n')\n", +"lambda = (x * b) / d // calculation for wavelength of light\n", +"printf('\n Standard formula used \n lambda = (x * b) / d.\n')\n", +"printf('\n Wavelength of light = %e meter. ',lambda)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.15: Calculation_of_Angular_position_of_second_and_third_minima.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.5e-7 // wavelength of light in meter\n", +"b = 2.2e-6 // slit-width in meter\n", +"// Sample Problem 15 on page no. 2.43\n", +"printf('\n # PROBLEM 15 # \n')\n", +"m2 = 2 // for second minima\n", +"theta2 = asin((m2 * lambda) / b) * (180 / %pi) // calculation for angular position of second minima\n", +"m3 = 3 // for third minima\n", +"theta3 = asin((m3 * lambda) / b) * (180 / %pi) // calculation for angular position of third minima\n", +"printf('\n Standard formula used \n theta = asin((m * lambda) / b) * (180 / pi). \n')\n", +"printf('\n Angular position of second and third minima = %f , %f degree respectively ',theta2 ,theta3)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.16: Calculation_of_Half_angular_width_of_the_central_bright_maxima.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.89e-7 // wavelength of light in meter\n", +"b = 1.2e-6 // slit-width in meter\n", +"// Sample Problem 16 on page no. 2.44\n", +"printf('\n # PROBLEM 16 # \n')\n", +"m = 1 // for first minima\n", +"theta = asin((m * lambda) / b) // calculation for half angular width of the central bright maxima in radian\n", +"theta_ = theta * (180 / %pi) // calculation for half angular width of the central bright maxima in degree\n", +"printf('\n Standard formula used \n theta = asin((m * lambda) / b).\n')\n", +"printf('\n Half angular width of the central bright maxima = %f degree ',theta_)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.17: Calculation_of_Slit_width.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5e-7 // wavelength of light in meter\n", +"theta = %pi / 6 // half angular width of central maximum in first case in radian\n", +"theta_ = %pi / 2 // half angular width of central maximum in second case in radian\n", +"// Sample Problem 17 on page no. 2.44\n", +"printf('\n # PROBLEM 17 # \n')\n", +"m = 1 // for first minima\n", +"b1 = (lambda * m) / sin(theta) // calculation for slit width in first case\n", +"b2 = (lambda * m) / sin(theta_) // calculation for slit width in second case\n", +"printf('\n Standard formula used \n b = (lambda * m) / sin(theta). \n')\n", +"printf('\n Slit width in first case = %e meter. \n Slit width in second case = %e meter',b1,b2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.18: Calculation_of_Angular_spread_and_linear_width.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.89e-7 // wavelength of light in meter\n", +"d = 1 // distance of screen from slit in meter\n", +"b = 1e-4 // slit-width in meter\n", +"// Sample Problem 18 on page no. 2.44\n", +"printf('\n # PROBLEM 18 # \n')\n", +"theta = (asin(lambda / b)) * (180 / %pi) // calculation for angular spread\n", +"x = (2 * d * lambda) / b// calculation for linear width\n", +"printf('\n Standard formula used \n theta = (asin(lambda / b)) * (180 / pi). \n x = (2 * d * lambda) / b. \n')\n", +"printf('\n Angular spread = %f degree\n Linear width = %e meter ',theta,x)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.1: Calculation_of_Radius_of_half_period_zone_and_Area_of_half_period_zone.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5e-7 // wavelength of light in meter\n", +"d = 1 // distance of wavefront received on the screen from the opening in meter\n", +"n = 80 // no. of half period zone\n", +"// Sample Problem 1 on page no. 2.38\n", +"printf('\n # PROBLEM 1 # \n')\n", +"Rn = sqrt(n * lambda * d)// calculation for radius of nth half period zone\n", +"A = %pi * d * lambda// calculation for area of half period zone\n", +"printf('Standard formula used\n Rn = sqrt(n*d*lambda).\n A = pi*d*lambda.\n')\n", +"printf('\n Radius of 80th half period zone = %f cm. \n Area of half period zone = %f square cm.',Rn*100,A*10000)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.20: Calculation_of_Angular_width_of_the_central_maxima.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 6e-7 // wavelength of light in meter\n", +"b = 1.2e-6 // slit-width in meter\n", +"// Sample Problem 20 on page no. 2.46\n", +"printf('\n # PROBLEM 20 # \n')\n", +"m = 1 // for first minima\n", +"theta = asin((m * lambda) / b) // calculation for angular width of the central maxima in radian\n", +"theta_ = theta * (180 / %pi) // calculation for angular width of the central maxima in degree\n", +"printf('\n Standard formula used \n theta = asin((m * lambda) / b). \n')\n", +"printf('\n Angular width of the central maxima = %f degree ',2 * theta_)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.21: Calculation_of_Separation_of_dark_band.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 4.890e-7 // wavelength of light in meter\n", +"b = 5e-3 // slit-width in meter\n", +"f = 0.4 // focal-length of convex lens in meter\n", +"// Sample Problem 21 on page no. 2.46\n", +"printf('\n # PROBLEM 21 # \n')\n", +"m = 1 // for first dark fringe\n", +"x = (f * m * lambda) / b \n", +"n = 1 // for first secondary maxima\n", +"x_ = ((2 * n + 1) * lambda * f) / (2 * b) \n", +"delta_x = x_ - x // calculation for separation of dark band \n", +"printf('\n Standard formula used \n x = (f * m * lambda) / b . \n delta_x = x_ - x. \n')\n", +"printf('\n Separation of dark band = %e meter.',delta_x)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.22: Calculation_of_Separation_of_dark_band_on_either_side_of_the_central_maximum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.893e-7 // wavelength of light in meter\n", +"b = 5e-4 // slit-width in meter\n", +"f = 1 // focal length of convex lens in meter\n", +"// Sample Problem 22 on page no. 2.47\n", +"printf('\n # PROBLEM 22 # \n')\n", +"x = (2 * lambda * f) / b // calculation for Separation of dark band on either side of the cenral maximum\n", +"printf('Standard formula used \n. \n')\n", +"printf('\n Separation of dark band on either side of the central maximum = %e meter',x)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.23: Calculation_of_Missing_orders.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"d = 4e-4 // separation between slits in meter\n", +"b = 8e-5 // slit-width in meter\n", +"// Sample Problem 23 on page no. 2.47\n", +"printf('\n # PROBLEM 23 # \n')\n", +"r = (b + d) / b // calculation for ratio of n with m\n", +"m1 = 1\n", +"n1 = r * m1 // calculation for Missing orders \n", +"m2 = 2\n", +"n2 = r * m2 // calculation for Missing orders \n", +"m3 = 3\n", +"n3 = r * m3 // calculation for Missing orders \n", +"printf('\n Standard formula used \n r = (b + d) / b. \n n = r * m. \n')\n", +"printf('\n Missing orders = %d,%d,%d,......',n1,n2,n3)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.24: Calculation_of_Wavelength_of_light_and_Missing_order.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"d = 4e-4 // separation between slits in meter\n", +"b = 2e-4 // slit-width in meter\n", +"fringe_width = 2.5e-3 // fringe width in meter\n", +"D = 1.6 // distance between screen and slits\n", +"// Sample Problem 24 on page no. 2.47\n", +"printf('\n # PROBLEM 24 # \n')\n", +"lambda = (fringe_width * d) / D // calculation for wavelength of light\n", +"r = (b + d) / b // calculation for ratio of n with m\n", +"m1 = 1\n", +"n1 = r * m1 // calculation for missing order\n", +"m2 = 2\n", +"n2 = r * m2 // calculation for missing order\n", +"m3 = 3\n", +"n3 = r * m3 // calculation for missing order\n", +"printf('\n Standard formula used \n lambda = (fringe_width * d) / D. \n r = (b + d) / b. \n n = r * m. \n')\n", +"printf('\n Wavelength of light = %e meter. \n Missing order = %d,%d,%d....',lambda,n1,n2,n3)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.25: Calculation_of_Wavelength_of_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"N = 425000 // no. of lines in plane transmission grating per meter\n", +"theta = %pi / 6 // angle at which second order spectral line is observed in radian\n", +"n = 2 // order of spectral line\n", +"// Sample Problem 25 on page no. 2.48\n", +"printf('\n # PROBLEM 25 # \n')\n", +"lambda = sin(theta) / (2 * N) // calculation for wavelength of light\n", +"printf('\n Standard formula used \n lambda = sin(theta) / (2 * N). \n')\n", +"printf('\n Wavelength of light = %e meter. ',lambda)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.26: Calculation_of_Wavelength_of_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"N = 500000 // no. of lines in plane transmission grating per meter\n", +"theta = %pi / 6 // angle at which second order spectral line is observed in radian\n", +"n = 2 // order of spectral line\n", +"// Sample Problem 26 on page no. 2.48\n", +"printf('\n # PROBLEM 26 # \n')\n", +"lambda = sin(theta) / (2 * N) // calculation for wavelength of light\n", +"printf('\n Standard formula used \n lambda = sin(theta) / (2 * N). \n ')\n", +"printf('\n wavelength of light = %e meter. ',lambda)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.27: Calculation_of_Wavelength_of_light.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda2 = 5.461e-7 // wavelength of light in second case in meter\n", +"n1 = 4 // no. of order in first case\n", +"n2 = 3 // no. of order in second case \n", +"// Sample Problem 27 on page no. 2.48\n", +"printf('\n # PROBLEM 27 # \n')\n", +"lambda1 = (n2 * lambda2) / n1 // calculation for Wavelength of light in first case\n", +"printf('Standard formula used \n lambda1 = (n2 * lambda2) / n1. \n')\n", +"printf('\n Wavelength of light in first case = %d A',ceil(lambda1*1e10))" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.28: Calculation_of_No_of_lines_in_per_cm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5e-7 // wavelength of light in meter\n", +"theta = %pi / 6 // angle at which second order spectral line is observed in radian\n", +"n = 2 // order of spectral line\n", +"// Sample Problem 28 on page no. 2.49\n", +"printf('\n # PROBLEM 28 # \n')\n", +"k = (n * lambda) / sin(theta) // calculation for (b+d)\n", +"N = 1 / k // calculation for no. of lines in per cm\n", +"printf('\n Standard formula used \n b+d = (n * lambda) / sin(theta). \n N = 1 / k. \n ')\n", +"printf('\n No. of lines per cm = %f ',N / 100)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.29: Calculation_of_Angle_of_separation.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda1 = 5.048e-7 // wavelength of light in first case in meter\n", +"lambda2 = 5.016e-7 // wavelength of light in second case in meter\n", +"n = 2 // no. of order in first case\n", +"N = 15000 // no. of lines in grating per inch \n", +"// Sample Problem 29 on page no. 2.49\n", +"printf('\n # PROBLEM 29 # \n')\n", +"k = 2.54 / 1500000 // in meter\n", +"theta1 = asin(n * lambda1 / k) * (180 / %pi) // calculation for angle in first case\n", +"theta2 = asin(n * lambda2 / k) * (180 / %pi) // calculation for angle in second case\n", +"delta_theta = theta1 - theta2 // calculation for angle of separation\n", +"printf('\n Standard formula used \n theta = asin(n * lambda / k) * (180 / pi). \n')\n", +"printf('\n Angle of separation = %f degree',delta_theta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.2: Calculation_of_Radius_of_half_period_zone.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 6e-7 // wavelength of light in meter\n", +"f = 0.6 // focal length of convex lens in meter\n", +"n = 1 // no. of half period zone\n", +"// Sample Problem 2 on page no. 2.38\n", +"printf('\n # PROBLEM 2 # \n')\n", +"Rn = sqrt(n * lambda * f)// calculation for radius of half period zone\n", +"printf('Standard formula used \n f = Rn^2/(n*lambda)\n')\n", +"printf('\n Radius of half period zone = %f mm ',Rn*1000)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.30: Calculation_of_Angle_of_separation.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda1 = 5.89e-7 // wavelength of light in first case in meter\n", +"lambda2 = 5.896e-7 // wavelength of light in second case in meter\n", +"n = 2 // no. of order in first case\n", +"N = 600000 // no. of lines in grating per meter \n", +"// Sample Problem 30 on page no. 2.50\n", +"printf('\n # PROBLEM 30 # \n')\n", +"k = 1 / N // in meter\n", +"theta1 = asin(n * lambda1 / k) * (180 / %pi) // calculation for angle in first case\n", +"theta2 = asin(n * lambda2 / k) * (180 / %pi) // calculation for angle in second case\n", +"delta_theta = theta2 - theta1 // calculation for angle of separation\n", +"printf('\n Standard formula used \n theta1 = asin(n * lambda1 / k) * (180 / pi). \n ')\n", +"printf('\n Angle of separation = %f degree',delta_theta)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.31: Calculation_of_No_of_lines_per_cm.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda1 = 5.4e-7 // wavelength of light for nth order in meter\n", +"lambda2 = 4.05e-7 // wavelength of light for (n+1)th order in meter \n", +"theta = %pi / 6 // angle of diffraction in radian \n", +"// Sample Problem 31 on page no. 2.50\n", +"printf('\n # PROBLEM 31 # \n')\n", +"k = (lambda1 * lambda2) / ((lambda1 - lambda2) * sin(theta)) // calculation for b+d\n", +"N = (1 / k) * (0.01) // calculation for no. of lines per cm\n", +"printf('\n Standard formula used \n b+d = (lambda1 * lambda2) / ((lambda1 - lambda2) * sin(theta)). \n N = (1 / k) * (0.01). \n')\n", +"printf('\n No. of lines per cm = %d ',N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.32: Calculation_of_Difference_in_two_wavelength.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"d_theta = 0.01 // angular separation between two wavelengths in radian \n", +"theta = %pi / 6 // angle of diffraction in radian \n", +"lambda = 5e-7 // wavelength of light in meter\n", +"// Sample Problem 32 on page no. 2.51\n", +"printf('\n # PROBLEM 32 # \n')\n", +"d_lambda = (lambda * cos(theta) * d_theta) / sin(theta) // calculation for difference in two waveligth\n", +"printf('Standard formula used \n d_lambda = (lambda * cos(theta) * d_theta) / sin(theta). \n\n')\n", +"printf('\n Difference in two wavelength = %e meter ',d_lambda)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.33: Calculation_of_Order_of_spectrum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"N = 2620 // no. of lines in plane transmission grating per inch\n", +"lambda = 5e-7 // wavelength of incident radiation in meter\n", +"// Sample Problem 33 on page no. 2.51\n", +"printf('\n # PROBLEM 33 # \n')\n", +"k = 2.54 / N * 1 / 100 // calculation for b+d in meter\n", +"n = k / lambda // calculation for order of spectrum\n", +"printf('\n Standard formula used \n n = k / lambda ')\n", +"printf('\n Order of spectrum = %d',n)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.34: Calculation_of_Order_of_spectrum.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"N = 500000 // no. of lines in plane transmission grating per meter\n", +"lambda = 5e-7 // wavelength of incident radiation in meter\n", +"// Sample Problem 34 on page no. 2.51\n", +"printf('\n # PROBLEM 34 # \n')\n", +"k = 1 / N // calculation for b+d in meter\n", +"n = k / lambda // calculation for order of spectrum \n", +"printf('\n Standard formula used \n k = 1 / N. \n n = k / lambda. \n')\n", +"printf('\n Order of spectrum = %d',n)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.35: Calculation_of_Observed_order.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"N = 400000 // no. of lines in plane transmission grating per meter\n", +"lambda1 = 4e-7 // wavelength of light in first case in meter\n", +"lambda2 = 7e-7 // wavelength of light in second case in meter\n", +"// Sample Problem 35 on page no. 2.52\n", +"printf('\n # PROBLEM 35 # \n')\n", +"n1 = 1 / (N * lambda1) // calculation for Observed order in first case\n", +"n2 = 1 / (N * lambda2) // calculation for Observed order in second case\n", +"printf('Standard formula used \n n = 1 / (N * lambda). \n')\n", +"printf('\n Observed order = %d,%d',n1,n2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.36: Calculation_of_Dispersive_power.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"N = 400000 // no. of lines in grating per meter\n", +"lambda = 5e-7 // wavelength of incident radiation in meter\n", +"n = 3 // no. of order\n", +"// Sample Problem 36 on page no. 2.52\n", +"printf('\n # PROBLEM 36 # \n')\n", +"p = (n * N) / (sqrt(1 - (N * n * lambda)))// dispersive power (p) = d(theta)/d(lambda)\n", +"printf('\n Standard formula used \n p = (n * N) / (sqrt(1 - (N * n * lambda))). \n')\n", +"printf('\n Dispersive power = %e rad/m',p)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.37: Calculation_of_Minimum_no_of_lines_in_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"n = 2 // no. of order\n", +"lambda1 = 5.89e-7 // wavelength of light in first case in meter\n", +"lambda2 = 5.896e-7 // wavelength of light in second case in meter\n", +"// Sample Problem 37 on page no. 2.52\n", +"printf('\n # PROBLEM 37 # \n')\n", +"N = lambda1 / (n * (lambda2 - lambda1)) // calculation for minimum no. of lines in grating \n", +"printf('\n Standard formula used \n N = lambda1 / (n * (lambda2 - lambda1)). \n') \n", +"printf('\n Minimum no. of lines in grating = %f,',N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.38: Calculation_of_Minimum_no_of_lines_in_grating.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"n = 1 // no. of order\n", +"lambda1 = 5.89e-7 // wavelength of light in first case in meter\n", +"lambda2 = 5.896e-7 // wavelength of light in second case in meter\n", +"// Sample Problem 38 on page no. 2.53\n", +"printf('\n # PROBLEM 38 # \n')\n", +"N = lambda1 / (n * (lambda2 - lambda1)) // calculation for minimum no. of lines in grating\n", +"printf('Standard formula used \n lambda/d(lambda)=n*N. \n')\n", +"printf('\n Minimum no. of lines in grating = %f,',N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.39: Calculation_of_Grating_space_and_Total_width_of_ruled_surface.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"n = 3 // no. of order\n", +"theta = %pi / 6 // view angle of third order in radian\n", +"lambda1 = 5.89e-7 // min. wavelength of light in meter\n", +"lambda2 = 5.896e-7 // max.wavelength of light in meter\n", +"// Sample Problem 39 on page no. 2.53\n", +"printf('\n # PROBLEM 39 # \n')\n", +"mean_lambda = (lambda1 + lambda2) / 2 // calculation for mean wavelength\n", +"s = (n * mean_lambda) / sin(theta) // calculation for grating space b+d\n", +"N = lambda1 / (n * (lambda2 - lambda1)) // calculation for minimum no. of lines in grating\n", +"printf('\n Standard formula used \n mean_lambda = (lambda1 + lambda2) / 2. \n s = (n * mean_lambda) / sin(theta). \n N = lambda1 / (n * (lambda2 - lambda1)). \n')\n", +"printf('\n Grating space = %e meter. \n Total width of ruled surface = %e meter. ',s,s * N)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.3: Calculation_of_Radius_of_half_period_zone.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5e-7 // wavelength of light in meter\n", +"d = 0.3 // distance of wavefront received on screen from the opening in meter\n", +"// Sample Problem 3 on page no. 2.38\n", +"printf('\n # PROBLEM 3 # \n')\n", +"n = 1 // no. of half period zone\n", +"Rn = sqrt(n * lambda * d) // because at maxima intensity is four time the individual intensity of light\n", +"printf('Standard formula used \n r = sqrt(d*lambda)\n')\n", +"printf('\n Radius of 80th half period zone = %f mm. ',Rn*1000)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.40: Calculation_of_The_separation_of_two_points_on_moon.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.5e-7 // wavelength of light in meter\n", +"a = 5 // diameter of objective lens of telescope in meter\n", +"R = 3.8e8 // distance of moon in meter\n", +"// Sample Problem 40 on page no. 2.53\n", +"printf('\n # PROBLEM 40 # \n')\n", +"theta = (1.22 * lambda) / a // calculation for angle \n", +"x = (R * theta) // calculation for the separation of two points on moon\n", +"printf('\n Standard formula used \n theta = (1.22 * lambda) / a. \n x = (R * theta). \n')\n", +"printf('\n The separation of two points on moon = %f meter',x)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.41: Calculation_of_Diameter_of_telescope_objective.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5e-7 // wavelength of light in meter\n", +"theta = (1e-3) * (%pi / 180) // separation angle of stars in radian\n", +"// Sample Problem 41 on page no. 2.54\n", +"printf('\n # PROBLEM 41 # \n')\n", +"a = (1.22 * lambda) / theta // calculation for diameter of telescope objective\n", +"printf('\n Standard formula used \n a = (1.22 * lambda) / theta. \n')\n", +"printf('\n Diameter of telescope objective = %f meter',a)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.42: Calculation_of_Diameter_of_telescope_objective.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 6e-7 // wavelength of light in meter\n", +"theta = 2.44e-6 // separation angle of stars in radian\n", +"// Sample Problem 42 on page no. 2.54\n", +"printf('\n # PROBLEM 42 # \n')\n", +"a = (1.22 * lambda) / theta // calculation for diameter of telescope objective\n", +"printf('\n Standard formula used \n a = (1.22 * lambda) / theta. \n')\n", +"printf('\n Diameter of telescope objective = %f meter',a)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.43: Calculation_of_Max_distance_of_pin_holes_from_microscope.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.5e-7 // wavelength of light in meter\n", +"a = 0.004 // diameter of objective lens of telescope in meter\n", +"x = 1.5e-3 // distance between two pin holes in meter\n", +"// Sample Problem 43 on page no. 2.54\n", +"printf('\n # PROBLEM 43 # \n')\n", +"theta = (1.22 * lambda) / a // calculation for angle \n", +"R = x / theta // calculation for max. distance of pin holes from microscope\n", +"printf('\n Standard formula used \n theta = (1.22 * lambda) / a. \n R = x / theta. \n ')\n", +"printf('\n Max. distance of pin holes from microscope = %f meter',R)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.44: Calculation_of_The_resolving_limit_of_microscope.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.5e-7 // wavelength of light in meter\n", +"theta = %pi / 6 // semi-angle of cone in radian\n", +"// Sample Problem 44 on page no. 2.55\n", +"printf('\n # PROBLEM 44 # \n')\n", +"d = (1.22 * lambda) / (2 * sin(theta)) // calculation for the resolving limit of microscope \n", +"printf('Standard formula used \n d*sin(theta)= 1.22*lamda. \n')\n", +"printf('\n The resolving limit of microscope = %e meter',d)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.45: Calculation_of_Numerical_aperture_of_objective.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.461e-7 // wavelength of light in meter\n", +"d = 4e-7 // separation between objects in meter\n", +"// Sample Problem 45 on page no. 2.55\n", +"printf('\n # PROBLEM 45 # \n')\n", +"NA = (1.22 * lambda) / (2 * d) // calculation for numerical aperture of objective \n", +"printf('\n Standard formula used \n NA = (1.22 * lambda) / (2 * d). \n')\n", +"printf('\n Numerical aperture of objective = %f',NA)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.4: Calculation_of_No_of_half_period_zone.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 6e-7 // wavelength of light in meter\n", +"d = 0.5 // distance of observation point from circular opening in meter\n", +"r1 = 2e-3 // radius of circular opening in first case in meter\n", +"r2 = 2e-2 // radius of circular opening in second case in meter \n", +"// Sample Problem 4 on page no. 2.39\n", +"printf('\n # PROBLEM 4 # \n')\n", +"n1 = (r1^2) / (d * lambda) // calculation for no. of half period zone in first case \n", +"n2 = (r2^2) / (d * lambda) // calculation for no. of half period zone in second case\n", +"printf('\n Standard formula used \n n = (r^2) / (d * lambda) \n')\n", +"printf('\n No. of half period zone in first case = %d \n no. of half period zone in second case = %d ',n1,n2)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.5: Calculation_of_Distance_of_screen_from_opening.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5e-7 // wavelength of light in meter\n", +"d = 1e-3 // diameter of the first ring of zone plate in meter\n", +"// Sample Problem 5 on page no. 2.39\n", +"printf('\n # PROBLEM 5 # \n')\n", +"n = 1 // no. of half period zone\n", +"D = (d^2) / (4 * lambda * n) // calculation for distance of screen from opening\n", +"printf('\n Standard formula used \n D = (d^2) / (4 * lambda * n). \n')\n", +"printf('\n Distance of screen from opening = %f meter ',D)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.6: Calculation_of_Radius_of_first_and_second_and_third_half_period_zone.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.893e-7 // wavelength of light in meter\n", +"f = 1 // focal-length of convex lens in meter\n", +"n1 = 1 // no. of first half period zone\n", +"n2 = 3 // no. of second half period zone\n", +"n3 = 5 // no. of third half period zone\n", +"// Sample Problem 6 on page no. 2.40\n", +"printf('\n # PROBLEM 6 # \n')\n", +"R1 = sqrt(n1 * lambda * f) // calculation for Radius of first half period zone\n", +"R2 = sqrt(n2 * lambda * f) // calculation for Radius of second half period zone\n", +"R3 = sqrt(n3 * lambda * f) // calculation for Radius of third half period zone\n", +"printf('Standard formula used \n R = sqrt(f*n*lambda)\n')\n", +"printf('\n Radius of first ,second and third half period zone = %e,%e and %e meter. ',R1,R2,R3)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.7: Calculation_of_Radius_of_half_period_zone.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5e-7 // wavelength of light in meter\n", +"f = 0.2 // focal length of convex lens in meter\n", +"n = 10 // no. of half period zone\n", +"// Sample Problem 7 on page no. 2.40\n", +"printf('\n # PROBLEM 7 # \n')\n", +"Rn = sqrt(n * lambda * f) // calculation for radius of 10th half period zone\n", +"printf('\n Standard formula used \n Rn = sqrt(n * lambda * f).\n')\n", +"printf('\n Radius of 10th half period zone = %f mm. ',Rn*1000)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.8: Calculation_of_Focal_length_and_Power_and_Diameter_of_first_zone.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda = 5.89e-7 // wavelength of light in meter\n", +"d1 = 1 // distance of wavefront recieved on the screen from the opening in first side in meter\n", +"d2 = 2 // distance of wavefront recieved on the screen from the opening in other side in meter\n", +"// Sample Problem 8 on page no. 2.40\n", +"printf('\n # PROBLEM 8 # \n')\n", +"f = (d1 * d2) / (d1 + d2)\n", +"p = 1 / f // beacause zone plate act as a convex lens\n", +"n = 1 // for first zone\n", +"Rn = sqrt(n * lambda * f) // calculation for radius of first zone\n", +"Dn = 2 * Rn // calculation for diameter of first zone\n", +"printf('\n Standard formula used \n ')\n", +"printf('\n Focal length = %f meter. \n Power = %f D. \n Diameter of first zone = %f mm. ',f,p,Dn*1000)" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2.9: Calculation_of_Focal_length.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc \n", +"// Given that\n", +"lambda1 = 6e-7 // wavelength of first light in meter\n", +"lambda2 = 5e-7 // wavelength of second light in meter\n", +"f1 = 1 // focal length in first case in meter \n", +"// Sample Problem 9 on page no. 2.41\n", +"printf('\n # PROBLEM 9 # \n')\n", +"f2 = (lambda1 * f1) / lambda2 // calculation for focal length in second case\n", +"printf('\n Standard formula used \n f2 = (lambda1 * f1) / lambda2')\n", +"printf('\n Focal length in second case = %f meter',f2)" + ] + } +], +"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 +} |