{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 3: Polarisation" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.1, Page 3.23" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi, atan\n", "\n", "# Given \n", "mu = 1.5 # refractive index of glass\n", "\n", "#Calculations\n", "Ip = atan(mu) * (180 / pi) # by brewster's law\n", "r = 90 - Ip # calculation for angle of refraction\n", "\n", "#Result\n", "print \"Brewster angle = %.f degree\\nAngle of refraction = %.f degree\"%(Ip,r)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Brewster angle = 56 degree\n", "Angle of refraction = 34 degree\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.2, Page 3.24" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi, atan\n", "\n", "# Given \n", "mu = 1.33 # refractive index of glass\n", "\n", "#Calculations\n", "Ip = atan(mu) * (180 / pi) # by Brewster's law\n", "\n", "#Result\n", "print \"Angle of brewster = %.2f degree\"%Ip" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angle of brewster = 53.06 degree\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.3, Page 3.24" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi, atan\n", "\n", "# Given \n", "mu_w = 1.33 # refractive index of water\n", "mu_g = 1.54 # refractive index of glass\n", "\n", "#Calculations\n", "Ip_1 = atan(mu_g / mu_w) * (180 / pi)#calculation for polarizing angle for water\n", "Ip_2 = atan(mu_w / mu_g) * (180 / pi) # calculation for polarizing angle for glass\n", "\n", "#Result\n", "print \"Polarizing angle for water to glass = %.2f degree,\\n Polarizing angle for glass to water = %.2f degree\"%(Ip_1,Ip_2)\n", "print \"So polarizing angle is greater for a beam incident from water to glass\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Polarizing angle for water to glass = 49.18 degree,\n", " Polarizing angle for glass to water = 40.82 degree\n", "So polarizing angle is greater for a beam incident from water to glass\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.4, Page 24" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi, asin, tan, sin\n", "\n", "# Given \n", "Ip = pi / 3 # polarizing angle of piece of glass for green light in radian\n", "a = pi / 3 # angle of prism in radian \n", "\n", "#Calculations\n", "mu = tan(Ip) # calculation for refractive index\n", "delta_m = 2 * (asin(mu * sin(a / 2)) - (a / 2)) * (180 / pi) # calculation for angle of minimum deviation\n", "\n", "#Result\n", "print \"Angle of minimum deviation = %.f degree\"%delta_m" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angle of minimum deviation = 60 degree\n" ] } ], "prompt_number": 47 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.5, Page 3.25" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi, atan\n", "\n", "# Given \n", "mu_w = 1.33 # refractive index of water\n", "mu_g = 1.5 # refractive index of glass\n", "\n", "#Calculations\n", "Ip = atan(mu_g / mu_w) * (180 / pi) # calculation for Brewster angle\n", "\n", "#Result\n", "print \"Brewster angle = %.1f degree\"%Ip\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Brewster angle = 48.4 degree\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.6, Page 3.25" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi, atan\n", "\n", "# Given \n", "mu = 1.732 # refractive index of glass\n", "\n", "#Calculations\n", "Ip = atan(mu) * (180 / pi) # by Brewster's law\n", "r = 90 - Ip# calculation for angle of refraction\n", "\n", "#Result\n", "print \"Angle of incidence = %.f degree\\nAngle of refraction = %.f degree\"%(Ip,r)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angle of incidence = 60 degree\n", "Angle of refraction = 30 degree\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.7, Page 3.25" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi, cos\n", "\n", "# Given \n", "alpha = pi / 3 # angle between polarizer and analyzer\n", "\n", "#Calculation\n", "r = (cos(alpha))**2 # where r = transmitted intensity / incident intensity\n", "\n", "#Result\n", "print \"Ratio between transmitted intensity to incident intensity = %.2f \"%r" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Ratio between transmitted intensity to incident intensity = 0.25 \n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.8, Page 3.25" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import sqrt,acos,degrees\n", "\n", "#Given \n", "r1 = 1./3 #ratio of intensity of transmitted light to the intensity of transmitted beam in first case\n", "r2 = 1./3 #ratio of intensity of transmitted light to the intensity of incident beam in second case\n", "p = 50 #percentage reduction in intensity of unpolarized light by the sheet \n", "\n", "#Calculations\n", "theta1 = degrees(acos(sqrt(r1))) #calculation for the angle between characteristics directions of the sheet in first case\n", "theta2 = degrees(acos(sqrt(2*r2))) #calculation for the angle between characteristics directions of the sheet in second case\n", "\n", "#Result\n", "print \"The angle between characteristics directions of the sheet in 1st case = %.2f degrees.\"%(theta1)\n", "print \"The angle between characteristics directions of the sheet in 2nd case = %.2f degrees.\"%(theta2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The angle between characteristics directions of the sheet in 1st case = 54.74 degrees.\n", "The angle between characteristics directions of the sheet in 2nd case = 35.26 degrees.\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.9, Page 3.26" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import acos, sqrt, pi\n", "\n", "# Given \n", "r = 3. / 4 # ratio of intensity of transmitted light to the intensity of incident light\n", "\n", "#Calculation\n", "theta = acos(sqrt(r)) * (180 / pi) # calculation for angle between the nicol prisms\n", "\n", "#Result\n", "print \"Angle between the nicol prisms = %.f degree\"%theta" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angle between the nicol prisms = 30 degree\n" ] } ], "prompt_number": 45 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.10, Page 3.26" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi, cos\n", "\n", "# Given \n", "theta1 = pi / 6 # angle between Nicole prisms in first case in radian\n", "theta2 = pi / 4 # angle between Nicole prisms in second case in radian\n", "theta3 = pi / 3 # angle between Nicole prisms in third case in radian\n", "theta4 = pi / 2 # angle between Nicole prisms in fourth case in radian\n", "\n", "#Calculations\n", "I1 = (1 - (cos(theta1))**2) * 100\n", "I2 = (1 - (cos(theta2))**2) * 100\n", "I3 = (1 - (cos(theta3))**2) * 100\n", "I4 = (1 - (cos(theta4))**2) * 100\n", "\n", "#Result\n", "print \"Percentage reduction in intensity of light-\\n(i)%.f %%\\n(ii)%.f %%\\n(iii)%.f %%\\n(iv)%.f %%\"%(I1,I2,I3,I4)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Percentage reduction in intensity of light-\n", "(i)25 %\n", "(ii)50 %\n", "(iii)75 %\n", "(iv)100 %\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.11, Page 3.27" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from math import pi, acos, sqrt \n", "\n", "# Given \n", "i1 = 1. / 2 # reduced intensity ratio in first case\n", "i2 = 1. / 4 # reduced intensity ratio in second case\n", "\n", "#Calculations\n", "theta1 = acos(sqrt(i1)) * (180 / pi)# calculation for angle between nicols in first case \n", "theta2 = acos(sqrt(i2)) * (180 / pi)# calculation for angle between nicols in second case\n", "\n", "#Result\n", "print \"Angle between the Nicols in first case = %.f degree\\nAnd in second case = %.f degree\"%(theta1,theta2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angle between the Nicols in first case = 45 degree\n", "And in second case = 60 degree\n" ] } ], "prompt_number": 44 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.12, Page 3.27" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "l = 5e-7 # wavelength of light in meter\n", "mu_e = 1.553 # refractive index for extraordinary light\n", "mu_o = 1.544 # refractive index for ordinary light\n", "\n", "#Calculations\n", "t = l / (2 * (mu_e - mu_o)) # calculation for thickness of half-wave plate of quartz\n", "\n", "#Result\n", "print \"Thickness of half-wave plate of quartz = %.2e meter\"%t" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of half-wave plate of quartz = 2.78e-05 meter\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.13, Page 3.27" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "l = 5.893e-7 # wavelength of light in meter\n", "mu_e = 1.533 # refractive index for extraordinary light\n", "mu_o = 1.554 # refractive index for ordinary light\n", "\n", "#Calculation\n", "t = l / (4 * (mu_o - mu_e)) # calculation for thickness of quartz plate\n", "\n", "#Result\n", "print \"Thickness of quartz plate = %.2e meter\"%t" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of quartz plate = 7.02e-06 meter\n" ] } ], "prompt_number": 21 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.14, Page 3.28" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "l = 5.89e-7 # wavelength of light in meter\n", "mu_e1 = 1.5 # refractive index for extraordinary light in first case\n", "mu_o1 = 1.55 # refractive index for ordinary light in first case\n", "mu_e2 = 1.57 # refractive index for extraordinary light in second case\n", "mu_o2 = 1.55 # refractive index for ordinary light in second case\n", "\n", "#Calculations\n", "t1 = l / (4 * (mu_o1 - mu_e1))\n", "t2 = l / (4 * (mu_e2 - mu_o2))\n", " # calculation for thickness of plate of quartz\n", "\n", "#Result\n", "print \"Thickness of plate of quartz in first case = %.3e meter,\\nAnd thickness of plate of quartz in second case = %.2e meter\"%(t1,t2)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of plate of quartz in first case = 2.945e-06 meter,\n", "And thickness of plate of quartz in second case = 7.36e-06 meter\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.15, Page 3.28" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "l = 5.89e-7 # wavelength of light in meter\n", "mu_e = 1.486 # refractive index for extraordinary light\n", "mu_o = 1.658 # refractive index for ordinary light\n", "\n", "#Calculation\n", "t = l / (4 * (mu_o - mu_e)) # calculation for thickness of calcite plate \n", "\n", "#Result\n", "print \"Thickness of calcite plate = %.2e meter\"%t" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of calcite plate = 8.56e-07 meter\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.16, Page 3.28" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "l = 5e-7 # wavelength of light in meter\n", "mu_e = 1.5533 # refractive index for extraordinary light\n", "mu_o = 1.5442 # refractive index for ordinary light\n", "\n", "#Calculation\n", "t = l / (4 * (mu_e - mu_o)) # calculation for thickness of quartz plate\n", "\n", "#Result\n", "print \"Thickness of quartz plate = %.2e meter\"%t" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of quartz plate = 1.37e-05 meter\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.17, Page 3.28" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "l = 5.89e-7 # wavelength of light in meter\n", "mu_e = 1.54 # refractive index for extraordinary light\n", "mu_o = 1.55 # refractive index for ordinary light\n", "\n", "#Calculation\n", "t = l / (4 * (mu_o - mu_e)) # calculation for thickness of quartz plate\n", "\n", "#Result\n", "print \"Thickness of quartz plate = %.2e meter\"%t" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of quartz plate = 1.47e-05 meter\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.18, Page 3.28" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "l = 5.89e-7 # wavelength of light in meter\n", "mu_e = 1.553 # refractive index for extraordinary light\n", "mu_o = 1.544 # refractive index for ordinary light\n", "\n", "#Calculation\n", "t = l / (4 * (mu_e - mu_o)) # calculation for thickness of quartz plate\n", "\n", "#Result\n", "print \"Thickness of quartz plate = %.2e meter\"%t" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of quartz plate = 1.64e-05 meter\n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.19, Page 3.29" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "mu_e = 1.5442 # refractive index for extraordinary light\n", "mu_o = 1.5533 # refractive index for ordinary light\n", "l = 5e-7 # wavelength of plane polarized light in meter\n", "\n", "#Calculation\n", "t = l / (2 * (mu_o - mu_e))# calculation for thickness of quartz plate\n", "\n", "#Result\n", "print \"Thickness of quartz plate = %.2e meter\"%t" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of quartz plate = 2.75e-05 meter\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.20, Page 3.29" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "theta = 10 # rotation of plane of polarization in degree\n", "s = 60 # specific rotation of sugar solution in degree per decimeter per unit concentration\n", "l = 2.5 # length of Polari meter in decimeter\n", "\n", "#Calculation\n", "c = theta / (s * l) # calculation for concentration of sugar solution\n", "\n", "#Result\n", "print \"Concentration of sugar solution = %.3f gm/cc\"%c" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Concentration of sugar solution = 0.067 gm/cc\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.21, Page 3.29" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "theta = 26.4 # rotation of plane of polarization in degree\n", "c = 0.2 # concentration of sugar solution in gm/cc\n", "l = 2 # length of polarizing tube in decimeter\n", "\n", "#Calculation\n", "s = theta / (l * c)# calculation for specific rotation of sugar solution\n", "\n", "#Result\n", "print \"Specific rotation of sugar solution = %.f degree/(dm-cc)\"%s" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Specific rotation of sugar solution = 66 degree/(dm-cc)\n" ] } ], "prompt_number": 43 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.22, Page 3.29" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "theta = 6.5 # rotation of plane of polarization in degree\n", "c = 0.05 # concentration of sugar solution in gm/cc\n", "l = 2 # length of polarizing tube in decimeter\n", "\n", "#Calculation\n", "s = theta / (l * c) # calculation for specific rotation of sugar solution\n", "\n", "#Result\n", "print \"Specific rotation of sugar solution = %.f degree/(dm-cc)\"%s" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Specific rotation of sugar solution = 65 degree/(dm-cc)\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.23, Page 3.30" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "w = 80 # weight of impure sugar in gm\n", "theta = 9.9 # rotation of plane of polarization in degree\n", "s = 66 # specific rotation of sugar solution in degree per decimeter per unit concentration\n", "l = 2 # length of Polari meter in decimeter\n", "\n", "#Calculations\n", "c = theta / (s * l) * (1000) # in gm/l\n", "per_c = (c * 100) / w # calculation for concentration of sugar solution\n", "\n", "#Result\n", "print \"Concentration of sugar solution = %.2f percent\"%per_c" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Concentration of sugar solution = 93.75 percent\n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.24, Page 3.30" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "theta = 11. # rotation of plane of polarization in degree\n", "s = 66 # specific rotation of sugar solution in degree per decimeter per unit concentration\n", "l = 2 # length of Polari meter in decimeter\n", "\n", "#Calculation\n", "c = theta / (s * l) # calculation for concentration of sugar solution\n", "\n", "#Result\n", "print \"Concentration of sugar solution = %.4f gm/cc\"%c" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Concentration of sugar solution = 0.0833 gm/cc\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.25, Page 3.30" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "theta = 26.4 # rotation of plane of polarization in degree\n", "c = 0.2 # concentration of sugar solution in gm/cc\n", "l = 2 # length of polarizing tube in decimeter\n", "\n", "#calculation\n", "s = theta / (l * c) # calculation for specific rotation of sugar solution\n", "\n", "#Result\n", "print \"Specific rotation of sugar solution = %.f degree/(dm-cc)\"%s" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Specific rotation of sugar solution = 66 degree/(dm-cc)\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 3.26, Page 3.30" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Given \n", "theta = 13 # rotation of plane of polarization in degree\n", "r = (1. / 3) # ratio of the final concentration to the initial solution\n", "l = 2 # length of Polari meter in decimeter\n", "l_ = 3 # length of second polarizing tube in decimeter \n", "\n", "#Calculation\n", "theta_ = (l_ * r * theta) / l# calculation for optical rotation of diluted solution\n", "\n", "#Result\n", "print \"Optical rotation of diluted solution = %.1f degree\"%theta_" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Optical rotation of diluted solution = 6.5 degree\n" ] } ], "prompt_number": 39 } ], "metadata": {} } ] }