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diff --git a/Engineering_Physics_Malik/Chapter_5.ipynb b/Engineering_Physics_Malik/Chapter_5.ipynb new file mode 100644 index 00000000..e9ebdd41 --- /dev/null +++ b/Engineering_Physics_Malik/Chapter_5.ipynb @@ -0,0 +1,549 @@ +{ + "metadata": { + "name": "" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "Chapter 5: Fibre Optics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.1, Page 5.15" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, asin\n", + "\n", + "# Given \n", + "mu1 = 1.52 # refractive index for core\n", + "mu2 = 1.41 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "theta_c = asin(mu2 / mu1) * (180 / pi)\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "theta_0 = asin(NA) * (180 / pi)\n", + "\n", + "#Result\n", + "print \"Critical angle = %.2f degree \\nNumerical aperture = %.3f\\nMaximum incidence angle = %.1f degree\"%(theta_c,NA,theta_0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical angle = 68.07 degree \n", + "Numerical aperture = 0.568\n", + "Maximum incidence angle = 34.6 degree\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.2, Page 5.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, asin\n", + "\n", + "# Given \n", + "mu1 = 1.6 # refractive index for core\n", + "mu2 = 1.5 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)#calculation for numerical aperture\n", + "theta_0 = asin(NA) * (180 / pi)#calculation for maximum incidence angle\n", + "\n", + "#Result\n", + "print \"Numerical aperture = %.3f\\nMaximum incidence angle = %.2f degree\"%(NA,theta_0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture = 0.557\n", + "Maximum incidence angle = 33.83 degree\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.3, Page 5.16" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, asin\n", + " \n", + "# Given \n", + "mu_0 = 1 # refractive index of air\n", + "mu1 = 1.5 # refractive index for core\n", + "mu2 = 1.48 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "theta_c = asin(mu2 / mu1) * (180 / pi)\n", + "delta_mu = (mu1 - mu2) / mu1\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "theta_0 = asin(NA) * (180 / pi)\n", + "\n", + "#Result\n", + "print \"Critical angle = %.2f degrees \\nNumerical aperture = %.3f \\nAcceptance angle = %.2f degrees\\nFractional refractive index = %.2f %%\"%(theta_c,NA,theta_0,delta_mu*100)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Critical angle = 80.63 degrees \n", + "Numerical aperture = 0.244 \n", + "Acceptance angle = 14.13 degrees\n", + "Fractional refractive index = 1.33 %\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.4, Page 5.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import * \n", + "# Given \n", + "mu1 = 1.62 # refractive index for core\n", + "mu2 = 1.52 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "theta_0 = asin(NA) * (180 / pi)\n", + "\n", + "#Results\n", + "print \"Numerical aperture = %.2f \\nMaximum incidence angle = %.1f degrees\"%(NA,theta_0)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture = 0.56 \n", + "Maximum incidence angle = 34.1 degrees\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.5, Page 5.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt\n", + "\n", + "# Given \n", + "NA = 0.22 # numerical aperture\n", + "delta_mu = 0.012 # fractional refractive index\n", + "\n", + "#Calculations\n", + "mu1 = sqrt(NA**2 / (1 - (1 - delta_mu)**2))\n", + "mu2 = (1 - delta_mu) * mu1\n", + "\n", + "#Result\n", + "print \"Refractive index for core = %.3f\\nRefractive index for cladding = %.2f\"%(mu1,mu2)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Refractive index for core = 1.424\n", + "Refractive index for cladding = 1.41\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.6, Page 5.17" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi, sqrt, asin, sin\n", + "\n", + "# Given \n", + "d = 0.0064 # diameter of fiber in cm\n", + "mu1 = 1.53 # refractive index for core\n", + "mu2 = 1.39 # refractive index for clad\n", + "L = 90 # length of fiber in cm\n", + "mu_0 = 1 # refractive index of air\n", + "\n", + "#calculations\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "theta_0 = asin(NA) * (180 / pi)\n", + "N1 = L / (d * sqrt((mu1 / (mu_0 * sin(theta_0 * (pi / 180))))**2 - 1))\n", + "N2 = L / (d * sqrt((mu1 / (mu_0 * sin(theta_0 * (pi / 360))))**2 - 1))\n", + "\n", + "#Result\n", + "print \"Numerical aperture = %.2f\\nAcceptance angle = %.1f degrees \\nNumber of reflections at maximum incidence = %.f \\nNumber of reflections in second case = %.f \"%(NA,theta_0,N1,N2)\n", + "#Incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture = 0.64\n", + "Acceptance angle = 39.7 degrees \n", + "Number of reflections at maximum incidence = 6468 \n", + "Number of reflections in second case = 3204 \n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.7, Page 5.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import pi\n", + "\n", + "# Given \n", + "d = 0.05 # diameter of fiber in mm\n", + "NA = 0.22 # numerical aperture\n", + "l = 8.5e-4 # wavelength of light in mm\n", + "\n", + "#calculations\n", + "Vn = (pi * d * NA) / l\n", + "Mm = 0.5 * (Vn)**2\n", + "\n", + "#Result\n", + "print \"The normalized frequency = %.2f\\nNumber of guided in the core = %d\"%(Vn,Mm)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The normalized frequency = 40.66\n", + "Number of guided in the core = 826\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.8, Page 5.18" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "l = 1.25e-6 #wavelength of light in meter\n", + "mu1 = 1.465 # refractive index for core\n", + "mu2 = 1.460 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "k = (2.4 * l) / ( pi * NA)\n", + "Mm = 0.5 * ((pi * 50e-6 * NA) / l)**2\n", + "\n", + "#Result\n", + "print \"Diameter of core < %.1e meter,\\n number of modes = %d\"%(k,Mm)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Diameter of core < 7.9e-06 meter,\n", + " number of modes = 115\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.9, Page 5.19" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "l = 0.85e-6 #wavelength of light in meter\n", + "mu1 = 1.461 # refractive index for core\n", + "mu2 = 1.456 # refractive index for clad\n", + "d = 4e-5 # diameter of core in meter\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)\n", + "Mm = 0.5 * ((pi * d * NA) / l)**2\n", + "\n", + "#Result\n", + "print \"Numerical aperture = %.3f\\n Number of modes = %d \"%(NA,Mm)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture = 0.121\n", + " Number of modes = 159 \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.10, Page 5.19\n" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given\n", + "mu1 = 3.6 # refractive index for core\n", + "mu2 = 3.55 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)#calculation for numerical aperture\n", + "Mm1 = 0.5 * (pi * 5 * NA)**2#calculation for no. of modes in first case\n", + "Mm2 = 0.5 * (pi * 50 * NA)**2#calculation for no. of modes in second case\n", + "\n", + "#Result\n", + "print \"Number of modes in first case = %d \\nNumber of modes in second case = %d\"%(Mm1,Mm2)\n", + "#Incorrect answer in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of modes in first case = 44 \n", + "Number of modes in second case = 4410\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.11, Page 5.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import sqrt, pi\n", + "\n", + "# Given \n", + "l = 1.25e-6 #wavelength of light in meter\n", + "mu1 = 1.46 # refractive index for core\n", + "mu2 = 1.457 # refractive index for cladding\n", + "\n", + "#Calculations\n", + "NA = sqrt(mu1**2 - mu2**2)#calculation for numerical aperture\n", + "k = (2.4 * l) / ( pi * NA)\n", + "\n", + "#Result\n", + "print \"Maximum diameter of core = %.2f micro meter\"%(k*1e6)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum diameter of core = 10.21 micro meter\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.12, Page 5.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import log10\n", + "\n", + "# Given \n", + "L = 0.1 # length of fiber in km\n", + "p = 5e-6 # power of signal in watt\n", + "p_ = 1e-6 # power of signal inside the fiber in watt\n", + "\n", + "#Calculation\n", + "alpha = (10 * log10(p / p_)) / L#calculation for absorption coefficient\n", + "\n", + "#Result\n", + "print \"Absorption coefficient = %d dB/km \"%alpha" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Absorption coefficient = 69 dB/km \n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 5.13, Page 5.20" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "from math import exp\n", + "\n", + "# Given \n", + "L = 3 # length of optical fiber in km\n", + "l = 6 # losses in dB\n", + "p = 5e-3 # input power in watt \n", + "\n", + "#calculations\n", + "alpha = (l * 3) / L\n", + "p_ = p / (exp((2.303 * alpha * L) / 10))\n", + "\n", + "#Result\n", + "print \"Output power = %.3f mW \"%(p_*1e3)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Output power = 0.079 mW \n" + ] + } + ], + "prompt_number": 19 + } + ], + "metadata": {} + } + ] +}
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