{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 1: Interference of Light" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.2.1, Page number 1-11" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Variable declaration\n", "i = 45 #angle of incidence(degrees)\n", "t = 4*10**-5 #thickness of film(cm)\n", "u = 1.2\n", "\n", "#Calculations & Result\n", "r = math.degrees(math.asin(math.sin(i*math.pi/180)/u))\n", "for n in range(1,4):\n", " lamda = (2*u*t*math.cos(r*math.pi/180))/n\n", " print \"For n = %d, wavelength = %.2f A\"%(n,lamda/10**-8)\n", "print \"Since the visible range of wavelengths lie between 4000 to 7000 A, none of the obtained wavelengths lie in this range\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "For n = 1, wavelength = 7756.29 A\n", "For n = 2, wavelength = 3878.14 A\n", "For n = 3, wavelength = 2585.43 A\n", "Since the visible range of wavelengths lie between 4000 to 7000 A, none of the obtained wavelengths lie in this range\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.2.2, Page number 1-12" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Variable declaration\n", "r = 90 #angle of refraction(degrees)\n", "t = 5*10**-5 #thickness of film(cm)\n", "u = 1.33\n", "\n", "#Calculations & Result\n", "for n in range(1,4):\n", " lamda = (4*u*t*int(math.cos(math.radians(90))))/((2*n)-1)\n", " print \"For n = %d, wavelength = %.2f A\"%(n,lamda)\n", "print \"Since the visible range of wavelengths lie between 4000 to 7000 A, none of the obtained wavelengths do not lie in this range\"\n", "\n", "print \"\\nPlease note: Since r=90, cos(r)=0\\nHence, the answers given in the textbook are incorrect\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "For n = 1, wavelength = 0.00 A\n", "For n = 2, wavelength = 0.00 A\n", "For n = 3, wavelength = 0.00 A\n", "Since the visible range of wavelengths lie between 4000 to 7000 A, none of the obtained wavelengths do not lie in this range\n", "\n", "Please note: Since r=90, cos(r)=0\n", "Hence, the answers given in the textbook are incorrect\n" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.2.3, Page number 1-12" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Variable declaration\n", "i = 45 #angle of incidence(degrees)\n", "t = 1.5*10**-4 #thickness of film(cm)\n", "lamda = 5*10**-5 #wavelength(cm)\n", "u = 4./3. #refractive index\n", "\n", "#Calculations\n", "r = math.degrees(math.asin(math.sin(i*math.pi/180)/u))\n", "n = (2*u*t*math.cos(r*math.pi/180))/lamda\n", "\n", "#Result\n", "print \"The order of interfernce is %.2f, close to 7\"%n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The order of interfernce is 6.78, close to 7\n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 12.2.4, Pae number 1-13" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "#Variable declaration\n", "i = 45 #angle of incidence(degrees)\n", "lamda = 5896*10**-8 #wavelength(cm)\n", "u = 1.33 #refractive index\n", "n = 1\n", "\n", "#Calculations\n", "r = math.degrees(math.asin(math.sin(i*math.pi/180)/u))\n", "t = ((2*n-1)*lamda)/(2*u*math.cos(r*math.pi/180)*2)\n", "\n", "#Result\n", "print \"The required thickness is\",round((t/1E-5),2),\"*10^-5 cm\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The required thickness is 1.31 *10^-5 cm\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.2.5, Page number 1-14" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "lamda1 = 7000 #wavelength(A)\n", "lamda2 = 5000 #wavelength(A)\n", "u = 1.3 #R.I. of oil\n", "\n", "#Calculations\n", "'''\n", "2utcosr = (2n-1)7000/2 ----(1)\n", "2utcosr = (2n+1)5000/2 ----(2)\n", "Divinding (1) by (2), we get the following expression\n", "1 = (2n+1)5000\n", " -----------\n", " (2n-1)7000\n", "Solving the above expression, we get,\n", "'''\n", "n = 12000/4000\n", "t = ((2*n-1)*lamda)/(2*u*math.cos(r*math.pi/180)*2)\n", "\n", "#Result\n", "print \"The required thickness is\",round((t/1E-5),4),\"*10^-5 cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The required thickness is 6.6936 *10^-5 cm\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.2.6, Page number 1-15" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "#Variable declaration\n", "i = 30 #angle of incidence(degrees)\n", "lamda = 5890*10**-8 #wavelength(cm)\n", "u = 1.46 #refractive index\n", "n = 8\n", "\n", "#Calculations\n", "r = math.degrees(math.asin(math.sin(i*math.pi/180)/u))\n", "t = (n*lamda)/(2*u*math.cos(r*math.pi/180))\n", "\n", "#Result\n", "print \"The required thickness is\",round((t/1E-4),3),\"*10^-4 cm\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The required thickness is 1.718 *10^-4 cm\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.2.7, Page number 1-15" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "#Variable declaration\n", "r = 60 #angle of refraction(degrees)\n", "lamda = 5890*10**-8 #wavelength(cm)\n", "u = 1.5 #refractive index\n", "n = 1 #for minimumm thickness\n", "\n", "#Calculations\n", "#For r = 60\n", "t1 = (n*lamda)/(2*u*math.cos(r*math.pi/180))\n", "\n", "#For normal incidence \n", "r = 0\n", "t2 = (n*lamda)/(2*u*math.cos(r*math.pi/180))\n", "\n", "#Result\n", "print \"For r = 60, the required thickness is\",round((t1/1E-5),2),\"*10^-5 cm\"\n", "print \"For r = 0, the required thickness is\",round((t2/1E-5),2),\"*10^-5 cm\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "For r = 60, the required thickness is 3.93 *10^-5 cm\n", "For r = 0, the required thickness is 1.96 *10^-5 cm\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.2.8, Page number 1-16" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "#Variable declaration\n", "r = 0 #for normal incidence(degrees)\n", "lamda = 5.5*10**-5 #wavelength(cm)\n", "n = 1 #for minimumm thickness\n", "A = 10**4 #area(cm^2)\n", "V = 0.2 #volume(cc)\n", "\n", "#Calculations\n", "t = V/A\n", "#for nth dark band,\n", "u = (n*lamda)/(2*t*math.cos(r*math.pi/180))\n", "\n", "#Result\n", "print \"Refractive index =\",u" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Refractive index = 1.375\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.2.9, Page number 1-17" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "import math\n", "\n", "#Variable declaration\n", "r = 60 #angle of incidence(degrees)\n", "t = 2*10**-7 #thickness of film(cm)\n", "u = 1.2\n", "\n", "#Calculations & Result\n", "for n in range(1,4):\n", " lamda = (4*u*t*math.cos(r*math.pi/180))/(2*n-1)\n", " print \"For n = %d, wavelength = %.2f A\"%(n,lamda/10**-10)\n", "print \"Since the visible range of wavelengths lie between 4000 to 7000 A, the wavelength in the visible spectrum is 4800 A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "For n = 1, wavelength = 4800.00 A\n", "For n = 2, wavelength = 1600.00 A\n", "For n = 3, wavelength = 960.00 A\n", "Since the visible range of wavelengths lie between 4000 to 7000 A, the wavelength in the visible spectrum is 4800 A\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.3.1, Page number 1-21" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration \n", "a = 40. #angle(sec)\n", "lamda = 1.2 #distance between fringes(cm)\n", "alpha = 10 #no. of fringes\n", "\n", "#Calculations\n", "Bair = lamda/alpha #cm\n", "alpha = (a*math.pi)/(3600*180) #radians\n", "lamda = 2*alpha*Bair\n", "\n", "#Result\n", "print \"Wavelength of monochromatic light =\",round((lamda/1E-8),1),\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Wavelength of monochromatic light = 4654.2 A\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.3.2, Page number 1-22" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration \n", "lamda = 5893*10**-8 #wavelength(cm)\n", "u = 1.52 #refractive index\n", "B = 0.1 #fringe spacing(cm)\n", "\n", "#Calculations\n", "alpha = (lamda/(2*u*B))*180*3600/math.pi #seconds\n", "\n", "#Result\n", "print \"Angle of wedge =\",round(alpha,2),\"secs\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angle of wedge = 39.98 secs\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.3.3, Page number 1-22" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration \n", "u = 1.4 #refractive index\n", "B = 0.25 #fringe spacing(cm)\n", "a = 20 #angle(secs)\n", "\n", "#Calculations\n", "alpha = (a*math.pi)/(3600*180) #radians\n", "lamda = 2*u*alpha*B\n", "\n", "#Result\n", "print \"Wavelength of light =\",round((lamda/1E-8),2),\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Wavelength of light = 6787.39 A\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.3.4, Page number 1-23" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration \n", "u = 1.5 #refractive index\n", "lamda = 5.82*10**-5 #wavelength(cm)\n", "a = 20 #angle(secs)\n", "\n", "#Calculations\n", "alpha = (a*math.pi)/(3600*180) #radians\n", "B = lamda/(2*u*alpha)\n", "N = 1/B\n", "\n", "#Result\n", "print \"Number of interfernce fronges pr cm is\",round(N)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Number of interfernce fronges pr cm is 5.0\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.3.5, Page number 1-24" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration \n", "u = 1 #refractive index for air film\n", "lamda = 6*10**-5 #wavelength(cm)\n", "B = 1./10 #distance between fringes(cm)\n", "\n", "#Calculations\n", "alpha = lamda/(2*u*B) #radians\n", "d = alpha*10\n", "\n", "#Result\n", "print \"Daimeter of wire =\",d,\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Daimeter of wire = 0.003 cm\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.3.6, Page number 1-24" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "alpha = 0.01*10**-1/10 #angle(radians)\n", "u = 1 #refractive index for air film\n", "lamda = 5900*10**-10 #wavlength(m)\n", "\n", "#Calculation\n", "B = lamda/(2*u*alpha)\n", "\n", "#Result\n", "print \"Seperation between fringes is\",B/10**-3,\"mm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Seperation between fringes is 2.95 mm\n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.1, Page number 1-32" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration \n", "n = 40\n", "\n", "#Calculation\n", "#Equating the equation 4*R*n*lamda=4*4R*n*lamda, we get\n", "\n", "N = (4*4*n)/4\n", "\n", "#result\n", "print \"Ring number =\",N" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Ring number = 160\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.2, Page number 1-32" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration \n", "n = 10\n", "Dn = 0.5 #diameter of dark ring(cm)\n", "lamda = 5*10**-5 #waelength(cm)\n", "\n", "#Calculations\n", "R = Dn**2/(4*n*lamda)\n", "\n", "#Result\n", "print \"Radius of curvature =\",R,\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Radius of curvature = 125.0 cm\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.3, Page number 1-33" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration \n", "n = 5\n", "p = 10\n", "D5 = 0.336 #diameter of 5th ring(cm)\n", "lamda = 5890*10**-8 #waelength(cm)\n", "D15 = 0.59 #diameter of 15th ringcm\n", "\n", "#Calculations\n", "R = (D15**2-D5**2)/(4*p*lamda)\n", "\n", "#Result\n", "print \"Radius of curvature =\",round(R,2),\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Radius of curvature = 99.83 cm\n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.4, Page number 1-33" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Varaible declaration\n", "Dn = 0.42 #diameter of dark ring(cm)\n", "p = 8 \n", "R = 200 #radius of curvature(cm)\n", "Dn8 = 0.7 #diameter of (n+8)th ring(cm)\n", "\n", "#Calculations\n", "lamda = (Dn8**2-Dn**2)/(4*R*p)\n", "\n", "#Result\n", "print \"Wavelength =\",lamda/1E-8,\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Wavelength = 4900.0 A\n" ] } ], "prompt_number": 36 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.5, Page number 1-34" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Varaible declaration\n", "Dn = 0.218 #cm\n", "Dn10 = 0.451 #cm\n", "lamda = 5893*10**-8 #wavelength(cm)\n", "R = 90 #radius of curvature(cm)\n", "p = 10\n", "\n", "#Calculation\n", "u = (4*p*lamda*R)/(Dn10**2-Dn**2)\n", "\n", "#Result\n", "print \"Refractive index =\",round(u,3)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Refractive index = 1.361\n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.6, Page number 1-34" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Varaible declaration\n", "D5 = 0.42 #diameter of dark ring(cm)\n", "\n", "#Calculations\n", "'''\n", "For 5th dark ring,\n", "D5^2 = 20*R*lamda -----1\n", "\n", "For 10th dark ring,\n", "D10^2 = 40*R*lamda -----2\n", "\n", "Substituting 1 in 2,\n", "'''\n", "\n", "D10 = math.sqrt((40*D5**2)/20)\n", "\n", "#Result\n", "print \"Diameter of the 10th dark ring =\",round(D10,3),\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Diameter of the 10th dark ring = 0.594 cm\n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.7, Page number 1-35" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Varaible declaration\n", "lamda_n = 6000 #wavelength of nth ring(A)\n", "lamda_n1 = 5000 #wavelength for (n+1)th ring(cm)\n", "\n", "#Calculations\n", "'''\n", "Dn^2 = 4*R*n*lamda_n ---1\n", "\n", "Dn+1^2 = 4*R(n+1)*lamda_n1 ---2\n", "\n", "Equating 1 and 2, we get,\n", "'''\n", "\n", "n = 5\n", "R = 2\n", "Dn = math.sqrt(4*R*n*lamda_n*10**-8)\n", "\n", "#Result\n", "print \"Diameter =\",round(Dn,3),\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Diameter = 0.049 cm\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.8, Page number 1-35" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Varaible declaration\n", "Dair = 2.3 #diameter of ring in air(cm)\n", "Dliq = 2 #diameter of ring in liquid(cm)\n", "\n", "#Calculations\n", "u = Dair**2/Dliq**2\n", "\n", "#Result\n", "print \"Refractive index =\",u" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Refractive index = 1.3225\n" ] } ], "prompt_number": 43 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.11, Page number 1-37" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "D4 = 0.4 #diameter of 4th ring(cm)\n", "D12 = 0.7 #diameter of 12th ring(cm)\n", "\n", "#Calculations\n", "'''\n", "For D4, \n", "D4 = math.sqrt(4R*4*lamda)\n", "'''\n", "rt_Rl = 0.1\n", "R = 80 \n", "\n", "#For D20,\n", "D20 = math.sqrt(R)*rt_Rl\n", "\n", "#Result\n", "print \"Diameter of 20th ring =\",round(D20,3),\"cm\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Diameter of 20th ring = 0.894 cm\n" ] } ], "prompt_number": 46 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.4.12, Page number 1-36" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration \n", "n = 5\n", "p = 10\n", "D5 = 0.336 #diameter of 5th ring(cm)\n", "D15 = 0.590 #diameter of 15th ring(cm)\n", "R = 100 #radius of curvature(cm)\n", "\n", "#Calculations\n", "lamda = (D15**2-D5**2)/(4*R*p)\n", "\n", "#Result\n", "print \"Wavlength =\",lamda/1E-8,\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Wavlength = 5880.1 A\n" ] } ], "prompt_number": 50 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.7.1, Page number 1-42" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "lamda = 560 #wavelength(nm)\n", "u = 2 #refractive index\n", "\n", "#Calculations\n", "lamda_dash = lamda/u\n", "t = lamda_dash/4\n", "\n", "#Result\n", "print \"Thickness of film =\",t,\"nm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of film = 70 nm\n" ] } ], "prompt_number": 55 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 1.7.2, Page number 1-42" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "#Variable declaration\n", "lamda = 6000 #wavelength(E)\n", "u = 1.2 #refractive index\n", "\n", "#Calculations\n", "lamda_dash = lamda/u\n", "t = lamda_dash/4\n", "\n", "#Result\n", "print \"Thickness of film =\",t,\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Thickness of film = 1250.0 A\n" ] } ], "prompt_number": 56 } ], "metadata": {} } ] }