{ "metadata": { "name": "", "signature": "sha256:5e77310b83fb16f4b45eb92df638029fc5fbb7881beb71539bf2e332dc67f090" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 2 Diffraction of light" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.1 Page no 85" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "w=6*10**-7\n", "a=12*10**-7\n", "\n", "#Calculation\n", "import math\n", "A=math.asin(w/a)*180/3.14\n", "\n", "#Result\n", "print\"Half angular width of central bright maxima is\",round(A,0),\"degree\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Half angular width of central bright maxima is 30.0 degree\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.2 Page no 85" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "a =0.2*10**-3 #m\n", "D =2.0 # n m\n", "x=5*10**-3\n", "\n", "#Calculation\n", "w=(a*x)/D\n", "w1=w*1*10**10\n", "\n", "#Result\n", "print\"Wavelength of light is\", w1,\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Wavelength of light is 5000.0 A\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.3 Page no 85" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "f=100 #cm\n", "L=6000*10**-8\n", "d=0.01\n", "\n", "#Calculation\n", "x=1.22*f*L/d\n", "\n", "#Result\n", "print\"Separation is\",x,\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Separation is 0.732 cm\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.4 Page no 86" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "w=6*10**-7 #m\n", "D=2\n", "x=5.0*10**-3\n", "\n", "#Calculation\n", "a=(w*D)/x\n", "\n", "#Result\n", "print\"Slit width is\", a*10**4,\"*10**-4 m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Slit width is 2.4 *10**-4 m\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.5 Page no 86" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "w=589*10**-9\n", "D=1\n", "a=0.1*10**-3\n", "\n", "#Calculation\n", "import math\n", "A=math.asin(w/a)\n", "A1=2*A\n", "y=D*A1\n", "y1=y*100\n", "\n", "#Result\n", "print\"Angular width of central maxima is\", round(A1,3),\"radian\"\n", "print\"Linear width of central maxima is\",round(y1,3),\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angular width of central maxima is 0.012 radian\n", "Linear width of central maxima is 1.178 cm\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.6 Page no 86" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "a=22.0*10**-5\n", "L=5500*10**-8\n", "n=1\n", "n1=2\n", "\n", "#Calculation\n", "import math\n", "a1=L/a\n", "A=math.asin(a1)*180/3.14\n", "a2=math.asin(2*L/a)*180/3.14\n", "\n", "#Result\n", "print\"Angular position of two minima is\",round(A,2), \"Degree and\", round(a2,0),\"Degree\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angular position of two minima is 14.48 Degree and 30.0 Degree\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.7 Page no 87" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "n=1\n", "L=5890*10**-10\n", "a=3*10**-4\n", "\n", "#Calculation\n", "import math\n", "A=math.asin((L/a)*180/3.14)\n", "A1=math.asin((3*L)/(2.0*a))*180/3.14\n", "\n", "#Result\n", "print\"Angle is\", round(A1*10**2,0),\"Degree\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angle is 17.0 Degree\n" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.8 Page no 87" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "L=4890*10**-10\n", "a=5*10**-3\n", "f=0.4\n", "\n", "#Calculation\n", "x1=f*L/a\n", "x2=3*L*f/(2*a)\n", "x=x2-x1\n", "\n", "#Result\n", "print\"Distance between first dark fringe and new bright fringe is\", x,\"m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Distance between first dark fringe and new bright fringe is 1.956e-05 m\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.9 Page no 88" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "L=5000*10**-8 #cm\n", "a=5000.0\n", "\n", "#Calculation\n", "n=1/(L*a)\n", "\n", "#Result\n", "print\"Highest order spectrum is\",n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Highest order spectrum is 4.0\n" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.10 Page no 88" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "c=1/5000.0\n", "w1=5890*10**-8 #cm\n", "n =2\n", "\n", "#Calculation\n", "import math\n", "theta = math.asin ((n*w1)/c)*180/3.14\n", "w2 =5896*10** -8\n", "theta1 = math.asin ((n*w2)/c)*180/3.14\n", "a= theta1 - theta \n", "w =5893*10**-8\n", "dw=w2 -w1\n", "N=w/( dw*n)\n", "N1= floor (N)\n", "\n", "#Result\n", "print\"(a) Angular width is\",round(theta,3),\"Degree\"\n", "print\"(b) Angular separation is\",round(a,3),\"Degree\"\n", "print\"(c) No. of lines is\",N1,\"Grating\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Angular width is 36.104 Degree\n", "(b) Angular separation is 0.043 Degree\n", "(c) No. of lines is 491.0 Grating\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.11 Page no 89" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "w1=589*10**-9\n", "w2 =5896*10**-10 \n", "dw=w2-w1 # change o f wave l eng th\n", "w=( w1+w2) /2.0 #mid wavelength\n", "n =1\n", "\n", "#Calculation\n", "N=w/(n*dw)\n", "N1= floor (N)\n", "\n", "#Result\n", "print\"Number of lines is\", N1,\"grating\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Number of lines is 982.0 grating\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.12 Page no 89" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "n1=2\n", "n2=3.0\n", "L=6360 #A\n", "\n", "#Calculation\n", "L2=n1*L/n2\n", "\n", "#Result\n", "print\"Wavelength is\",L2,\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Wavelength is 4240.0 A\n" ] } ], "prompt_number": 44 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.13 Page no 89" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "L1=5400*10**-8\n", "L2=4050.0*10**-8\n", "a=30 #Degree\n", "b=1350.0*10**-8\n", "\n", "#Calculation\n", "A=b/(L1*L2*2)\n", "\n", "#Result\n", "print\"Number of lines is\", round(A,0)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Number of lines is 3086.0\n" ] } ], "prompt_number": 48 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.14 Page no 90" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "a=30 #Degree\n", "L=5000*10**-8\n", "x=0.01 #Radian\n", "\n", "#Calculation\n", "import math\n", "A=math.tan(a*3.14/180.0)\n", "X=1/A\n", "L1=L*x*X\n", "\n", "#Result\n", "print\"Difference in two wavelength is\", round(L1*10**8,1),\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Difference in two wavelength is 86.7 A\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.15 Page no 90" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "#Given\n", "c=1/4000.0 # grating element\n", "w=5000*10**-8\n", "n =3\n", "\n", "#Calculation\n", "import math\n", "D=n/(c* math.sqrt (1 -((n*w/c)**2) ))\n", "\n", "#Result\n", "print\"Dispersive power is\",D*10**-4,\"*10**4 rad/sec\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Dispersive power is 1.5 *10**4 rad/sec\n" ] } ], "prompt_number": 59 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.16 Page no 90" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "a=30 #Degree\n", "n=2.0\n", "A=5000.0\n", "\n", "#Calculation\n", "import math\n", "L=math.sin(a*3.14/180.0)/(n*A)\n", "\n", "#Result\n", "print\"Wavelength is\", round(L*10**8,0),\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Wavelength is 4998.0 A\n" ] } ], "prompt_number": 84 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.17 Page no 91" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "l =5 #length of grating\n", "N =16000\n", "w =6000\n", "n =2.0\n", "\n", "#Calculation\n", "T=N*l\n", "R=T*n\n", "dw=w/(T*n)\n", "\n", "#Result\n", "print\"(a) Resolving power is\",R\n", "print\"(b) Wavelength is\",dw,\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "(a) Resolving power is 160000.0\n", "(b) Wavelength is 0.0375 A\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.18 Page no 91" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "w1=5500 #A\n", "w2=5501\n", "n=2\n", "W1=8500\n", "W2=8501\n", "\n", "#Calculation\n", "w=(w1+w2)/2.0\n", "W=w2-w1\n", "N=w/W\n", "W11=(W1+W2)/2.0\n", "W12=W2-W1\n", "N1=W11/W12\n", "\n", "#Result\n", "print\"The required rosolving power\", N1,\"is less than the actual power\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The required rosolving power 8500.5 is less than the actual power\n" ] } ], "prompt_number": 94 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.19 Page no 92" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "c =12.5*10**-5\n", "w=5*10**-5\n", "N =40000\n", "\n", "#Calculation\n", "n=c/w\n", "n1= floor (n)\n", "P=n1*N\n", "\n", "#Result\n", "print\"Resolving power is\",P" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resolving power is 80000.0\n" ] } ], "prompt_number": 87 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.20 Page no 92" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "n=2500.0\n", "w=0.5\n", "n1=1\n", "L=5890*10**-8\n", "a=5000\n", "L2=5896*10**-8\n", "L3=5893*10**-8\n", "c=6*10**-8\n", "\n", "#Calculation\n", "import math\n", "A=w/n\n", "A1=math.asin(L*a)*180/3.14\n", "A2=math.asin(L2*a)*180/3.14\n", "A3=A2-A1\n", "N=L3/c\n", "\n", "#Result\n", "print\"Angular separation between Two sodium lines are\", round(A1,1),\"degree and\",round(A2,1),\"degree\"\n", "print\"Number of lines required is\",round(N,0),\"lines\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Angular separation between Two sodium lines are 17.1 degree and 17.2 degree\n", "Number of lines required is 982.0 lines\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.21 Page no 93" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "l=2 #inches\n", "n=40000\n", "N=3\n", "\n", "#Calculation\n", "r=n*l\n", "p=N*r\n", "\n", "#Result\n", "print\"The resolving power in third order is\",p" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The resolving power in third order is 240000\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.22 Page no 93" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "N=40000.0\n", "a=12.5*10**-5\n", "w=80000\n", "\n", "#Calculation\n", "n=w/N\n", "L=a/n\n", "L1=L*10**8/(n*N)\n", "L2=L*10**8+L1\n", "\n", "#Result\n", "print\"Range of wavelength is\", round(L2,2),\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Range of wavelength is 6250.08 A\n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.23 Page no 93" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "L=0.5*10**-8\n", "\n", "#Calculation\n", "import math\n", "w=math.sin(10*3.14/180.0)*L/(math.cos(10*3.14/180.0)*(3/(60.0*60.0))*(math.pi/180.0))\n", "W=w+L\n", "N=W/(L*2)\n", "N1=(N*2*w)/(L*2)\n", "\n", "#Result\n", "print\"Minimum grating is\", round(w*10**5,0)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Minimum grating is 6.0\n" ] } ], "prompt_number": 60 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.24 Page no 94" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "w=5000 #A\n", "N=30000\n", "n=2.0\n", "\n", "#Calculation\n", "W=w/(n*N)\n", "\n", "#Result\n", "print\"Smallest wavelength separation is\", round(W,3),\"A\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Smallest wavelength separation is 0.083 A\n" ] } ], "prompt_number": 64 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.25 Page no 95" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "f =50 #focal length of convex lens in cm\n", "w=5*10**-5 #wavelength used in cm\n", "n =1\n", "\n", "#Calculation\n", "import math\n", "r= math.sqrt (n*f*w)\n", "\n", "#Result\n", "print\"Radius is\",r,\"cm\"\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Radius is 0.05 cm\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.26 Page no 95" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "d =0.2 #diameter of ring\n", "n =1\n", "w=5*10**-5\n", "\n", "#Calculation\n", "r=d/2.0\n", "f=(r**2) /(w*n)\n", "\n", "#Result\n", "print\"Position of brightest spot is\",f,\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Position of brightest spot is 200.0 cm\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.27 Page no 95" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "f =1 #focal length in m\n", "n =1\n", "w =5893*10**-10\n", "n1 =3\n", "n2=5\n", "\n", "#Calculation\n", "r= math.sqrt (n*f*w)\n", "r1= math.sqrt (n1*f*w)\n", "r2= math.sqrt (n2*f*w)\n", "\n", "#Result\n", "print\"Radius is\",round(r*10**4,2),\"*10**-4 m,\",round(r1*10**3,3),\"*10**-3 m,\",round(r2*10**3,3),\"*10**-3 m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Radius is 7.68 *10**-4 m, 1.33 *10**-3 m, 1.717 *10**-3 m\n" ] } ], "prompt_number": 72 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.28 Page no 95" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "f1=8\n", "w1=6000*10**-8\n", "w2=4800.0*10**-8\n", "\n", "#Calculation\n", "f2=f1*w1/w2\n", "\n", "#Result\n", "print\"Focal length is\",f2,\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Focal length is 10.0 cm\n" ] } ], "prompt_number": 76 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.29 Page no 95" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "n=1\n", "\n", "#Calculation\n", "f1=n\n", "\n", "#Result\n", "print\"Principal focal length is\",f1,\"cm\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Principal focal length is 1 cm\n" ] } ], "prompt_number": 78 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.30 Page no 96" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#Given\n", "r =200 #radius of curvature in cm\n", "\n", "#Calculation\n", "f=r\n", "\n", "#Result\n", "print\"Principle focal length is\",f*10**-2,\"m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Principle focal length is 2.0 m\n" ] } ], "prompt_number": 74 } ], "metadata": {} } ] }