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diff --git a/Applied_Physics-II/chapter2.ipynb b/Applied_Physics-II/chapter2.ipynb new file mode 100755 index 00000000..6af9170f --- /dev/null +++ b/Applied_Physics-II/chapter2.ipynb @@ -0,0 +1,1480 @@ +{ + "metadata": { + "celltoolbar": "Raw Cell Format", + "name": "", + "signature": "sha256:1b2e4fb9c2f216cbf762800ac72003e90570cd62834a70860272dd5120eea60f" + }, + "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 number 2-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=4 #order\n", + "N=1./5000*10**-2 #N=(a+b) grating element(cm)\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "#for longest wavelength, sin(theta)=1\n", + "lamda=(N/m) #longest wavelength\n", + "print\"The longest wavelength is =\" ,lamda,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The longest wavelength is = 5e-07 m\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.2,Page number 2-30" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1 #order\n", + "lamda=6.5*10**-7 #Wavelength of red light\n", + "theta=30*3.142/180 #angle of diffraction\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, a*sin(theta)=m*lamda\n", + "a=m*lamda/math.sin(theta) #width of slit\n", + "print\"width of slit is = \",a,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "width of slit is = 1.29984715296e-06 m\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.3,Page number 2-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1 #order\n", + "lamda=4*10**-7 #Wavelength of light\n", + "a=10**-6 #width of slit\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, a*sin(theta)=m*lamda\n", + "theta=math.asin(m*lamda/a)*180/3.142 #angular position in first minima\n", + "print\"angular position in first minima is =\",theta,\"degrees\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "angular position in first minima is = 23.5751216716 degrees\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.4,Page number 2-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1 #order\n", + "lamda1=4*10**-7 #Wavelength of light\n", + "lamda2=7*10**-7 #Wavelength of light\n", + "n=1./6000*10**-2 #n=(a+b) grating element\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "theta1=math.asin(m*lamda1/n)*(180/3.142) #angle of diffraction\n", + "theta2=math.asin(m*lamda2/n)*(180/3.142) #angle of diffraction\n", + "d=theta2-theta1 #angular breadth of first order visible spectrum\n", + "print\"angular breadth of first order visible spectrum is = \",d,\"degrees\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "angular breadth of first order visible spectrum is = 10.9466277612 degrees\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.5,Page number 2-31" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1 #order\n", + "lamda=6.56*10**-7 #Wavelength of red light\n", + "theta=18.25*math.pi/180 #angle of diffraction\n", + "W=2*10**-2 #width of grating\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "N=math.sin(theta)/(m*lamda) #N-number of lines per m, N=1/(a+b)\n", + "Tn=N*W #Total number of lines on grating\n", + "print\"Total number of lines on grating is =\",Tn\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total number of lines on grating is = 9547.67702694\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.7,Page number 2-33" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "GE=2.54/15000*10**-2 #GE=(a+b) grating element\n", + "lamda1=4*10**-7 #Wavelength of light\n", + "lamda2=7*10**-7 #Wavelength of light\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "theta11=math.asin(1*lamda1/GE)*180/math.pi #angular position of first minima for lamda1\n", + "theta12=math.asin(2*lamda1/GE)*180/math.pi #angular position of second minima for lamda1\n", + "theta13=math.asin(3*lamda1/GE)*180/math.pi #angular position of third minima for lamda1\n", + "\n", + "theta21=math.asin(1*lamda2/GE)*180/math.pi #angular position of first minima for lamda2\n", + "theta22=math.asin(2*lamda2/GE)*180/math.pi #angular position of second minima for lamda2\n", + "theta23=math.asin(1)*180/math.pi #angular position of third minima for lamda2\n", + "\n", + "print\"Thus the angular position for lamda1 and lamda2 are as follows:\"\n", + "print\"First order:\",theta11,\"degrees\"\n", + "print\"\",theta21,\"degrees --Isolated\"\n", + "\n", + "print\"Second order:\",theta12,\"degrees\"\n", + "print\"\",theta22,\"degrees --Overlap\"\n", + "\n", + "print\"Third order: \",theta13,\"degrees\"\n", + "print\"\",theta23,\" degrees --Overlap \"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Thus the angular position for lamda1 and lamda2 are as follows:\n", + "First order: 13.6635763633 degrees\n", + " 24.4177053663 degrees --Isolated\n", + "Second order: 28.1928605617 degrees\n", + " 55.7685229906 degrees --Overlap\n", + "Third order: 45.1261086702 degrees\n", + " 90.0 degrees --Overlap \n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.8,Page number 2-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "lamda=5.893*10**-7 #Wavelength of light\n", + "d=0.01*10**-2 #width of slit (a=d)\n", + "f=1 #distance between screen and slit\n", + "\n", + "#Calculations:\n", + "x=f*lamda/d #separation between central maxima and first minima\n", + "print\"Separation between central maxima and first minima is = \",x,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + " Separation between central maxima and first minima is = 0.005893 m\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.9,Page number 2-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1 #order\n", + "lamda=6*10**-7 #Wavelength of light\n", + "a=12*10**-7 #width of slit\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, a*sin(theta)=m*lamda\n", + "theta=math.asin(m*lamda/a)*180/math.pi #angular position in first minima\n", + "print\"Half angular width of first maxima is =\",theta,\"Degrees\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Half angular width of first maxima is = 30.0 Degrees\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.10,Page number 2-34" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "lamda=6*10**-7 #Wavelength of light\n", + "a=0.02*10**-2 #width of slit (a=d)\n", + "f=2 #distance between screen and slit\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, a*sin(theta)=m*lamda, here m=1\n", + "theta=math.asin(lamda/a)*180*60/math.pi #angular position in first minima (1 degree=60 minutes)\n", + "print\"Total angular width is =\",2*theta,\"minutes\"\n", + "\n", + "x=f*lamda/a #separation between central maxima and first minima\n", + "print\"Linear width is = \",2*x,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Total angular width is = 20.6265115646 minutes\n", + "Linear width is = 0.012 m\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.11,Page number 2-35" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "a=0.14*10**-3 #width of slit\n", + "n=2 #order\n", + "y=1.6*10**-2 #separation between second dark band and central bright band\n", + "D=2 #distance between screen and slit\n", + "\n", + "#Calculations:\n", + "\n", + "theta=y/D #from diagram \n", + "\n", + "#We know, a*sin(theta)=n*lamda\n", + "#here sin(theta)=theta\n", + "lamda=a*theta/n #wavelength of light\n", + "print\"wavelength of light is =\",lamda,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavelength of light is = 5.6e-07 m\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.13,Page number 2-36" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "lamda=6.328*10**-7 #Wavelength of light\n", + "N=1./6000*10**-2 #N=(a+b) grating element\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, N*sin(theta)=m*lamda\n", + "theta1=math.asin(1*lamda/N)*180/math.pi #angular position in first order maxima,m=1\n", + "print\"Angular position in first order maxima is =\",theta1,\"Degrees\"\n", + "\n", + "theta2=math.asin(2*lamda/N)*180/math.pi #angular position in second order maxima,m=2\n", + "print\"Angular position in second order maxima is = \",theta2,\"Degrees\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular position in first order maxima is = 22.3138625335 Degrees\n", + "Angular position in second order maxima is = 49.4078093436 Degrees\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.14,Page number 2-37" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "lamda1=6*10**-7 #wavelength of yellow light\n", + "lamda2=4.8*10**-7 #wavelength of blue light\n", + "theta=(math.asin(3/4)) #angle of diffraction\n", + "\n", + "#Calculations:\n", + "\n", + "#for consecutive bands, n*lamda1=(n+1)*lamda2. thus,\n", + "n=lamda2/(lamda1-lamda2) #order\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "N=n*lamda1/(3./4) #N=(a+b) grating element\n", + "print\"Grating element (a+b) is =\",N,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Grating element (a+b) is = 3.2e-06 m\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.15.1,Page number 2-54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "a=0.2*10**-3 #width of slit\n", + "n=1 #order\n", + "y=0.5*10**-2 #separation between first minima and central bright band\n", + "D=2 #distance between screen and slit\n", + "\n", + "#Calculations:\n", + "\n", + "theta=y/D #from diagram \n", + "\n", + "#We know, a*sin(theta)=n*lamda\n", + "#here sin(theta)=theta\n", + "lamda=a*theta/n #wavelength of light\n", + "print\"wavelength of light is = \",lamda,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "wavelength of light is = 5e-07 m\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.15.2,Page number 2-55" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "lamda1=5.4*10**-7 #Wavelength of light\n", + "lamda2=4.05*10**-7 #Wavelength of light\n", + "theta=30*math.pi/180 #angle of diffraction\n", + "\n", + "#Calculations:\n", + "#We know, (a+b)*sin(theta)=n*lamda\n", + "#n*lamda1=(n+1)*lamda2, we get \n", + "n=3\n", + "N=math.sin(theta)/(n*lamda1)*10**-2 #Number of lines per m= 1/(a+b)*10^-2\n", + "print\"Number of lines per cm is = \",N\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of lines per cm is = 3086.41975309\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.15.4,Page number 2-56" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "GE=1./6000*10**-2 #GE=(a+b) grating element\n", + "lamda1=5.893*10**-7 #Wavelength of light\n", + "lamda2=5.896*10**-7 #Wavelength of light\n", + "m=2 #order\n", + "\n", + "#Calculations:\n", + "theta1=math.asin(m*lamda1/GE)*180/math.pi #angular position in first minima\n", + "theta2=math.asin(m*lamda2/GE)*180/math.pi #angular position in second minima\n", + "\n", + "a_s=(theta2-theta1) #Angular separation in minutes\n", + "print\"Angular separation is =\",a_s,\"Degrees\"\n", + "\n", + "dlamda=lamda2-lamda1 #difference in wavelength\n", + "lamda=(lamda2+lamda1)/2 #Mean wavelength\n", + "\n", + "#We know that R.P.=lamda/dlamda=m*N\n", + "N=lamda/dlamda/m #Number of lines on grating for first order\n", + "print\"Number of lines on grating for first order is =\",N\n", + "print\"But, number of lines per cm on grating is 6000. \\n Which is greater than number of lines per cm needed for resolution.\"\n", + "print\"Hence, both lines will be well resolved in 2nd order.\"\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular separation is = 0.0291798772234 Degrees\n", + "Number of lines on grating for first order is = 982.416666667\n", + "But, number of lines per cm on grating is 6000. \n", + " Which is greater than number of lines per cm needed for resolution.\n", + "Hence, both lines will be well resolved in 2nd order.\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.17,Page number 2-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "d=0.04*10**-2 #Separation between slits\n", + "D=1.7 #distance between screen and slit\n", + "B=0.25*10**-2 #Fringe spacing\n", + "\n", + "#Calculations:\n", + "#We know,B=D*lamda/d\n", + "lamda=B*d/D #Wavelength of light\n", + "print\"Wavelength of light is = \",lamda,\"m\"\n", + "\n", + "#The condition for missing order is,\n", + "#(a+b)/a = m/n\n", + "b=0.04*10**-2 #Separation in slits\n", + "a=0.08*10**-3 #Slit width\n", + "n=(a+b)/a #missing orders for m=1,2,3\n", + "\n", + "n1=1*n\n", + "n2=2*n\n", + "n3=3*n\n", + "print\"Missing orders are =\",n1,\",\",n2,\",\",n3\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Wavelength of light is = 5.88235294118e-07 m\n", + "Missing orders are = 6.0 , 12.0 , 18.0\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.18,Page number 2-39" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "N=2.54/2620*10**-2 #N=(a+b) grating element\n", + "lamda=5*10**-7 #Wavelength of red light\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=n*lamda\n", + "#maximum value of sin(theta)=1\n", + "n=N/lamda #Maximum number of orders visible\n", + "print\"Maximum number of orders visible is =\",n\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum number of orders visible is = 19.3893129771\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.19,Page number 2-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "N=1./4000*10**-2 #N=(a+b) grating element\n", + "lamda1=5*10**-7 #Wavelength of light\n", + "lamda2=7.5*10**-7 #Wavelength of light\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=n*lamda\n", + "#maximum value of sin(theta)=1\n", + "n1=N/lamda1 #Maximum number of orders visible\n", + "n2=N/lamda2 #Maximum number of orders visible\n", + "print\"The observed number of orders range between =\",n2,\"to\",n1\n", + "\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The observed number of orders range between = 3.33333333333 to 5.0\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.20,Page number 2-40" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "n=5 #order\n", + "lamda=6*10**-7 #Wavelength of light\n", + "\n", + "#Calculations:\n", + "#We know, a*sin(theta)=n*lamda\n", + "#n*lamda=n1*lamda1\n", + "lamda1=n*lamda/4 #for n1=4\n", + "print\"For n1=4 wavelength is =\",lamda1,\"m\"\n", + "\n", + "lamda2=n*lamda/5 #for n1=5\n", + "print\"For n1=5 wavelength is =\",lamda2,\"m\"\n", + "\n", + "lamda3=n*lamda/6 #for n1=6\n", + "print\"For n1=5 wavelength is =\",lamda3,\"m\"\n", + "\n", + "lamda4=n*lamda/7 #for n1=7\n", + "print\"For n1=5 wavelength is =\",lamda4,\"m\"\n", + "\n", + "lamda5=n*lamda/8 #for n1=8\n", + "print\"For n1=5 wavelength is =\",lamda5,\"m\"\n", + "\n", + "\n", + "print\"So,in the grating spectrum spectrum lines with wavelengths n1=6 and n1=7 will coincide with fifth order line of 6*10^-7 m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "For n1=4 wavelength is = 7.5e-07 m\n", + "For n1=5 wavelength is = 6e-07 m\n", + "For n1=5 wavelength is = 5e-07 m\n", + "For n1=5 wavelength is = 4.28571428571e-07 m\n", + "For n1=5 wavelength is = 3.75e-07 m\n", + "So,in the grating spectrum spectrum lines with wavelengths n1=6 and n1=7 will coincide with fifth order line of 6*10^-7 m\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.21,Page number 2-41" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "GE=18000*10**-10 #GE=(a+b) grating element\n", + "lamda=5*10**-7 #Wavelength of red light\n", + "\n", + "#Calculations:\n", + "DP1=1./sqrt(GE**2-lamda**2)*10**-10 #Dispersive power\n", + "print\"Dispersive power for first order is =\",DP1,\"rad/Angstrom\"\n", + "\n", + "m=3\n", + "DP2=1/sqrt((GE/m)**2-lamda**2)*10**-10 #Dispersive power\n", + "print\"Dispersive power for second order is =\",DP2,\"rad/Angstrom\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Dispersive power for first order is = 5.78314931966e-05 rad/Angstrom\n", + "Dispersive power for second order is = 0.000301511344578 rad/Angstrom\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.22,Page number 2-42" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "N=2.54/15000*10**-2 #N=(a+b) grating element\n", + "lamda=5.9*10**-7 #Wavelength of light\n", + "m=2 #order\n", + "f=25*10**-2 #focal length of lens\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "theta=math.asin(m*lamda/N) #angular position in first minima\n", + "\n", + "Ad=m/N/cos(theta) #angular dispersion\n", + "\n", + "ld=f*Ad*10**-8 #linear dispersion (dx/dl) in cm/angstrom\n", + "print\"Linear dispersion in spectrograph is =\",ld,\"cm/angstrom\"\n", + "\n", + "dlamda=(5896-5890) #difference in wavelength\n", + "dx=ld*dlamda*10**-2 #separation between spectral lines in meter\n", + "print\"Separation between spectral lines is =\",dx,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Linear dispersion in spectrograph is = 0.00411696586101 cm/angstrom\n", + "Separation between spectral lines is = 0.00024701795166 m\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.23,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1 #order\n", + "lamda1=5.89*10**-7 #Wavelength of light\n", + "lamda2=5.896*10**-7 #Wavelength of light\n", + "\n", + "#Calculations:\n", + "dlamda=lamda2-lamda1 #difference in wavelength\n", + "lamda=(lamda2+lamda1)/2 #Mean wavelength\n", + "\n", + "#We know that R.P.=m*N=lamda/dlamda\n", + "N=lamda/dlamda/m #minimum number of lines which will just resolve\n", + "print\"Minimum number of lines which will just resolve is =\",N\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Minimum number of lines which will just resolve is = 982.166666667\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.24,Page number 2-47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "N=5*5000 #N=W/(a+b) Number of lines on grating\n", + "m=2 #order\n", + "lamda=6*10**-7 #Wavelength of light\n", + "\n", + "#Calculations:\n", + "#(i)\n", + "RP=m*N #Resolving power\n", + "print\"(i)Resolving power is =\",RP\n", + "\n", + "#(ii)\n", + "#We know that R.P.=lamda/dlamda\n", + "dlamda=lamda/RP #Smallest wavelength which can be resolved\n", + "print\"(ii)Smallest wavelength which can be resolved is =\",dlamda,\"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i)Resolving power is = 50000\n", + "(ii)Smallest wavelength which can be resolved is = 1.2e-11 m\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.25,Page number 2-48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "GE=1./4000*10**-2 #GE=(a+b) grating element\n", + "lamda=5*10**-7 #Wavelength of red light\n", + "m=3 #order\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "theta=math.asin(m*lamda/GE) #ngular position in first minima\n", + "\n", + "DP=m/(GE*math.cos(theta))*10**-2 #Dispersive power\n", + "print\"Dispersive power is =\",DP\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Dispersive power is = 15000.0\n" + ] + } + ], + "prompt_number": 22 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.26,Page number 2-48" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=2 #order\n", + "lamda=6*10**-7 #Wavelength of light\n", + "dlamda=6*10**-10 #difference in wavelength\n", + "W=2*10**-2 #Width of surface\n", + "\n", + "#Calculations:\n", + "\n", + "#We know that R.P.=lamda/dlamda=m*N\n", + "N=lamda/dlamda/m #Number of lines on grating\n", + "GE=W/N #Grating element=(a+b)\n", + "print\"Grating element is =\",GE,\"cm\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Grating element is = 4e-05 cm\n" + ] + } + ], + "prompt_number": 23 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.27,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=2 #order\n", + "lamda1=5.77*10**-7 #Wavelength of light\n", + "lamda2=5.791*10**-7 #Wavelength of light\n", + "GE=1./6000*10**-2 #GE=(a+b) grating element\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "theta1=math.asin(m*lamda1/GE)*180/math.pi #angular position in first minima\n", + "theta2=math.asin(m*lamda2/GE)*180/math.pi #angular position in second minima\n", + "\n", + "a_s=(theta2-theta1)*60 #Angular separation in minutes\n", + "print\"Angular separation is = \",a_s,\"minutes\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular separation is = 12.0270825521 minutes\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.28,Page number 2-49" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "n=1 #order\n", + "lam=5.89*10**-7 #Wavelength of light\n", + "a=0.3*10**-3 #width of slit\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, a*sin(theta)=n*lamda\n", + "theta1=math.asin(n*lamda/a)*180/math.pi*60 #angular position in first dark band in minutes\n", + "print\"Angular position in first dark band is = \",theta1,\"mimutes\"\n", + "\n", + "#We know,for bright band a*sin(theta)=(2n+1)*lamda/2\n", + "theta2=math.asin(1.5*lamda/a)*180/math.pi*60 #angular position in first bright band in minutes\n", + "print\"Angular position in first bright band is =\",theta2,\"minutes\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular position in first dark band is = 6.87549812524 mimutes\n", + "Angular position in first bright band is = 10.3132557823 minutes\n" + ] + } + ], + "prompt_number": 26 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.29,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "GE=2.54/16000*10**-2 #GE=(a+b) grating element\n", + "lamda=6*10**-7 #Wavelength of light\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "#maximum value of sin(theta)=1\n", + "m=GE/lamda #Maximum order of spectra\n", + "print\"Maximum order of spectra is =\",m\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum order of spectra is = 2.64583333333\n" + ] + } + ], + "prompt_number": 28 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.30,Page number 2-50" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "GE=1./5000*10**-2 #GE=(a+b) grating element\n", + "lamda=5.89*10**-7 #Wavelength of light\n", + "N=3*5000 #N=W/(a+b) Number of lines on grating\n", + " \n", + "#Calculations:\n", + "\n", + "#We know, (a+b)*sin(theta)=m*lamda\n", + "#maximum value of sin(theta)=1\n", + "m=GE/lamda #Maximum order of spectra\n", + "print\"Maximum order of spectra is =\",m\n", + "\n", + "RP=3*N #Resolving power (round of m to 3)\n", + "print\"Resolving power is =\",RP\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Maximum order of spectra is = 3.39558573854\n", + "Resolving power is = 45000\n" + ] + } + ], + "prompt_number": 29 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.32,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "lamda1=5.89*10**-7 #Wavelength of light\n", + "lamda2=5.896*10**-7 #Wavelength of light\n", + "\n", + "#Calculations:\n", + "dlamda=lamda2-lamda1 #difference in wavelength\n", + "lamda=(lamda2+lamda1)/2 #Mean wavelength\n", + "\n", + "#(i)\n", + "m1=1 #first order\n", + "#We know that R.P.=lamda/dlamda=m*N\n", + "N1=lamda/dlamda/m1 #Number of lines on grating\n", + "print\"(i)Number of lines on grating for first order is =\",N1\n", + "\n", + "#(ii)\n", + "m2=2 #second order\n", + "#We know that R.P.=lamda/dlamda=m*N\n", + "N2=lamda/dlamda/m2 #Number of lines on grating\n", + "print\"(ii)Number of lines on grating for second order is =\",N2\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "(i)Number of lines on grating for first order is = 982.166666667\n", + "(ii)Number of lines on grating for second order is = 491.083333333\n" + ] + } + ], + "prompt_number": 30 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.33,Page number 2-52" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "m=1 #order\n", + "lamda=6.553*10**-7 #Wavelength of light\n", + "dlamda=1.8*10**-10 #difference in wavelength\n", + "\n", + "\n", + "#Calculations:\n", + "\n", + "#We know that R.P.=lam/dlam=m*N\n", + "N=lamda/dlamda/m #Number of lines on grating\n", + "print\"Number of lines on grating is =\",N\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of lines on grating is = 3640.55555556\n" + ] + } + ], + "prompt_number": 31 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.34,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "lamda1=5.14034*10**-7 #Wavelength of light\n", + "lamda2=5.14085*10**-7 #Wavelength of light\n", + "\n", + "#Calculations:\n", + "dlamda=lamda2-lamda1 #difference in wavelength\n", + "lamda=(lamda2+lamda1)/2 #Mean wavelength\n", + "\n", + "#We know that R.P.=lamda/dlamda=m*N\n", + "N=lamda/dlamda/1 #Number of lines on grating\n", + "print\"Number of lines on grating for first order is =\",N\n", + "\n", + "#Hence R.P. for second order should be\n", + "RP1=2*N\n", + "print\"Resolving power in second order should be is= \",RP1\n", + "\n", + "#But here,\n", + "\n", + "lamda3=8.03720*10**-7 #Wavelength of light\n", + "lamda4=8.03750*10**-7 #Wavelength of light\n", + "dlamda2=lamda4-lamda3 #difference in wavelength\n", + "lamda2=(lamda4+lamda3)/2 #Mean wavelength\n", + "\n", + "RP2=lamda2/dlamda2\n", + "print\"Resolving power in second order is= \",RP2\n", + "\n", + "print\"So, the grating will not be able to resolve 8.0372*10^-7 and 8.03750*10^-7 in second order.\"\n", + "print\"Because Resolving power is greter than actual Resolving power.\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Number of lines on grating for first order is = 10079.5980392\n", + "Resolving power in second order should be is= 20159.1960784\n", + "Resolving power in second order is= 26791.1666667\n", + "So, the grating will not be able to resolve 8.0372*10^-7 and 8.03750*10^-7 in second order.\n", + "Because Resolving power is greter than actual Resolving power.\n" + ] + } + ], + "prompt_number": 32 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.35,Page number 2-53" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#For grating , Condition of maxima is (a+b)sin(theta)=n*lamda\n", + "#Given (a+b) < 2*lamda\n", + "#For maximum order, sin(90)=1\n", + "#So, n must be less than 2\n", + "#i.e. only first order possible if width of grating element is less than twice the wavelength\n", + "print\"Hence, Only first order possible if width of grating element is less than twice the wavelength.\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Hence, Only first order possible if width of grating element is less than twice the wavelength.\n" + ] + } + ], + "prompt_number": 33 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example 2.36,Page number 2-54" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "import math\n", + "\n", + "#Given Data:\n", + "n=1 #order\n", + "lamda=5.89*10**-7 #Wavelength of light\n", + "a=0.3*10**-3 #width of slit\n", + "\n", + "#Calculations:\n", + "\n", + "#We know, a*sin(theta)=n*lamda\n", + "theta1=math.asin(n*lam/a)*180/math.pi #angular position in first dark band\n", + "print\"Angular position in first dark band is =\",theta1,\"Degrees\"\n", + "\n", + "#We know,for bright band a*sin(theta)=(2n+1)*lamda/2\n", + "theta2=math.asin(1.5*lamda/a)*180/math.pi #angular position in first bright band\n", + "print\"Angular position in first bright band is =\",theta2,\"Degrees\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Angular position in first dark band is = 0.112490786047 Degrees\n", + "Angular position in first bright band is = 0.168736314576 Degrees\n" + ] + } + ], + "prompt_number": 35 + } + ], + "metadata": {} + } + ] +}
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