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diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter3_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter3_1.ipynb new file mode 100755 index 00000000..645d7595 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter3_1.ipynb @@ -0,0 +1,476 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:bdc5e7b39dc3529751aa6372cd3db8b0870c9abab4c9b51855fb3bce7de6dc73" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "3: Interference" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.1, Page number 71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "beta = 0.51; #Fringe width(mm)\n", + "d = 2.2; #Distance between the slits(mm)\n", + "D = 2; #Distance between the slits and the screen(m)\n", + "\n", + "#Calculation\n", + "beta = beta*10**-1; #Fringe width(cm)\n", + "d = d*10**-1; #Distance between the slits(cm)\n", + "D=D*10**2; #Distance between the slits and the screen(cm)\n", + "lamda = beta*d/D; #Wavelength of light(cm)\n", + "lamda = lamda*10**8; #Wavelength of light(A)\n", + "\n", + "#Result\n", + "print \"The wavelength of light is\",lamda, \"angstrom\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The wavelength of light is 5610.0 angstrom\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.2, Page number 71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lambda1 = 4250; #First wavelength emitted by source of light(A)\n", + "lambda2 = 5050; #Second wavelength emitted by source of light(A)\n", + "D = 1.5; #Distance between the source and the screen(m)\n", + "d = 0.025; #Distance between the slits(mm)\n", + "n = 3; #Number of fringe from the centre\n", + "\n", + "#Calculation\n", + "lambda1 = lambda1*10**-10; #First wavelength emitted(m)\n", + "lambda2 = lambda2*10**-10; #Second wavelength emitted(m)\n", + "d = d*10**-3; #Distance between the slits(m)\n", + "x3 = n*lambda1*D/d; #Position of third bright fringe due to lambda1(m)\n", + "x3_prime = n*lambda2*D/d; #Position of third bright fringe due to lambda2(m)\n", + "x = x3_prime-x3; #separation between the third bright fringe(m)\n", + "x = x*10**2; #separation between the third bright fringe(cm)\n", + "\n", + "#Result\n", + "print \"The separation between the third bright fringe due to the two wavelengths is\",x, \"cm\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The separation between the third bright fringe due to the two wavelengths is 1.44 cm\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.3, Page number 71" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lamda = 5.5*10**-5; #Wavelength emitted by source of light(cm)\n", + "n = 4; #Number of fringes shifted\n", + "t = 3.9*10**-4; #Thickness of the thin glass sheet(cm)\n", + "\n", + "#Calculation\n", + "mew = (n*lamda/t)+1; #Refractive index of the sheet of glass\n", + "mew = math.ceil(mew*10**4)/10**4; #rounding off the value of v to 4 decimals\n", + "\n", + "#Result\n", + "print \"The refractive index of the sheet of glass is\",mew" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The refractive index of the sheet of glass is 1.5642\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.4, Page number 72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lamda = 5893; #Wavelength of monochromatic lihgt used(A)\n", + "n = 1; #Number of fringe for the least thickness of the film\n", + "cosr = 1; #for normal incidence\n", + "mew = 1.42; #refractive index of the soap film\n", + "\n", + "#Calculation\n", + "#As for constructive interference, \n", + "#2*mew*t*cos(r) = (2*n-1)*lambda/2, solving for t\n", + "t = (2*n-1)*lamda/(4*mew*cosr); #Thickness of the film that appears bright(A)\n", + "#As for destructive interference, \n", + "#2*mu*t*cos(r) = n*lambda, solving for t\n", + "t1 = n*lamda/(2*mew*cosr); #Thickness of the film that appears bright(A)\n", + "\n", + "#Result\n", + "print \"The thickness of the film that appears bright is\",t, \"angstrom\"\n", + "print \"The thickness of the film that appears dark is\",t1, \"angstrom\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The thickness of the film that appears bright is 1037.5 angstrom\n", + "The thickness of the film that appears dark is 2075.0 angstrom\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.5, Page number 72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lamda = 5893; #Wavelength of monochromatic lihgt used(A)\n", + "n = 10; #Number of fringe that are found \n", + "d = 1; #Distance of 10 fringes(cm)\n", + "\n", + "#Calculation\n", + "beta = d/n; #Fringe width(cm)\n", + "lamda = lamda*10**-8; #Wavelength of monochromatic lihgt used(cm)\n", + "theta = lamda/(2*beta); #Angle of the wedge(rad)\n", + "theta = theta*10**4;\n", + "theta = math.ceil(theta*10**4)/10**4; #rounding off the value of theta to 4 decimals\n", + "\n", + "#Result\n", + "print \"The angle of the wedge is\",theta,\"*10**-4 rad\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The angle of the wedge is 2.9465 *10**-4 rad\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.6, Page number 72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "lamda = 5900; #Wavelength of monochromatic lihgt used(A)\n", + "t = 0.010; #Spacer thickness(mm)\n", + "l = 10; #Wedge length(cm)\n", + "\n", + "#Calculation\n", + "t = t*10**-1; #Spacer thickness(cm)\n", + "theta = t/l; #Angle of the wedge(rad)\n", + "lamda = lamda*10**-8; #Wavelength of monochromatic lihgt used(cm)\n", + "beta = lamda/(2*theta); #Fringe width(cm)\n", + "\n", + "#Result\n", + "print \"The separation between consecutive bright fringes is\",beta, \"cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The separation between consecutive bright fringes is 0.295 cm\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.7, Page number 72" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "D4 = 0.4; #Diameter of 4th dark ring(cm)\n", + "D12 = 0.7; #Diameter of 12th dark ring(cm)\n", + "\n", + "#Calculation\n", + "#We have (dn_plus_k**2)-Dn**2 = 4*k*R*lamda\n", + "#D12**2-D4**2 = 32*R*lamda and D20**2-D12**2 = 32*R*lamda for k = 8\n", + "#since RHS are equal, by equating the LHS we get D12**2-D4**2 = D20**2-D12**2\n", + "D20 = math.sqrt((2*D12**2)-D4**2); #Diameter of 20th dark ring(cm)\n", + "D20 = math.ceil(D20*10**4)/10**4; #rounding off the value of D20 to 4 decimals\n", + "\n", + "#Result\n", + "print \"The diameter of 20th dark ring is\",D20, \"cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The diameter of 20th dark ring is 0.9056 cm\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.8, Page number 73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "Dn = 0.30; #Diameter of nth dark ring with air film(cm)\n", + "dn = 0.25; #Diameter of nth dark ring with liquid film(cm)\n", + "\n", + "#Calculation\n", + "mew = (Dn/dn)**2; #Refractive index of the liquid\n", + "\n", + "#Result\n", + "print \"The refractive index of the liquid is\", mew\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The refractive index of the liquid is 1.44\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.9, Page number 73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "x = 0.002945; #Distance through which movable mirror is shifted(cm)\n", + "N = 100; #Number of fringes shifted\n", + "\n", + "#Calculation\n", + "x = x*10**-2; #Distance through which movable mirror is shifted(m)\n", + "lamda = 2*x/N; #Wavelength of light(m)\n", + "lamda = lamda*10**10; #Wavelength of light(A)\n", + "\n", + "#Result\n", + "print \"The wavelength of light is\",lamda, \"angstrom\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The wavelength of light is 5890.0 angstrom\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 3.10, Page number 73" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lambda1 = 5896; #Wavelength of D1 line of sodium(A)\n", + "lambda2 = 5890; #Wavelength of D2 line of sodium(A)\n", + "\n", + "#Calculation\n", + "lamda = (lambda1+lambda2)/2;\n", + "x = (lamda**2)/(2*(lambda1-lambda2)); #Shift in movable mirror of Michelson Interferometer(A)\n", + "x = x*10**-7; #Shift in movable mirror of Michelson Interferometer(mm)\n", + "x = math.ceil(x*10**4)/10**4; #rounding off the value of D20 to 4 decimals\n", + "\n", + "#Result\n", + "print \"The shift in movable mirror is\",x, \"mm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The shift in movable mirror is 0.2894 mm\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
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