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diff --git a/Engineering_Physics_by_Uma_Mukherji/Chapter7.ipynb b/Engineering_Physics_by_Uma_Mukherji/Chapter7.ipynb new file mode 100755 index 00000000..d5043163 --- /dev/null +++ b/Engineering_Physics_by_Uma_Mukherji/Chapter7.ipynb @@ -0,0 +1,680 @@ +{
+ "metadata": {
+ "name": "",
+ "signature": "sha256:faf80c20562ef1fa5d737b0d74b9cf873ec0d412505987698b0fa170ec356db4"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "7: Thin film interference and diffraction"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.1, Page number 158"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "alpha=0.01; #angle(radian)\n",
+ "n=10; #number of fringe\n",
+ "lamda=6000*10**-8; #wavelength(cm)\n",
+ "\n",
+ "#Calculation\n",
+ "#for dark fringe 2*u*t*cos(alpha)=n*lam\n",
+ "#t=xtan(alpha)\n",
+ "x=(n*lamda)/(2*alpha); #distance of 10th fringe from edge of wedge(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"distance of 10th fringe from edge of wedge is\",x,\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "distance of 10th fringe from edge of wedge is 0.03 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.2, Page number 159"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "t=5*10**-5; #thickness of soap film(cm)\n",
+ "u=1.33; \n",
+ "\n",
+ "#Calculation\n",
+ "#for constructive interference of reflected light\n",
+ "#2*u*t*cos(r)=(2*n+1)(lam/2), where n=0,1,2,3\n",
+ "#for normal incidence r=0, cos(r)=1\n",
+ "#for n=0 lamda=lamda1\n",
+ "lamda1=4*u*t; #wavelength for zero order(cm)\n",
+ "#for n=1 lamda=lamda2\n",
+ "lamda2=4*u*t*(1/3); #wavelength for first order(cm)\n",
+ "#for n=2 lamda=lamda3\n",
+ "lamda3=4*u*t*(1/5); #wavelength for second order(cm)\n",
+ "#for n=3 lamda=lamda4\n",
+ "lamda4=4*u*t*(1/7); #wavelength for third order(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"wavelength that is strongly reflected in visible spectrum is\",lamda3*10**8,\"angstrom\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "wavelength that is strongly reflected in visible spectrum is 5320.0 angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.3, Page number 159"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=10; #10th dark ring\n",
+ "D10=0.5; #diameter of ring(cm)\n",
+ "lamda=5000*10**-8; #wavelength of light(cm) \n",
+ "\n",
+ "#Calculation\n",
+ "R=(D10**2)/(4*n*lamda); #radius of curvature of lens(cm)\n",
+ "D50=math.sqrt(4*50*R*lamda); #diameter of 50th dark ring(cm)\n",
+ "r50=D50/2; #radius of 50th dark ring(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"radius of 50th dark ring is\",round(r50,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "radius of 50th dark ring is 0.56 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.4, Page number 160"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "i=45; #angle of incidence(degrees)\n",
+ "mew=1.33; #refractive index\n",
+ "lamda=5000; #wavelength(angstrom)\n",
+ "\n",
+ "#Calculation\n",
+ "i=i*(math.pi/180); #angle of incidence(radian)\n",
+ "sin_r=math.sin(i)/mew; #value of sin(r)\n",
+ "r=math.asin(sin_r); #angle of refraction(radian) \n",
+ "r1=r*(180/math.pi); #angle of refraction(degrees)\n",
+ "#for bright fringe 2*u*t*cos(r)=(2*n+1)(lamda/2)\n",
+ "#for minimum thickness n=0\n",
+ "t=lamda/(4*mew*math.cos(r)); #minimum thickness(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"minimum thickness of film is\",int(t),\"angstrom\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "minimum thickness of film is 1109 angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.5, Page number 160"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=5500*10**-8; #wavelength(cm)\n",
+ "V=0.2; #volume of oil drop(cc)\n",
+ "A=100*100; #surface area(sq.cm)\n",
+ "\n",
+ "#Calculation\n",
+ "#since both reflections occur at surface of denser medium\n",
+ "#condition for brightness for min thickness, n=1\n",
+ "#for normal incidence r=0, cos(r)=1\n",
+ "t=V/A; #thickness of film(cm)\n",
+ "mew0=lamda/(2*t); #refractive index of oil\n",
+ "\n",
+ "#Result\n",
+ "print \"refractive index of oil is\",mew0"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "refractive index of oil is 1.375\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.6, Page number 161"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=6300; #wavelength of light(angstrom)\n",
+ "mew=1.5; #refractive index\n",
+ "n=10;\n",
+ "\n",
+ "#Calculation\n",
+ "#condition for dark 2*u*t=n*lam\n",
+ "#condition for bright 2*u*t=(2*n-1)(lam/2)\n",
+ "#when t=0 n=0 order dark band will come and at edge 10th bright band will come \n",
+ "t=(((2*n)-1)*(lamda))/(4*mew); #thickness of air film(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"thickness of air film is\",t,\"angstrom\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "thickness of air film is 19950.0 angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.7, Page number 161"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "mewg=1.5; #refractive index of glass\n",
+ "mewo=1.3; #refractive index of oil\n",
+ "lamda1=7000; #wavelength(angstrom)\n",
+ "lamda2=5000; #wavelength(angstrom)\n",
+ "r=0; #for nth minimum\n",
+ "\n",
+ "#Calculation\n",
+ "#here reflection occurs both time at surface of denser medium\n",
+ "#condition for distructive interference in reflected side\n",
+ "#2*u*t*cos(r)=(2*n-1)(lam1/2), for nth min.\n",
+ "#2*u*t=(2*n+1)(lam1/2), n=0,1,2,3\n",
+ "#for (n+1)th min.\n",
+ "#2*u*t=(2*(n+1)+1)(lam2/2), n=0,1,2,3\n",
+ "t=(2/(4*mewo))*((lamda1*lamda2)/(lamda1-lamda2)); #thickness of layer(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"thickness of layer is\",int(t),\"angstrom\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "thickness of layer is 6730 angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.8, Page number 162"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "Dn=1.40; #diameter of 10th ring(cm)\n",
+ "D=1.27; #changed diameter(cm)\n",
+ "\n",
+ "#Calculation\n",
+ "#when mew=1\n",
+ "#(Dn^2)=4*n*lam*R=(1.40^2)\n",
+ "#when mew=mew1\n",
+ "#(D^2)=(4*n*lam*R)/u1=(1.27^2)\n",
+ "mewl=((Dn**2)/(D**2)); #refractive index of liquid \n",
+ "\n",
+ "#Result\n",
+ "print \"refractive index of liquid is\",round(mewl,4)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "refractive index of liquid is 1.2152\n"
+ ]
+ }
+ ],
+ "prompt_number": 34
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.9, Page number 162"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "B=0.5; #fringe width(cm)\n",
+ "mew=1.4; #refractive index\n",
+ "\n",
+ "#Calculation\n",
+ "alpha=((math.pi*10)/(60*60*180)); #converting into radian\n",
+ "lamda=2*B*alpha*mew; #wavelength of light(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"wavelength of light used is\",int(lamda*10**8),\"angstrom\"\n",
+ "print \"answer given in the book varies due to rounding off errors\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "wavelength of light used is 6787 angstrom\n",
+ "answer given in the book varies due to rounding off errors\n"
+ ]
+ }
+ ],
+ "prompt_number": 40
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.10, Page number 163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=6000*10**-8; #wavelengh of light(cm)\n",
+ "mew=1.5; #refractive index\n",
+ "\n",
+ "#Calculation\n",
+ "#condition for dark fringe is 2*t=n*lam\n",
+ "#but B=(lam/(2*alpha*u))\n",
+ "#delta_t=alpha*x\n",
+ "delta_t=(10*lamda)/(2*mew); #difference t2-t1(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"difference t2-t1 is\",delta_t,\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "difference t2-t1 is 0.0002 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 41
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.11, Page number 163"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=5890; #wavelength of light(angstrom)\n",
+ "mew=1.5; #refractive index\n",
+ "r=60; #angle of refraction(degrees)\n",
+ "\n",
+ "#Calculation\n",
+ "#condition for dark is 2*mew*t*cos(r)=n*lamda\n",
+ "r=60*(math.pi/180); #angle of refraction(radian)\n",
+ "#for n=1\n",
+ "t=(lamda)/(2*mew*math.cos(r)); #smallest thickness of glass plate(angstrom)\n",
+ "\n",
+ "#Result\n",
+ "print \"smallest thickness of glass plate is\",int(t),\"angstrom\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "smallest thickness of glass plate is 3926 angstrom\n"
+ ]
+ }
+ ],
+ "prompt_number": 43
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.13, Page number 180"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "aplusb=1/1250; #transmission grating(lines/cm)\n",
+ "n=2; #order of spectral line\n",
+ "theta=30; #deviation angle(degrees)\n",
+ "\n",
+ "#Calculation\n",
+ "theta=theta*(math.pi/180); #deviation angle(radian)\n",
+ "#(a+b)sin(theta)=n*lamda\n",
+ "lamda=(aplusb*math.sin(theta))/n; #wavelength of spectral line(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"wavelength of spectral line is\",lamda,\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "wavelength of spectral line is 0.0002 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 45
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.14, Page number 180"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda=5893*10**-8; #wavelength(cm)\n",
+ "aplusb=2.54/2540; #grating(lines/cm)\n",
+ "\n",
+ "#Calculation\n",
+ "#n=nmax, if sin(theta)=1\n",
+ "nmax=(aplusb/lamda); #maximum order\n",
+ "\n",
+ "#Result\n",
+ "print \"maximum order is\",int(nmax)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "maximum order is 16\n"
+ ]
+ }
+ ],
+ "prompt_number": 47
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.15, Page number 180"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "n=2; #second order\n",
+ "aplusb=1/5000; #transmission grating(lines/cm)\n",
+ "lamda=5893*10**-8; #wavelength(cm)\n",
+ "f=30; #focal length(cm)\n",
+ "\n",
+ "#Calculation\n",
+ "dtheta=(2.5*3.14)/(180*60); #change in angular displacement(radian)\n",
+ "#dlamda=((a+b)cos(theta)/n)dtheta\n",
+ "costheta=math.sqrt(1-(((n*lamda)/aplusb)**2));\n",
+ "dlamda=(dtheta*aplusb*costheta)/n; #difference in wavelength(cm)\n",
+ "dl=f*dtheta; #linear separation(cm)\n",
+ "\n",
+ "#Result\n",
+ "print \"difference in wavelength of two yellow lines\",round(dlamda*10**8),\"angstrom\"\n",
+ "print \"linear separation is\",round(dl*10**2,2),\"*10**-2 cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "difference in wavelength of two yellow lines 6.0 angstrom\n",
+ "linear separation is 2.18 *10**-2 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 2,
+ "metadata": {},
+ "source": [
+ "Example number 7.16, Page number 181"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#importing modules\n",
+ "import math\n",
+ "from __future__ import division\n",
+ "\n",
+ "#Variable declaration\n",
+ "lamda1=5400*10**-8; #wavelength1(cm)\n",
+ "lamda2=4050*10**-8; #wavelength(cm)\n",
+ "theta=30; #angle of diffraction(degrees)\n",
+ "\n",
+ "#Calculation\n",
+ "#nth order of lamda1 is superimposed on (n+1)th order of lamda2 for theta=30\n",
+ "#(a+b)sin(30)=n*5400*10^-8=(n+1)*4050*10^-8\n",
+ "n=(lamda2/(lamda1-lamda2)); #nth order\n",
+ "theta=30*(math.pi/180); #angle of diffraction(radian)\n",
+ "N=math.sin(theta)/(n*lamda1); #lines/cm in grating\n",
+ "\n",
+ "#Result\n",
+ "print \"lines/cm in grating is\",int(N),\"lines/cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "lines/cm in grating is 3086 lines/cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 51
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file |