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Diffstat (limited to 'Engineering_Physics_by_G._Aruldhas')
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diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter10_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter10_1.ipynb new file mode 100755 index 00000000..a64ad6b4 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter10_1.ipynb @@ -0,0 +1,300 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:78b8d610d2cc37c12bbe36fc70ba217f440b3e2b1b7e7cbb3aa498d471c77bb0" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "10: Statistical Mechanics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 10.1, Page number 222" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "g1 = 2; #The degeneracy of ground state\n", + "g2 = 8; #The degeneracy of excited state\n", + "delta_E = 10.2; #Energy of excited state above the ground state(eV)\n", + "T = 6000; #Temperature of the state(K)\n", + "\n", + "#Calculation\n", + "D_ratio = g2/g1; #Ratio of degeneracy of states\n", + "x = k*T/e;\n", + "N_ratio = D_ratio*math.exp(-delta_E/x); #Ratio of occupancy of the excited to the ground state\n", + "\n", + "#Result\n", + "print \"The ratio of occupancy of the excited to the ground state is\",N_ratio" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio of occupancy of the excited to the ground state is 1.10167326887e-08\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 10.2, Page number 222" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "a = 10/2;\n", + "#enegy of 10 bosons is E = (10*pi**2*h**2)/(2*m*a**2) = (5*pi**2*h**2)/(m*a**2)\n", + "\n", + "#Result\n", + "print \"enegy of 10 bosons is E = \",int(a),\"(pi**2*h**2)/(m*a**2)\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "enegy of 10 bosons is E = 5 (pi**2*h**2)/(m*a**2)\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 10.3, Page number 223" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "n1=1; #1st level\n", + "n2=2; #2nd level\n", + "n3=3; #3rd level\n", + "n4=4; #4th level\n", + "n5=5; #5th level\n", + "\n", + "#Calculation\n", + "#an energy level can accomodate only 2 fermions. hence there will be 2 fermions in each level\n", + "#thus total ground state energy will be E = (2*E1)+(2*E2)+(2*E3)+(2*E4)+E5\n", + "#let X = ((pi**2)*(h**2)/(2*m*a**2)). E = X*((2*n1**2)+(2*n2**2)+(2*n3**2)+(2*n4**2)+(n5**2))\n", + "A = (2*n1**2)+(2*n2**2)+(2*n3**2)+(2*n4**2)+(n5**2);\n", + "#thus E = A*X\n", + "\n", + "#Result\n", + "print \"the ground state energy of the system is\",A,\"(pi**2)*(h**2)/(2*m*a**2)\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "the ground state energy of the system is 85 (pi**2)*(h**2)/(2*m*a**2)\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 10.4, Page number 223" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "N_A = 6.02*10**23; #Avogadro's number\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "me = 9.1*10**-31; #Mass of electron(kg)\n", + "rho = 10.5; #Density of silver(g/cm)\n", + "m = 108; #Molecular mass of silver(g/mol)\n", + "\n", + "#Calculation\n", + "N_D = rho*N_A/m; #Number density of conduction electrons(per cm**3)\n", + "N_D = N_D*10**6; #Number density of conduction electrons(per m**3)\n", + "E_F = ((h**2)/(8*me))*(3/math.pi*N_D)**(2/3); #fermi energy(J)\n", + "E_F = E_F/e; #fermi energy(eV)\n", + "E_F = math.ceil(E_F*10**2)/10**2; #rounding off the value of E_F to 2 decimals\n", + "\n", + "#Result\n", + "print \"The number density of conduction electrons is\",N_D, \"per metre cube\"\n", + "print \"The Fermi energy of silver is\",E_F, \"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The number density of conduction electrons is 5.85277777778e+28 per metre cube\n", + "The Fermi energy of silver is 5.51 eV\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 10.5, Page number 224" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N_A = 6.02*10**23; #Avogadro's number\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "T = 293; #Temperature of sodium(K)\n", + "E_F = 3.24; #Fermi energy of sodium(eV)\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "\n", + "#Calculation\n", + "C_v = math.pi**2*N_A*k**2*T/(2*E_F*e); #Molar specific heat of sodium(per mole)\n", + "C_v = math.ceil(C_v*10**2)/10**2; #rounding off the value of C_v to 2 decimals\n", + "\n", + "#Result\n", + "print \"The electronic contribution to molar specific heat of sodium is\",C_v, \"per mole\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The electronic contribution to molar specific heat of sodium is 0.32 per mole\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 10.6, Page number 224" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "m = 9.1*10**-31; #Mass of the electron(kg)\n", + "N_D = 18.1*10**28; #Number density of conduction electrons in Al(per metre cube)\n", + "\n", + "#Calculation\n", + "E_F = h**2/(8*m)*(3/math.pi*N_D)**(2/3); #N_D = N/V. Fermi energy of aluminium(J)\n", + "E_F = E_F/e; #Fermi energy of aluminium(eV)\n", + "E_F = math.ceil(E_F*10**3)/10**3; #rounding off the value of E_F to 3 decimals\n", + "Em_0 = 3/5*E_F; #Mean energy of the electron at 0K(eV)\n", + "Em_0 = math.ceil(Em_0*10**3)/10**3; #rounding off the value of Em_0 to 3 decimals\n", + "\n", + "#Result\n", + "print \"The Fermi energy of aluminium is\",E_F, \"eV\"\n", + "print \"The mean energy of the electron is\",Em_0, \"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Fermi energy of aluminium is 11.696 eV\n", + "The mean energy of the electron is 7.018 eV\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter11_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter11_1.ipynb new file mode 100755 index 00000000..d5495309 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter11_1.ipynb @@ -0,0 +1,326 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:ecf05dc207884a73f4d33d07fdee310eee827214d9664476e0cf941cf4d4f512" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "11: Lasers" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 11.1, Page number 249" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "c = 3*10**8; #Speed of light in free space(m/s)\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "T = 300; #Temperature at absolute scale(K)\n", + "lamda1 = 5500; #Wavelength of visible light(A)\n", + "lamda2 = 10**-2; #Wavelength of microwave(m)\n", + "\n", + "#Calculation\n", + "lamda1 = lamda1*10**-10; #Wavelength of visible light(m)\n", + "rate_ratio = math.exp(h*c/(lamda1*k*T))-1; #Ratio of spontaneous emission to stimulated emission\n", + "rate_ratio1 = math.exp(h*c/(lamda2*k*T))-1; #Ratio of spontaneous emission to stimulated emission\n", + "rate_ratio1 = math.ceil(rate_ratio1*10**5)/10**5; #rounding off the value of rate_ratio1 to 5 decimals\n", + "\n", + "#Result\n", + "print \"The ratio of spontaneous emission to stimulated emission for visible region is\",rate_ratio\n", + "print \"The ratio of spontaneous emission to stimulated emission for microwave region is\", rate_ratio1" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio of spontaneous emission to stimulated emission for visible region is 8.19422217477e+37\n", + "The ratio of spontaneous emission to stimulated emission for microwave region is 0.00482\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 11.2, Page number 250" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "c = 3*10**8; #Speed of light in free space(m/s)\n", + "lamda = 690; #Wavelength of laser light(nm)\n", + "E_lower = 30.5; #Energy of lower state(eV)\n", + "\n", + "#Calculation\n", + "lamda = lamda*10**-9; #Wavelength of laser light(m)\n", + "E = h*c/lamda; #Energy of the laser light(J)\n", + "E = E/e; #Energy of the laser light(eV)\n", + "E_ex = E_lower + E; #Energy of excited state of laser system(eV)\n", + "E_ex = math.ceil(E_ex*10**2)/10**2; #rounding off the value of E_ex to 2 decimals\n", + "\n", + "#Result\n", + "print \"The energy of excited state of laser system is\",E_ex, \"eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The energy of excited state of laser system is 32.31 eV\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 11.3, Page number 250" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "\n", + "#Calculation\n", + "#Stimulated Emission = Spontaneous Emission <=> exp(h*f/(k*T))-1 = 1 i.e.\n", + "#f/T = log(2)*k/h = A\n", + "A = np.log(2)*k/h; #Frequency per unit temperature(Hz/K)\n", + "A = A/10**10;\n", + "A = math.ceil(A*10**3)/10**3; #rounding off the value of A to 3 decimals\n", + "\n", + "#Result\n", + "print \"The stimulated emission equals spontaneous emission iff f/T =\",A,\"*10**10 Hz/k\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The stimulated emission equals spontaneous emission iff f/T = 1.444 *10**10 Hz/k\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 11.4, Page number 250" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "lamda = 500; #Wavelength of laser light(nm)\n", + "f = 15; #Focal length of the lens(cm)\n", + "d = 2; #Diameter of the aperture of source(cm)\n", + "P = 5; #Power of the laser(mW)\n", + "\n", + "#Calculation\n", + "P = P*10**-3; #Power of the laser(W)\n", + "lamda = lamda*10**-9; #Wavelength of laser light(m)\n", + "d = d*10**-2; #Diameter of the aperture of source(m)\n", + "f = f*10**-2; #Focal length of the lens(m)\n", + "a = d/2; #Radius of the aperture of source(m)\n", + "A = math.pi*lamda**2*f**2/a**2; #Area of the spot at the focal plane, metre square\n", + "I = P/A; #Intensity at the focus(W/m**2)\n", + "I = I/10**7;\n", + "I = math.ceil(I*10**4)/10**4; #rounding off the value of I to 1 decimal\n", + "\n", + "#Result\n", + "print \"The area of the spot at the focal plane is\",A, \"m**2\"\n", + "print \"The intensity at the focus is\",I,\"*10**7 W/m**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The area of the spot at the focal plane is 1.76714586764e-10 m**2\n", + "The intensity at the focus is 2.8295 *10**7 W/m**2\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 11.5, Page number 251" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "c = 3*10**8; #Speed of light in free space(m/s)\n", + "lamda = 1064; #Wavelength of laser light(nm)\n", + "P = 0.8; #Average power output per laser pulse(W)\n", + "dt = 25; #Pulse width of laser(ms)\n", + "\n", + "#Calculation\n", + "dt = dt*10**-3; #Pulse width of laser(s)\n", + "lamda = lamda*10**-9; #Wavelength of laser light(m)\n", + "E = P*dt; #Energy released per pulse(J)\n", + "E1 = E*10**3;\n", + "N = E/(h*c/lamda); #Number of photons in a pulse\n", + "\n", + "#Result\n", + "print \"The energy released per pulse is\",E1,\"*10**-3 J\"\n", + "print \"The number of photons in a pulse is\", N\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The energy released per pulse is 20.0 *10**-3 J\n", + "The number of photons in a pulse is 1.07053023443e+17\n" + ] + } + ], + "prompt_number": 17 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 11.6, Page number 251" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "lamda = 693; #Wavelength of laser beam(nm)\n", + "D = 3; #Diameter of laser beam(mm)\n", + "d = 300; #Height of a satellite above the surface of earth(km)\n", + "\n", + "#Calculation\n", + "D = D*10**-3; #Diameter of laser beam(m)\n", + "lamda = lamda*10**-9; #Wavelength of laser beam(m)\n", + "d = d*10**3; #Height of a satellite above the surface of earth(m)\n", + "d_theta = 1.22*lamda/D; #Angular spread of laser beam(rad)\n", + "dtheta = d_theta*10**4;\n", + "dtheta = math.ceil(dtheta*10**2)/10**2; #rounding off the value of dtheta to 2 decimals\n", + "a = d_theta*d; #Diameter of the beam on the satellite(m)\n", + "a = math.ceil(a*10)/10; #rounding off the value of a to 1 decimal\n", + "\n", + "#Result\n", + "print \"The height of a satellite above the surface of earth is\",dtheta,\"*10**-4 rad\"\n", + "print \"The diameter of the beam on the satellite is\",a, \"m\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The height of a satellite above the surface of earth is 2.82 *10**-4 rad\n", + "The diameter of the beam on the satellite is 84.6 m\n" + ] + } + ], + "prompt_number": 25 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter12_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter12_1.ipynb new file mode 100755 index 00000000..7fa73024 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter12_1.ipynb @@ -0,0 +1,237 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:aab26783619c45961eca2004893b5ed3a4fe23aa4a44df9efa3d63c5d1ff3388" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "12: Holography and Fibre Optics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 12.1, Page number 271" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "n1 = 1.43; #Refractive index of fibre core\n", + "n2 = 1.4; #Refractive index of fibre cladding\n", + "\n", + "#Calculation\n", + "#As sin (alpha_c) = n2/n1, solving for alpha_c\n", + "alpha_c = math.asin(n2/n1); #Critical angle for optical fibre(rad)\n", + "alpha_c = alpha_c*57.2957795; #Critical angle for optical fibre(degrees)\n", + "alpha_c = math.ceil(alpha_c*10**3)/10**3; #rounding off the value of alpha_c to 3 decimals\n", + "#AS cos(theta_c) = n2/n1, solving for theta_c\n", + "theta_c = math.acos(n2/n1); #Critical propagation angle for optical fibre(rad)\n", + "theta_c = theta_c*57.2957795; #Critical propagation angle for optical fibre(degrees)\n", + "theta_c = math.ceil(theta_c*10**2)/10**2; #rounding off the value of theta_c to 2 decimals\n", + "NA = math.sqrt(n1**2 - n2**2); #Numerical aperture for optical fibre\n", + "NA = math.ceil(NA*10**3)/10**3; #rounding off the value of NA to 3 decimals\n", + "\n", + "#Result\n", + "print \"The critical angle for optical fibre is\",alpha_c, \"degrees\"\n", + "print \"The critical propagation angle for optical fibre is\",theta_c, \"degrees\"\n", + "print \"Numerical aperture for optical fibre is\",NA\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The critical angle for optical fibre is 78.244 degrees\n", + "The critical propagation angle for optical fibre is 11.76 degrees\n", + "Numerical aperture for optical fibre is 0.292\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 12.2, Page number 271" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "n1 = 1.45; #Refractive index of fibre core\n", + "n2 = 1.4; #Refractive index of fibre cladding\n", + "\n", + "#Calculation\n", + "NA = math.sqrt(n1**2 - n2**2); #Numerical aperture for optical fibre\n", + "NA = math.ceil(NA*10**4)/10**4; #rounding off the value of NA to 4 decimals\n", + "#As sin(theta_a) = sqrt(n1^2 - n2^2), solving for theta_a\n", + "theta_a = math.asin(math.sqrt(n1**2 - n2**2)); #Half of acceptance angle of optical fibre(rad)\n", + "theta_a = theta_a*57.2957795; #Half of acceptance angle of optical fibre(degrees)\n", + "theta_accp = 2*theta_a; #Acceptance angle of optical fibre(degrees)\n", + "theta_accp = math.ceil(theta_accp*10**2)/10**2; #rounding off the value of theta_accp to 2 decimals\n", + "Delta = (n1 - n2)/n1; #Relative refractive index difference\n", + "Delta = math.ceil(Delta*10**4)/10**4; #rounding off the value of Delta to 4 decimals\n", + "\n", + "#Result\n", + "print \"Numerical aperture for optical fibre is\", NA\n", + "print \"The acceptance angle of optical fibre is\",theta_accp, \"degrees\"\n", + "print \"Relative refractive index difference is\", Delta\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture for optical fibre is 0.3775\n", + "The acceptance angle of optical fibre is 44.36 degrees\n", + "Relative refractive index difference is 0.0345\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 12.3, Page number 271" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "n1 = 1.55; #Refractive index of fibre core\n", + "n2 = 1.53; #Refractive index of fibre cladding\n", + "n0 = 1.3; #Refractive index of medium\n", + "\n", + "#Calculation\n", + "NA = math.sqrt(n1**2 - n2**2); #Numerical aperture for optical fibre\n", + "NA = math.ceil(NA*10**4)/10**4; #rounding off the value of NA to 4 decimals\n", + "#n0*sin(theta_a) = sqrt(n1^2 - n2^2) = NA, solving for theta_a\n", + "theta_a = math.asin(math.sqrt(n1**2 - n2**2)/n0); #Half of acceptance angle of optical fibre(rad)\n", + "theta_a = theta_a*57.2957795; #Half of acceptance angle of optical fibre(degrees)\n", + "theta_accp = 2*theta_a; #Acceptance angle of optical fibre(degrees)\n", + "\n", + "#Result\n", + "print \"Numerical aperture for step index fibre is\",NA\n", + "print \"The acceptance angle of step index fibre is\",int(theta_accp), \"degrees\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Numerical aperture for step index fibre is 0.2482\n", + "The acceptance angle of step index fibre is 22 degrees\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 12.4, Page number 271 Theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 12.5, Page number 272" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "alpha = 2; #Power loss through optical fibre(dB/km)\n", + "P_in = 500; #Poer input of optical fibre(micro-watt)\n", + "z = 10; #Length of the optical fibre(km)\n", + "\n", + "#Calculation\n", + "#As alpha = 10/z*log10(P_in/P_out), solving for P_out\n", + "P_out = P_in/10**(alpha*z/10); #Output power in fibre optic communication(micro-Watt)\n", + "\n", + "#Result\n", + "print \"The output power in fibre optic communication is\",P_out, \"micro-Watt\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The output power in fibre optic communication is 5.0 micro-Watt\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter13_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter13_1.ipynb new file mode 100755 index 00000000..06b2e844 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter13_1.ipynb @@ -0,0 +1,341 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:23fe0a698ddd73a9b73b082e06aebc62f797877523bf19c5324fc5a8330a2aa8" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "13: Dielectric Properties of Materials" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 13.1, Page number 287" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "epsilon_0 = 8.85*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "R = 0.52; #Radius of hydrogen atom(A)\n", + "n = 9.7*10**26; #Number density of hydrogen(per metre cube)\n", + "\n", + "#Calculation\n", + "R = R*10**-10; #Radius of hydrogen atom(m)\n", + "alpha_e = 4*math.pi*epsilon_0*R**3; #Electronic polarizability of hydrogen atom(Fm**2)\n", + "\n", + "#Result\n", + "print \"The electronic polarizability of hydrogen atom is\", alpha_e, \"Fm**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The electronic polarizability of hydrogen atom is 1.56373503182e-41 Fm**2\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 13.2, Page number 287" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "A = 100; #Area of a plate of parallel plate capacitor(cm**2)\n", + "d = 1; #Distance between the plates of the capacitor(cm)\n", + "V = 100; #Potential applied to the plates of the capacitor(V)\n", + "\n", + "#Calculation\n", + "A= A*10**-4; #Area of a plate of parallel plate capacitor(m**2)\n", + "d = d*10**-2; #Distance between the plates of the capacitor(m)\n", + "C = epsilon_0*A/d; #Capacitance of parallel plate capacitor(F)\n", + "Q = C*V; #Charge on the plates of the capacitor(C)\n", + "\n", + "#Result\n", + "print \"The capacitance of parallel plate capacitor is\",C, \"F\"\n", + "print \"The charge on the plates of the capacitor is\",Q, \"C\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The capacitance of parallel plate capacitor is 8.854e-12 F\n", + "The charge on the plates of the capacitor is 8.854e-10 C\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 13.3, Page number 288" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "epsilon_r = 5.0; #Dielectric constant of the material between the plates of capacitor\n", + "V = 15; #Potential difference applied between the plates of the capacitor(V)\n", + "d = 1.5; #Separation between the plates of the capacitor(mm)\n", + "\n", + "#Calculation\n", + "d = d*10**-3; #Separation between the plates of the capacitor(m)\n", + "#Electric displacement, D = epsilon_0*epsilon_r*E, as E = V/d, so \n", + "D = epsilon_0*epsilon_r*V/d; #Dielectric displacement(C/m**2)\n", + "\n", + "#Result\n", + "print \"The dielectric displacement is\",D, \"C/m**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The dielectric displacement is 4.427e-07 C/m**2\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 13.4, Page number 288" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "N = 3*10**28; #Number density of solid elemental dielectric(atoms/metre cube)\n", + "alpha_e = 10**-40; #Electronic polarizability(Fm**2)\n", + "\n", + "#Calculation\n", + "epsilon_r = 1 + (N*alpha_e/epsilon_0); #Relative dielectric constant of the material\n", + "epsilon_r = math.ceil(epsilon_r*10**3)/10**3; #rounding off the value of epsilon_r to 3 decimals\n", + "\n", + "#Result\n", + "print \"The Relative dielectric constant of the material is\",epsilon_r\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Relative dielectric constant of the material is 1.339\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 13.5, Page number 288" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N_A = 6.02*10**23; #Avogadro's number(per mole)\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "epsilon_r = 3.75; #Relative dielectric constant\n", + "d = 2050; #Density of sulphur(kg/metre cube)\n", + "y = 1/3; #Internal field constant\n", + "M = 32; #Atomic weight of sulphur(g/mol)\n", + "\n", + "#Calculation\n", + "N = N_A*10**3*d/M; #Number density of atoms of sulphur(per metre cube)\n", + "#Lorentz relation for local fields give E_local = E + P/(3*epsilon_0) which gives\n", + "#(epsilon_r - 1)/(epsilon_r + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e\n", + "alpha_e = (epsilon_r - 1)/(epsilon_r + 2)*3*epsilon_0/N; #Electronic polarizability of sulphur(Fm**2)\n", + "\n", + "#Result\n", + "print \"The electronic polarizability of sulphur is\",alpha_e, \"Fm**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The electronic polarizability of sulphur is 3.2940125351e-40 Fm**2\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 13.6, Page number 289" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N = 3*10**28; #Number density of atoms of dielectric material(per metre cube)\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "n = 1.6; #Refractive index of dielectric material\n", + "\n", + "#Calculation\n", + "#As (n^2 - 1)/(n^2 + 2) = N*alpha_e/(3*epsilon_0), solving for alpha_e\n", + "alpha_e = (n**2 - 1)/(n**2 + 2)*3*epsilon_0/N; #Electronic polarizability of dielectric material(Fm**2)\n", + "\n", + "#Result\n", + "print \"The electronic polarizability of dielectric material is\",alpha_e, \"Fm**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The electronic polarizability of dielectric material is 3.029e-40 Fm**2\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 13.7, Page number 289" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "epsilon_r = 4.9; #Absolute relative dielectric constant of material(F/m)\n", + "n = 1.6; #Refractive index of dielectric material\n", + "\n", + "#Calculation\n", + "#As (n^2 - 1)/(n^2 + 2)*(alpha_e + alpha_i)/alpha_e = N*(alpha_e + alpha_i)/(3*epsilon_0) = (epsilon_r - 1)/(epsilon_r + 2)\n", + "#let alpha_ratio = alpha_i/alpha_e\n", + "alpha_ratio = ((epsilon_r - 1)/(epsilon_r + 2)*(n**2 + 2)/(n**2 - 1) - 1)**(-1); #Ratio of electronic polarizability to ionic polarizability\n", + "alpha_ratio = math.ceil(alpha_ratio*10**3)/10**3; #rounding off the value of alpha_ratio to 3 decimals\n", + "\n", + "#Result\n", + "print \"The ratio of electronic polarizability to ionic polarizability is\",alpha_ratio" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The ratio of electronic polarizability to ionic polarizability is 1.534\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter14_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter14_1.ipynb new file mode 100755 index 00000000..63e03042 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter14_1.ipynb @@ -0,0 +1,365 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:396480b86092e159711151589922125e5821f00167a65ea8819e3cd4725bf191" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "14: Magnetic Properties of Materials" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 14.1, Page number 306" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N = 6.02*10**23; #Avogadro's number(per mole)\n", + "A = 56; #Atomic weight of the substance(g/mole)\n", + "d = 7.9; #Density of the substance(g/cm**3)\n", + "m_B = 9.27*10**-24; #Bohr's Magneton(J/T)\n", + "\n", + "#Calculation\n", + "m = 2.2*m_B; #Magnetic moment of substance(J/T)\n", + "n = d*N/A ; #Number of atoms per unit volume of the substance(per cm**3)\n", + "n = n*10**6; #Number of atoms per unit volume of the substance(per m**3)\n", + "M = n*m; #Spontaneous magnetisation of the substance(A/m)\n", + "M = M/10**6;\n", + "M = math.ceil(M*10**3)/10**3; #rounding off the value of M to 3 decimals\n", + "\n", + "#Result\n", + "print \"The spontaneous magnetisation of the substance is\",M,\"*10**6 A/m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The spontaneous magnetisation of the substance is 1.732 *10**6 A/m\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 14.2, Page number 307" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "H = 200; #Field strength to which the ferromagnetic material is subjected(A/m)\n", + "M = 3100; #Magnetisation of the ferromagnetic material(A/m)\n", + "\n", + "#Calculation\n", + "chi = M/H; #Magnetic susceptibility\n", + "mew_r = 1 + chi; #Relative permeability of ferromagnetic material\n", + "\n", + "#Result\n", + "print \"The relative permeability of ferromagnetic material is\",mew_r" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The relative permeability of ferromagnetic material is 16.5\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 14.3, Page number 307" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "H = 300; #Field strength to which the ferromagnetic material is subjected(A/m)\n", + "M = 4400; #Magnetisation of the ferromagnetic material(A/m)\n", + "\n", + "#Calculation\n", + "chi = M/H; #Magnetic susceptibility\n", + "mew_r = 1 + chi; #Relative permeability of ferromagnetic material\n", + "mew_r = math.ceil(mew_r*100)/100; #rounding off the value of mew_r to 2 decimals\n", + "\n", + "#Result\n", + "print \"The relative permeability of ferromagnetic material is\",mew_r\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The relative permeability of ferromagnetic material is 15.67\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 14.4, Page number 307" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "mew_0 = 4*math.pi*10**-7; #Magnetic permeability of free space(Tm/A)\n", + "H = 10000; #Field strength to which the diamagnetic material is subjected(A/m)\n", + "chi = -0.4*10**-5; #Magnetic susceptibility\n", + "\n", + "#Calculation\n", + "M = chi*H; #Magnetisation of the diamagnetic material(A/m)\n", + "B = mew_0*(H + M); #Magnetic flux density of diamagnetic material(T)\n", + "B = math.ceil(B*10**4)/10**4; #rounding off the value of B to 4 decimals\n", + "\n", + "#Result\n", + "print \"The magnetisation of diamagnetic material is\",M, \"A/m\"\n", + "print \"The magnetic flux density of diamagnetic material is\",B, \"T\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The magnetisation of diamagnetic material is -0.04 A/m\n", + "The magnetic flux density of diamagnetic material is 0.0126 T\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 14.5, Page number 307" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "mew_0 = 4*math.pi*10**-7; #Magnetic permeability of free space(Tm/A)\n", + "H = 1.2*10**5; #Field strength to which the diamagnetic material is subjected(A/m)\n", + "chi = -4.2*10**-6; #Magnetic susceptibility\n", + "\n", + "#Calculation\n", + "M = chi*H; #Magnetisation of the diamagnetic material(A/m)\n", + "B = mew_0*(H + M); #Magnetic flux density of diamagnetic material(T)\n", + "B = math.ceil(B*10**3)/10**3; #rounding off the value of B to 3 decimals\n", + "mew_r = M/H + 1; #The relative permeability of diamagnetic material\n", + "mew_r = math.ceil(mew_r*10**6)/10**6; #rounding off the value of mew_r to 6 decimals\n", + "\n", + "#Result\n", + "print \"The magnetisation of diamagnetic material is\",M, \"A/m\"\n", + "print \"The magnetic flux density of diamagnetic material is\",B, \"T\"\n", + "print \"The relative permeability of diamagnetic material is\",mew_r\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The magnetisation of diamagnetic material is -0.504 A/m\n", + "The magnetic flux density of diamagnetic material is 0.151 T\n", + "The relative permeability of diamagnetic material is 0.999996\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 14.6, Page number 308" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "chi = 5.6*10**-6; #Magnetic susceptibility of diamagnetic material\n", + "m = 9.1*10**-31; #Mass of an electron(kg)\n", + "mew_0 = 4*math.pi*10**-7; #Magnetic permeability of free space(Tm/A)\n", + "Z = 1; #Atomic number\n", + "e = 1.6*10**-19; #Electronic charge(C)\n", + "a = 2.53; #Lattice parameter of bcc structure(A)\n", + "\n", + "#Calculation\n", + "a = a*10**-10; #Lattice parameter of bcc structure(m)\n", + "N = 2/a**3; #The number of electrons per unit volume(per metre cube)\n", + "r = math.sqrt(chi*6*m/(mew_0*Z*e**2*N)); #Mean radius of body centered cubic structure(m)\n", + "r = r*10**10; #Mean radius of body centered cubic structure(A)\n", + "r = math.ceil(r*100)/100; #rounding off the value of r to 2 decimals\n", + "\n", + "#Result\n", + "print \"The mean radius of body centered cubic structure is\",r, \"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The mean radius of body centered cubic structure is 0.88 A\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 14.7, Page number 308" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "mew_0 = 4*math.pi*10**-7; #Magnetic permeability of free space(Tm/A)\n", + "N_A = 6.02*10**26; #Avogadro's number(per kmol)\n", + "rho = 4370; #Density of paramegnetic salt(kg/metre cube)\n", + "M = 168.5; #Molecular weight of paramagnetic salt(g/mol)\n", + "T = 27; #Temperature of paramagnetic salt(C)\n", + "H = 2*10**5; #Field strength to which the paramagnetic salt is subjected(A/m)\n", + "mew_B = 9.27*10**-24; #Bohr's magneton(Am**2)\n", + "p = 2; #Number of Bohr magnetons per molecule\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "\n", + "#Calculation\n", + "T = T+273; #Temperature of paramagnetic salt(K)\n", + "N = rho*N_A/M; #Total density of atoms in the paramagnetic salt(per meter cube)\n", + "chi_para = mew_0*N*p**2*mew_B**2/(3*k*T); #Magnetic susceptibility of paramagnetic salt\n", + "chi_para = chi_para*10**4;\n", + "chi_para = math.ceil(chi_para*10**2)/10**2; #rounding off the value of chi_para to 2 decimals\n", + "M = chi*H; #Magnetisation of paramagnetic salt(A/m)\n", + "M = math.ceil(M*10)/10; #rounding off the value of M to 1 decimal\n", + "\n", + "#Result\n", + "print \"The magnetic susceptibility of paramagnetic salt is\",chi_para,\"*10**-4\"\n", + "print \"The magnetisation of paramagnetic salt is\",M, \"A/m\"\n", + "\n", + "#answer for magnetisation is not given in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The magnetic susceptibility of paramagnetic salt is 5.43 *10**-4\n", + "The magnetisation of paramagnetic salt is 1.2 A/m\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter15_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter15_1.ipynb new file mode 100755 index 00000000..7bc435f1 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter15_1.ipynb @@ -0,0 +1,309 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:2292e5def6e87e01b63e6b748e8fe3955bb5676e5121c51dac319cd9531c4833" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "15: Thermal Properties " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 15.1, Page number 323" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "f_D = 64*10**11; #Debye frequency for Al(Hz)\n", + "\n", + "#Calculation\n", + "theta_D = h*f_D/k; #Debye temperature(K)\n", + "theta_D = math.ceil(theta_D*10)/10; #rounding off the value of theta_D to 1 decimal\n", + "\n", + "#Result\n", + "print \"The Debye temperature of aluminium is\",theta_D, \"K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Debye temperature of aluminium is 307.3 K\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 15.2, Page number 323" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "N = 6.02*10**26; #Avogadro's number(per kmol)\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "f_D = 40.5*10**12; #Debye frequency for Al(Hz)\n", + "T = 30; #Temperature of carbon(Ks)\n", + "\n", + "#Calculation\n", + "theta_D = h*f_D/k; #Debye temperature(K)\n", + "C_l = 12/5*math.pi**4*N*k*(T/theta_D)**3; #Lattice specific heat of carbon(J/k-mol/K)\n", + "C_l = math.ceil(C_l*10**3)/10**3; #rounding off the value of C_l to 3 decimals\n", + "\n", + "#Result\n", + "print \"The lattice specific heat of carbon is\",C_l, \"J/k-mol/K\"\n", + "\n", + "#answer given in the book is wrong in the 2nd decimal" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The lattice specific heat of carbon is 7.132 J/k-mol/K\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 15.3, Page number 323" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "theta_E = 1990; #Einstein temperature of Cu(K)\n", + "\n", + "#Calculation\n", + "f_E = k*theta_E/h; #Einstein frequency for Cu(K)\n", + "\n", + "#Result\n", + "print \"The Einstein frequency for Cu is\",f_E, \"Hz\"\n", + "print \"The frequency falls in the near infrared region\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Einstein frequency for Cu is 4.14458194989e+13 Hz\n", + "The frequency falls in the near infrared region\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 15.4, Page number 323" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "N = 6.02*10**23; #Avogadro's number(per mol)\n", + "T = 0.05; #Temperature of Cu(K)\n", + "E_F = 7; #Fermi energy of Cu(eV)\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "theta_D = 348; #Debye temperature of Cu(K)\n", + "\n", + "#Calculation\n", + "C_e = math.pi**2*N*k**2*T/(2*E_F*e); #Electronic heat capacity of Cu(J/mol/K)\n", + "C_V = (12/5)*math.pi**4*(N*k)*(T/theta_D)**3; #Lattice heat capacity of Cu(J/mol/K)\n", + "\n", + "#Result\n", + "print \"The electronic heat capacity of Cu is\",C_e, \"J/mol/K\"\n", + "print \"The lattice heat capacity of Cu is\",C_V, \"J/mol/K\"\n", + "\n", + "#answer for lattice heat capacity given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The electronic heat capacity of Cu is 2.52566877726e-05 J/mol/K\n", + "The lattice heat capacity of Cu is 5.76047891492e-09 J/mol/K\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 15.5, Page number 324" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "T = 1; #For simplicity assume temperature to be unity(K)\n", + "R = 1; #For simplicity assume molar gas constant to be unity(J/mol/K)\n", + "theta_E = T; #Einstein temperature(K)\n", + "\n", + "#Calculation\n", + "C_V = 3*R*(theta_E/T)**2*math.exp(theta_E/T)/(math.exp(theta_E/T)-1)**2; #Einstein lattice specific heat(J/mol/K)\n", + "C_V = C_V/3;\n", + "C_V = math.ceil(C_V*10**3)/10**3; #rounding off the value of C_V to 3 decimals\n", + "\n", + "#Result\n", + "print \"The Einstein lattice specific heat is\",C_V, \"X 3R\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Einstein lattice specific heat is 0.921 X 3R\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 15.6, Page number 324" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "v = 2; #Valency of Zn atom\n", + "N = v*6.02*10**23; #Avogadro's number(per mol)\n", + "T = 300; #Temperature of Zn(K)\n", + "E_F = 9.38; #Fermi energy of Zn(eV)\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "\n", + "#Calculation\n", + "N = v*6.02*10**23; #Avogadro's number(per mol)\n", + "C_e = math.pi**2*N*k**2*T/(2*E_F*e); #Electronic heat capacity of Zn(J/mol/K)\n", + "C_e = math.ceil(C_e*10**4)/10**4; #rounding off the value of C_e to 4 decimals\n", + "\n", + "#Result\n", + "print \"The molar electronic heat capacity of zinc is\",C_e, \"J/mol/K\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The molar electronic heat capacity of zinc is 0.2262 J/mol/K\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter17_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter17_1.ipynb new file mode 100755 index 00000000..891f2d43 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter17_1.ipynb @@ -0,0 +1,76 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:d4400dbe9ddae05e5ab81173c9df50e2e9dde25edf961941bd9c8dc15f5a6fe1" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "17: Ultrasonics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 17.1, Page number 352" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "f = 3; #Fundamental vibrational frequency of quartz crystal(MHz)\n", + "Y = 7.9*10**10; #Young's modulus of quartz(N/m**2)\n", + "rho = 2650; #Density of quartz(kg/m**3)\n", + "\n", + "#Calculation\n", + "f = f*10**6; #Fundamental vibrational frequency of quartz crystal(Hz)\n", + "l = 1/(2*f)*math.sqrt(Y/rho); #Thickness of vibrating quartz at resonance(m)\n", + "l = l*10**3; #Thickness of vibrating quartz at resonance(mm)\n", + "l = math.ceil(l*100)/100; #rounding off the value of l to 2 decimals\n", + "\n", + "#Result\n", + "print \"The thickness of vibrating quartz at resonance is\",l, \"mm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The thickness of vibrating quartz at resonance is 0.91 mm\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter18_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter18_1.ipynb new file mode 100755 index 00000000..553fe50f --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter18_1.ipynb @@ -0,0 +1,300 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:c2afbaf4a700c8f5f48d1946053d882d86bb1b0270a68b2bbedc639668ea43be" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "18: Acoustics of Buildings" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 18.1, Page number 361" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "r = 200; #Distance of the point of reduction from the source(m)\n", + "I_0 = 10**-12; #Final intensity of sound(W/m**2)\n", + "I_f = 60; #Intensity gain of sound at the point of reduction(dB)\n", + "\n", + "#Calculation\n", + "#As A_I = 10*log10(I/I_0), solving for I\n", + "I = I_0*10**(I_f/10); #Initial Intensity of sound(W/m**2)\n", + "P = 4*math.pi*r**2*I; #Output power of the sound source(W)\n", + "P = math.ceil(P*100)/100; #rounding off the value of P to 2 decimals\n", + "\n", + "#Result\n", + "print \"The output power of the sound source is\",P, \"W\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The output power of the sound source is 0.51 W\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 18.2, Page number 361" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "import numpy as np\n", + "\n", + "#Variable declaration\n", + "I1 = 1; #For simplicity assume first intensity level to be unity(W/m**2)\n", + "\n", + "#Calculation\n", + "I2 = 2*I1; #Intensity level after doubling(W/m**2)\n", + "dA_I = 10*np.log10(I2/I1); #Difference in gain level(dB)\n", + "\n", + "#Result\n", + "print \"The sound intensity level is increased by\",int(dA_I), \"dB\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The sound intensity level is increased by 3 dB\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 18.3, Page number 361" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "V = 8000; #Volume of the hall(m**3)\n", + "T = 1.5; #Reverbration time of the hall(s)\n", + "\n", + "#Calculation\n", + "alpha_s = 0.167*V/T; #Sabine Formula giving total absorption of sound in the hall(OWU)\n", + "alpha_s = math.ceil(alpha_s*10)/10; #rounding off the value of alpha_s to 1 decimal\n", + "\n", + "#Result\n", + "print \"The total absorption of sound in the hall is\",alpha_s, \"OWU\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The total absorption of sound in the hall is 890.7 OWU\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 18.4, Page number 362" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "V = 25*20*8; #Volume of the hall(m**3)\n", + "T = 4; #Reverbration time of the hall(s)\n", + "\n", + "#Calculation\n", + "S = 2*(25*20+25*8+20*8); #Total surface area of the hall(m**2)\n", + "alpha = 0.167*V/(T*S); #Sabine Formule giving total absorption in the hall(OWU)\n", + "alpha = math.ceil(alpha*10**4)/10**4; #rounding off the value of alpha to 4 decimals\n", + "\n", + "#Result\n", + "print \"The average absorption coefficient of the surfaces is\",alpha, \"OWU/m**2\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The average absorption coefficient of the surfaces is 0.0971 OWU/m**2\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 18.5, Page number 362" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "V = 475; #Volume of the hall(m**3)\n", + "A_f = 100; #Area of the floor(m**2)\n", + "A_c = 100; #Area of the ceiling(m**2)\n", + "A_w = 200; #Area of the wall(m**2)\n", + "alpha_w = 0.025; #Absorption coefficients of the wall(OWU/m**2)\n", + "alpha_c = 0.02; #Absorption coefficients of the ceiling(OWU/m**2)\n", + "alpha_f = 0.55; #Absorption coefficients of the floor(OWU/m**2)\n", + "\n", + "#Calculation\n", + "alpha_s = (A_w*alpha_w)+(A_c*alpha_c)+(A_f*alpha_f); \n", + "T = 0.167*V/alpha_s; #Sabine Formula for reverbration time(s)\n", + "T = math.ceil(T*100)/100; #rounding off the value of T to 2 decimals\n", + "\n", + "#Result\n", + "print \"The reverbration time for the hall is\",T, \"s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The reverbration time for the hall is 1.28 s\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 18.6, Page number 362" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "I0 = 1; #For simplicity assume initial sound intensity to be unity(W/m**2)\n", + "A_I1 = 80; #First intensity gain of sound(dB)\n", + "A_I2 = 70; #Second intensity gain of sound(dB)\n", + "\n", + "#Calculation\n", + "#As A_I = 10*log10(I/I_0), solving for I1 and I2\n", + "I1 = 10**(A_I1/10)*I0; #First intensity of sound(W/m**2)\n", + "I2 = 10**(A_I2/10)*I0; #Second intensity of sound(W/m**2)\n", + "I = I1 + I2; #Resultant intensity level of sound(W/m**2)\n", + "A_I = 10*np.log10(I/I0); #Intensity gain of resultant sound(dB)\n", + "A_I = math.ceil(A_I*10**3)/10**3; #rounding off the value of A_I to 3 decimals\n", + "\n", + "#Result\n", + "print \"The intensity gain of resultant sound is\",A_I, \"dB\"\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The intensity gain of resultant sound is 80.414 dB\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter1_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter1_1.ipynb new file mode 100755 index 00000000..7872d7ab --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter1_1.ipynb @@ -0,0 +1,475 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:381979e560591138195a6149a5aa889c9c7e2cfe41c7a482a0ea4bbe4c24f150" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "1: Oscillations and Waves" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.1, Page number 23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#import modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "S=4; #SHM described by a particle(cm)\n", + "x=0; #mean position\n", + "v=12; #velocity at mean position(cm/s)\n", + "\n", + "#Calculation\n", + "A=S/2; #amplitude of motion(cm)\n", + "omega=v/A; #angular frequency(sec-1)\n", + "T=(2*math.pi)/omega; #time period(sec)\n", + "T=math.ceil(T*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print \"time period of motion is\",T, \"sec\"\n", + "print \"time period of motion is pi/3 sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "time period of motion is 1.048 sec\n", + "time period of motion is pi/3 sec\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.2, Page number 23" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#import modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "T=0.1; #time period(sec)\n", + "A=4; #amplitude of motion(cm)\n", + "x=0.2; #distance from mean position(cm)\n", + "\n", + "#Calculation\n", + "omega=(2*math.pi)/T; #angular frequency(sec-1)\n", + "a=(omega**2)*x; #acceleration(cm/sec^2)\n", + "a=math.ceil(a*10**2)/10**2; #rounding off to 2 decimals\n", + "#maximum velocity is when particle is in the mean position\n", + "v_max=omega*A; #maximum velocity(cm/sec)\n", + "v_max=math.ceil(v_max*10**2)/10**2; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print \"acceleration is\",a, \"cm/sec^2\"\n", + "print \"maximum velocity is\",v_max, \"cm/sec\"\n", + "\n", + "#answers given in the book are wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "acceleration is 789.57 cm/sec^2\n", + "maximum velocity is 251.33 cm/sec\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.3, Page number 24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#import modules\n", + "import math\n", + "import numpy as np\n", + "\n", + "#Variable declaration\n", + "A1 = 40; #First amplitude of oscillation(cm)\n", + "An_plus_1 = 4; #Amplitude after 100 oscillations(cm)\n", + "n = 100; #Number of oscillations\n", + "T = 2.5; #Time period of oscillations(s)\n", + "\n", + "#Calculation\n", + "t = T/4; #Time taken to reach the first amplitude from the mean position(s)\n", + "#Now A1 = x0*math.exp(-lambda*t) and An_plus_1 = x0*math.exp(-lambda*(t+nT))\n", + "#A1/An_plus_1 = math.exp(n*lambda*T)\n", + "x=A1/An_plus_1;\n", + "lamda=np.log(x)/(n*T); #Damping constant(per sec)\n", + "lamda=lamda*10**2;\n", + "lamda=math.ceil(lamda*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print \"Damping constant is\",lamda,\"*10**-2 per sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Damping constant is 0.922 *10**-2 per sec\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.4, Page number 24" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#import modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "x1 = 3; #First position of the particle(cm)\n", + "x2 = 4; #Second position of the particle(cm)\n", + "v1 = 16; #Velocity of particle executing SHM at 1st position(cm/s)\n", + "v2 = 12; #Velocity of particle executing SHM at 2nd position (cm/s)\n", + "\n", + "#Calculation\n", + "#As v = omega*sqrt(A**2 - x**2) so\n", + "#(v1/v2)**2=(A**2 - x1**2)/(A**2 - x2**2)\n", + "#RHS gives (A**2-9)/(A**2-16)\n", + "#(v2**2)*(A**2 - x1**2)=(v1**2)*(A**2 - x2**2), on solving we get\n", + "A=math.sqrt((((v1**2)*(x2**2))-((v2**2)*(x1**2)))/((v1**2)-(v2**2))); #amplitude in cm\n", + "omega=v1/math.sqrt(A**2-x1**2); #Angular speed of the particle(per sec)\n", + "T=2*math.pi/omega; #Time period of oscillation(sec)\n", + "T=math.ceil(T*10**3)/10**3; #rounding off to 3 decimals\n", + "\n", + "#Result\n", + "print \"The amplitude of SHM is\",A, \"cm\"\n", + "print \"The time period of oscillation is\",T, \"sec\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The amplitude of SHM is 5.0 cm\n", + "The time period of oscillation is 1.571 sec\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.5, Page number 25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#import modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "m = 0.3; #Mass attached to the string(kg)\n", + "g = 9.8; #Acceleration due to gravity(m/sec**2)\n", + "x = 0.15; #Stretchness produced in the spring(m)\n", + "s = 0.1; #spring is stretched and released(m)\n", + "\n", + "#Calculation\n", + "F = m*g; #Restoring force acting on the mass(N)\n", + "k = F/x; #Spring constant(N/m)\n", + "A = s; #amplitude equals to the spring stretched and released\n", + "omega = math.sqrt(k/m); #Angular frequency of oscillation(rad per sec)\n", + "v0 = omega*A; #Maximum velocity during the oscillations(m/s)\n", + "v0=math.ceil(v0*100)/100; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print \"The spring constant is\",k, \"N/m\"\n", + "print \"The amplitude of oscillation is\",A, \"m\"\n", + "print \"The maximum velocity during oscillations is\",v0, \"m/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The spring constant is 19.6 N/m\n", + "The amplitude of oscillation is 0.1 m\n", + "The maximum velocity during oscillations is 0.81 m/s\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.6, Page number 25" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#import modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lambda1 = 400; #Lower limit of wavelength of visible region(nm)\n", + "lambda2 = 700; #Upper limit of wavelength of visible region(nm)\n", + "c = 3*10**8; #Speed of light in vacuum(m/s)\n", + "\n", + "#Calculation\n", + "lambda1 = lambda1*10**-9 #Lower limit of wavelength(m) \n", + "lambda2 = lambda2*10**-9 #upper limit of wavelength(m) \n", + "new_1 = c/lambda1; #Upper limit of frequency of visible region(m)\n", + "new_2 = c/lambda2; #Lower limit of frequency of visible region(m)\n", + "\n", + "#Result\n", + "print \"The frequency equivalent of 400 nm is\",new_1, \"Hz\"\n", + "print \"The frequency equivalent of 700 nm is\",new_2, \"Hz\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency equivalent of 400 nm is 7.5e+14 Hz\n", + "The frequency equivalent of 700 nm is 4.28571428571e+14 Hz\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.7, Page number 26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#import modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "#Comparing the standard equation u(x,t) = A*sin(2*%pi(x/lambda-t/T)) with the given equation, we get\n", + "A = 1.5*10**-3; #Amplitude of the sound wave(m)\n", + "lamda = 8; #Wavelength of the sound wave(m)\n", + "T = 1/40; #Time period of the sound wave(s)\n", + "\n", + "#Calculation\n", + "A = A*10**3;\n", + "new = 1/T; #Frequency of the sound wave(Hz)\n", + "v = new*lamda; #Velocity of the sound wave(m/s)\n", + "T=math.ceil(T*100)/100; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print \"The amplitude of the sound wave is\",A,\"*10**-3 m\"\n", + "print \"The wavelength of the sound wave is\",lamda, \"m\"\n", + "print \"The time period of the sound wave is\",T, \"s\"\n", + "print \"The frequency of the sound wave is\",new, \"Hz\"\n", + "print \"The velocity of the sound wave is\",v, \"m/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The amplitude of the sound wave is 1.5 *10**-3 m\n", + "The wavelength of the sound wave is 8 m\n", + "The time period of the sound wave is 0.03 s\n", + "The frequency of the sound wave is 40.0 Hz\n", + "The velocity of the sound wave is 320.0 m/s\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.8, Page number 26" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#import modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "A = 2; #Amplitude of the wave(cm)\n", + "T = 0.5; #Time period of the wave(sec)\n", + "v = 200; #Wave velocity(cm/s)\n", + "\n", + "#Calculation\n", + "f = 1/T; #Frequency of the wave(Hz)\n", + "lamda = v/f; #Wavelength of the wave(cm)\n", + "\n", + "#Result\n", + "print \"frequency of wave is\",f, \"Hz\"\n", + "print \"wavelength of wave is\",lamda, \"cm\"\n", + "print \"The Equation of the wave moving along X-axis :\"\n", + "print \"u = \",A,\"*sin*2*math.pi*(x/\",lamda,\"- t/\",T,\")\" #x and y are in cm and t is in sec" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "frequency of wave is 2.0 Hz\n", + "wavelength of wave is 100.0 cm\n", + "The Equation of the wave moving along X-axis :\n", + "u = 2 *sin*2*math.pi*(x/ 100.0 - t/ 0.5 )\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 1.9, Page number 27" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#import modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "T = 1000; #Tension in the wire(N)\n", + "M=15; #mass of the wire(kg)\n", + "l=300; #length of the wire(m)\n", + "lamda = 0.30; #Wavelength of wave along wire(m)\n", + "\n", + "#Calculation\n", + "m = M/l; #Mass per unit length of the wire(kg/m)\n", + "v = math.sqrt(T/m); #Velocity of wave through wire(m/s)\n", + "v=math.ceil(v*100)/100; #rounding off to 2 decimals\n", + "new = v/lamda; #Frequency of wave through string(Hz)\n", + "new=math.ceil(new*100)/100; #rounding off to 2 decimals\n", + "\n", + "#Result\n", + "print \"The velocity of the wave through wire is\",v, \"m/s\"\n", + "print \"The frequency of the wave through wire is\",new, \"Hz\"\n", + "\n", + "#answer for frequency of the wave is wrong in the textbook" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The velocity of the wave through wire is 141.43 m/s\n", + "The frequency of the wave through wire is 471.44 Hz\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter2_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter2_1.ipynb new file mode 100755 index 00000000..fdbf44b5 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter2_1.ipynb @@ -0,0 +1,248 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:de195a4faed398c9714bc27769421926f24c448f7ad7f1d4cb04dd3cfbb18334" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "2: Electromagnetic Theory" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.1, Page number 46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "from sympy import *\n", + "import math\n", + "\n", + "#Variable declaration\n", + "C = 10; #Capacitance of the capacitor(pF)\n", + "#given V=0.2*sin(120*math.pi*t) in volts\n", + "\n", + "#Calculation\n", + "C=C*10**-12; #Capacitance of the capacitor(F)\n", + "x, y, z, t = symbols('x y z t')\n", + "k, m, n = symbols('k m n', integer=True)\n", + "f, g, h = symbols('f g h', cls=Function)\n", + "#I = C*dV/dt\n", + "#let dV/dt be a\n", + "a=diff(0.2*sin(120*math.pi*t),t) #dV/dt\n", + "#value of dV/dt is 75.398223686155*cos(376.991118430775*t)\n", + "#for cosine function peak value occurs when 120*math.pi*t = 0\n", + "#therefore value of dV/dt becomes d = 75.398223686155\n", + "d = 75.398223686155; #value of dV/dt \n", + "I=C*d; #displacement current(A)\n", + "\n", + "#Result\n", + "print \"value of dV/dt is\",a\n", + "print \"displacement current is\",I, \"A\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "value of dV/dt is 75.398223686155*cos(376.991118430775*t)\n", + "displacement current is 7.53982236862e-10 A\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.2, Page number 46" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "from sympy import *\n", + "import math\n", + "\n", + "#Variable declaration\n", + "epsilon_r = 1; #Relative electrical permittivity of free space\n", + "epsilon_0 = 8.854*10**-12; #Absolute electrical permittivity of free space(F/m)\n", + "#given E=sin(120*math.pi*t) in volts\n", + "\n", + "#Calculation\n", + "x, y, z, t = symbols('x y z t')\n", + "k, m, n = symbols('k m n', integer=True)\n", + "f, g, h = symbols('f g h', cls=Function)\n", + "#J2 = epsilon*dE/dt\n", + "epsilon=epsilon_0*epsilon_r;\n", + "#let dE/dt be a\n", + "a=diff(sin(120*math.pi*t),t) #dE/dt\n", + "#value of dE/dt is 376.991118430775*cos(376.991118430775*t)\n", + "#for cosine function peak value occurs when 120*math.pi*t = 0\n", + "#therefore value of dE/dt becomes d = 376.991118430775\n", + "d = 376.991118430775; #value of dE/dt\n", + "J2=epsilon*d; #displacement current density(A/m**2)\n", + "\n", + "#Result\n", + "print \"value of dE/dt is\",a\n", + "print \"The peak value of displacement current density is\",J2, \"A/m**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "value of dE/dt is 376.991118430775*cos(376.991118430775*t)\n", + "The peak value of displacement current density is 3.33787936259e-09 A/m**2\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.3, Page number 47 (Theoritical proof)" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.4, Page number 47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "p = 60; #Power rating of bulb(W)\n", + "d = 0.5; #Distance from the bulb(m)\n", + "\n", + "#Calculation\n", + "A=4*math.pi*d**2; #area(m**2)\n", + "P = p/A; #Value of Poynting vector(W/m**2)\n", + "P = math.ceil(P*100)/100; #rounding off value of P to 1 decimal\n", + "\n", + "#Result\n", + "print \"The value of Poynting vector is\",P, \"W/m**2\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The value of Poynting vector is 19.1 W/m**2\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 2.5, Page number 47" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "E_peak = 6; #Peak value of electric field intensity(V/m)\n", + "c = 3*10**8; #Speed of electromagnetic wave in free space(m/s)\n", + "mew_0 = 4*math.pi*10**-7; #Absolute permeability of free space(Tm/A)\n", + "epsilon_0 = 8.854*10**-12; #Absolute permittivity of free space(F/m)\n", + "mew_r = 1; #Relative permeability of medium\n", + "epsilon_r = 3; #Relative permittivity of the medium\n", + "\n", + "#Calculation\n", + "v = c/math.sqrt(mew_r*epsilon_r); #Wave velocity(m/s)\n", + "v = v/10**8;\n", + "v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals\n", + "eta = math.sqrt((mew_0/epsilon_0)*(mew_r/epsilon_r)); #Intrinsic impedance of the medium(ohm)\n", + "eta = math.ceil(eta*10)/10; #rounding off the value of v to 1 decimal\n", + "H_P = E_peak/eta; #Peak value of the magnetic intensity(A/m)\n", + "H_P = H_P*10**2;\n", + "H_P = math.ceil(H_P*10**2)/10**2; #rounding off the value of v to 2 decimals\n", + "\n", + "#Result\n", + "print \"The wave velocity is\",v,\"*10**8 m/s\"\n", + "print \"The intrinsic impedance of the medium is\",eta, \"ohm\"\n", + "print \"The peak value of the magnetic intensity is\",H_P,\"*10**-2 A/m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The wave velocity is 1.7321 *10**8 m/s\n", + "The intrinsic impedance of the medium is 217.6 ohm\n", + "The peak value of the magnetic intensity is 2.76 *10**-2 A/m\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file 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": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter4_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter4_1.ipynb new file mode 100755 index 00000000..cc3fca78 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter4_1.ipynb @@ -0,0 +1,490 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:3ba769656e990801d788b85df0bb013daae3fbdec7e19bc6ba653a53dfdabcb2" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "4: Diffraction" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.1, Page number 91" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "D = 50; #Distance between source and the screen(cm)\n", + "lamda = 6563; #Wavelength of light of parallel rays(A)\n", + "d = 0.385; #Width of the slit(mm)\n", + "n1 = 1; #Order of diffraction for first minimum\n", + "n2 = 5; #Order of diffraction for fifth minimum\n", + "\n", + "#Calculation\n", + "lamda = lamda*10**-8; #Wavelength of light of parallel rays(cm)\n", + "d = d*10**-1; #Width of the slit(cm)\n", + "#As sin(theta1) = n*lambda/d = x1/D, solving for x1\n", + "x1 = n1*lamda*D/d; #Distance from the centre of the principal maximum to the first minimum(cm)\n", + "x1 = x1*10; #Distance from the centre of the principal maximum to the first minimum(mm)\n", + "x1 = math.ceil(x1*10**3)/10**3; #rounding off the value of x1 to 3 decimals\n", + "x2 = n2*lamda*D/d; #Distance from the centre of the principal maximum to the fifth minimum(cm)\n", + "x2 = x2*10; #Distance from the centre of the principal maximum to the fifth minimum(mm)\n", + "x2 = math.ceil(x2*10**3)/10**3; #rounding off the value of x2 to 3 decimals\n", + "\n", + "#Result\n", + "print \"The Distance from the centre of the principal maximum to the first minimum is\",x1, \"mm\"\n", + "print \"The Distance from the centre of the principal maximum to the fifth minimum is\",x2, \"mm\"\n", + "\n", + "#answer for x2 given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Distance from the centre of the principal maximum to the first minimum is 0.853 mm\n", + "The Distance from the centre of the principal maximum to the fifth minimum is 4.262 mm\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.2, Page number 91" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "D = 0.04; #Diameter of circular aperture(cm)\n", + "f = 20; #Focal length of convex lens(cm)\n", + "lamda = 6000; #Wavelength of light used(A)\n", + "\n", + "#Calculation\n", + "lamda = lamda*10**-8; #Wavelength of light used(cm)\n", + "#We have sin(theta) = 1.22*lambda/D = theta, for small theta\n", + "#For first dark ring\n", + "theta = 1.22*lamda/D; #The half angular width at central maximum(rad)\n", + "r1 = theta*f; #The half width of central maximum for first dark ring(cm)\n", + "r1 = r1*10**2;\n", + "#We have sin(theta) = 5.136*lambda/(%pi*D) = theta, for small theta\n", + "#For second dark ring\n", + "theta = 5.136*lamda/(math.pi*D); #The half angular width at central maximum(rad)\n", + "r2 = theta*f; #The half width of central maximum for second dark ring(cm)\n", + "r2 = r2*10**2;\n", + "r2 = math.ceil(r2*100)/100; #rounding off the value of r2 to 2 decimals\n", + "\n", + "#Result\n", + "print \"The radius of first dark ring is\",r1,\"*10**-2 cm\"\n", + "print \"The radius of second dark ring is\",r2,\"*10**-2 cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The radius of first dark ring is 3.66 *10**-2 cm\n", + "The radius of second dark ring is 4.91 *10**-2 cm\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.3, Page number 92" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "n = 2; #Order of diffraction\n", + "lamda = 650; #Wavelength of light used(nm)\n", + "d = 1.2*10**-3; #Distance between two consecutive slits of grating(cm)\n", + "\n", + "#Calculation\n", + "#We have sin(theta) = n*N*lambda = n*lambda/d, solving for theta\n", + "lamda = lamda*10**-9; #Wavelength of light used(m)\n", + "d = d*10**-2; #Distance between two consecutive slits of grating(m)\n", + "a=n*lamda/d;\n", + "theta = math.asin(a); #Angle at which the 650 nm light produces a second order maximum(rad)\n", + "theta = theta*57.2957795; #angle in degrees\n", + "theta = math.ceil(theta*10**2)/10**2; #rounding off the value of theta to 2 decimals\n", + "\n", + "#Result\n", + "print \"The angle at which the light produces a second order maximum is\",theta, \"degrees\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The angle at which the light produces a second order maximum is 6.22 degrees\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.4, Page number 92" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "lamda = 650; #Wavelength of light used(nm)\n", + "N = 6000; #Number of lines per cm on grating\n", + "theta = 90; #Angle at which the highest spectral order is obtained(degrees)\n", + "\n", + "#Calculation\n", + "theta = theta*0.0174532925; #Angle at which the highest spectral order is obtained(rad)\n", + "#We have sin(theta) = n*N*lambda, solving for n\n", + "lamda = lamda*10**-9; #Wavelength of light used(m)\n", + "N = N*10**2; #Number of lines per m on grating\n", + "n = math.sin(theta)/(N*lamda); #The highest order of spectra with diffraction grating\n", + "n = math.ceil(n*10**3)/10**3; #rounding off the value of theta to 3 decimals\n", + "i,d = divmod(n, 1); #divides the value of n into integer and decimal parts where i is integer\n", + "\n", + "#Result\n", + "print \"value of n is\",n\n", + "print \"The highest order of spectra obtained with diffraction grating is\",i\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "value of n is 2.565\n", + "The highest order of spectra obtained with diffraction grating is 2.0\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.5, Page number 92" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "N = 4000; #Number of lines per cm on grating\n", + "#For Blue Line\n", + "lamda1 = 450; #Wavelength of blue light(nm)\n", + "n1 = 3; #Order of diffraction spectrum\n", + "#For Red Line\n", + "lamda2 = 700; #Wavelength of red light(nm)\n", + "n2 = 2; #Order of diffraction spectrum\n", + "\n", + "#Calculation\n", + "N = N*10**2; #Number of lines per m on grating\n", + "lamda1 = lamda1*10**-9; #Wavelength of blue light(m)\n", + "lamda2 = lamda2*10**-9; #Wavelength of red light(m)\n", + "#We have sin(theta) = n*N*lambda, solving for sin(theta)\n", + "sin_theta_3 = n1*N*lamda1; #Sine of angle at third order diffraction \n", + "sin_theta_2 = n2*N*lamda2; #Sine of angle at second order diffraction\n", + "\n", + "#Result\n", + "print \"Sine of angle at third order diffraction is\",sin_theta_3\n", + "print \"Sine of angle at second order diffraction is\",sin_theta_2 \n", + "#Check for overlapping\n", + "if (sin_theta_2-sin_theta_3)<0.05:\n", + " print \"The two orders overlap\"\n", + "else:\n", + " print \"The two orders do not overlap\" " + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Sine of angle at third order diffraction is 0.54\n", + "Sine of angle at second order diffraction is 0.56\n", + "The two orders overlap\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.6, Page number 93" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "n = 1; #Order of diffraction spectrum\n", + "N = 6000; #Number of lines per cm on diffraction grating\n", + "D = 2; #Distance of screen from the source(m)\n", + "lamda1 = 400; #Wavelength of blue light(nm)\n", + "lamda2 = 750; #Wavelength of blue light(nm)\n", + "\n", + "#Calculation\n", + "N = N*10**2; #Number of lines per m on grating\n", + "lamda1 = lamda1*10**-9; #Wavelength of blue light(m)\n", + "lamda2 = lamda2*10**-9; #Wavelength of blue light(m)\n", + "#We have sin(theta1) = n*N*lamda1, solving for theta1\n", + "theta1 = math.asin(n*N*lamda1); #Angle at first order diffraction for Blue light(rad)\n", + "theta1_d = theta1*57.2957795; #Angle at first order diffraction for Blue light(degrees)\n", + "theta2 = math.asin(n*N*lamda2); #Angle at first order diffraction for Red light(rad)\n", + "theta2_d = theta2*57.2957795; #Angle at first order diffraction for Red light(degrees)\n", + "x1 = D*math.tan(theta1); #Half width position at central maximum for blue color(m)\n", + "x2 = D*math.tan(theta2); #Half width position at central maximum for red color(m)\n", + "x = x2-x1; #width of first order spectrum on the screen(m)\n", + "x = x*10**2; #width of first order spectrum on the screen(cm)\n", + "x = math.ceil(x*10**2)/10**2; #rounding off the value of x to 2 decimals\n", + "\n", + "#Result\n", + "print \"The width of first order spectrum on the screen is\",x, \"cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The width of first order spectrum on the screen is 51.34 cm\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.7, Page number 93" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "w = 5; #Width of the grating(cm)\n", + "N = 32; #Number of lines per mm on grating\n", + "lamda = 640; #Wavelength of light(nm)\n", + "n = 2; #Order of diffraction\n", + "\n", + "#Calculation\n", + "N= N*10; #Number of lines per cm on grating\n", + "N0 = w*N; #Total number of lines on the grating\n", + "d_lambda = lamda/(n*N0); #Separation between wavelengths(nm)\n", + "\n", + "#Result\n", + "print \"The separation between wavelengths which the grating can just resolve is\",d_lambda, \"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The separation between wavelengths which the grating can just resolve is 0.2 nm\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.8, Page number 93" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lamda = 550; #Wavelength of light(nm)\n", + "D = 3.2; #Diameter of circular lens(cm)\n", + "f = 24; #Focal length of the lens(cm) \n", + "\n", + "#Calculation\n", + "lamda = lamda*10**-9; #Wavelength of light(m)\n", + "D = D*10**-2; #Diameter of circular lens(m)\n", + "theta_min = 1.22*lamda/D; #Minimum angle of resolution provided by the lens(rad)\n", + "#As delta_x/f = theta_min, solving for delta_x\n", + "f = f*10**-2; #Focal length of the lens(m) \n", + "delta_x = theta_min*f; #Separation of the centres of the images in the focal plane of lens(m)\n", + "delta_x = delta_x*10**6; #Separation of the centres of the images in the focal plane of lens(micro m)\n", + " \n", + "#Result\n", + "print \"The separation of the centres of the images in the focal plane is\",round(delta_x), \"micro-metre\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The separation of the centres of the images in the focal plane is 5.0 micro-metre\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 4.9, Page number 94" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "lamda = 550; #Wavelength of light(nm)\n", + "D = 20; #Diameter of objective of telescope(cm)\n", + "d = 6; #Distance of two points from the objective of telescope(km)\n", + "\n", + "#Calculation\n", + "lamda = lamda*10**-9; #Wavelength of light(m)\n", + "D = D*10**-2; #Diameter of objective of telescope(m)\n", + "d = d*10**3; #Distance of two points from the objective of telescope(m)\n", + "theta = 1.22*lamda/D; #Angular separation between two points(rad)\n", + "x = theta*d; #Linear separation between two points(m)\n", + "x = x*10**3; #Linear separation between two points(mm)\n", + "\n", + "#Result\n", + "print \"The linear separation between two points is\",x, \"mm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The linear separation between two points is 20.13 mm\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter5_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter5_1.ipynb new file mode 100755 index 00000000..8b5822ee --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter5_1.ipynb @@ -0,0 +1,299 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:d6b4557b658267af4573aff55394c33f7ae58a19c1bc5291838cb933f306de2e" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "5: Polarization" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 5.1, Page number 113" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "mew_g = 1.72; #Refractive index of glass\n", + "mew_w = 4/3; #Refractive index of water\n", + "\n", + "#Calculation\n", + "#For polarization to occur on flint glass, tan(i) = mew_g/mew_w\n", + "#Solving for i\n", + "i_g = math.atan(mew_g/mew_w); #angle of incidence for complete polarization for flint glass(rad)\n", + "a = 180/math.pi; #conversion factor from radians to degrees\n", + "i_g = i_g*a; #angle of incidence(degrees)\n", + "i_g = math.ceil(i_g*10**2)/10**2; #rounding off the value of i_g to 2 decimals\n", + "#For polarization to occur on water, tan(i) = mew_w/mew_g\n", + "#Solving for i\n", + "i_w = math.atan(mew_w/mew_g); #angle of incidence for complete polarization for water(rad)\n", + "i_w = i_w*a; #angle of incidence(degrees)\n", + "i_w = math.ceil(i_w*10**3)/10**3; #rounding off the value of i_w to 3 decimals\n", + "\n", + "#Result\n", + "print \"The angle of incidence for complete polarization to occur on flint glass is\",i_g, \"degrees\"\n", + "print \"The angle of incidence for complete polarization to occur on water is\",i_w, \"degrees\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The angle of incidence for complete polarization to occur on flint glass is 52.22 degrees\n", + "The angle of incidence for complete polarization to occur on water is 37.783 degrees\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 5.2, Page number 113" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "I0 = 1; #For simplicity, we assume the intensity of light falling on the second Nicol prism to be unity(W/m**2)\n", + "theta = 30; #Angle through which the crossed Nicol is rotated(degrees)\n", + "\n", + "#Calculation\n", + "theeta = 90-theta; #angle between the planes of transmission after rotating through 30 degrees\n", + "a = math.pi/180; #conversion factor from degrees to radians\n", + "theeta = theeta*a; ##angle between the planes of transmission(rad)\n", + "I = I0*math.cos(theeta)**2; #Intensity of the emerging light from second Nicol(W/m**2)\n", + "T = (I/(2*I0))*100; #Percentage transmission of incident light\n", + "T = math.ceil(T*100)/100; #rounding off the value of T to 2 decimals\n", + "\n", + "#Result\n", + "print \"The percentage transmission of incident light after emerging through the Nicol prism is\",T, \"%\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The percentage transmission of incident light after emerging through the Nicol prism is 12.51 %\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 5.3, Page number 113" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lamda = 6000; #Wavelength of incident light(A)\n", + "mew_e = 1.55; #Refractive index of extraordinary ray\n", + "mew_o = 1.54; #Refractive index of ordinary ray\n", + "\n", + "#Calculation\n", + "lamda = lamda*10**-8; #Wavelength of incident light(cm)\n", + "t = lamda/(4*(mew_e-mew_o)); #Thickness of Quarter Wave plate of positive crystal(cm)\n", + "\n", + "#Result\n", + "print \"The thickness of Quarter Wave plate is\",t, \"cm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The thickness of Quarter Wave plate is 0.0015 cm\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 5.4, Page number 114" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#Calculation\n", + "#the thickness of a half wave plate of calcite for wavelength lamda is\n", + "#t = lamda/(2*(mew_e - mew_o)) = (2*lamda)/(4*(mew_e - mew_o))\n", + "\n", + "#Result\n", + "print \"The half wave plate for lamda will behave as a quarter wave plate for 2*lamda for negligible variation of refractive index with wavelength\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The half wave plate for lamda will behave as a quarter wave plate for 2*lamda for negligible variation of refractive index with wavelength\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 5.5, Page number 114" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lamda = 500; #Wavelength of incident light(nm)\n", + "mew_e = 1.5508; #Refractive index of extraordinary ray\n", + "mew_o = 1.5418; #Refractive index of ordinary ray\n", + "t = 0.032; #Thickness of quartz plate(mm)\n", + "\n", + "#Calculation\n", + "lamda = lamda*10**-9; #Wavelength of incident light(m)\n", + "t = t*10**-3; #Thickness of quartz plate(m)\n", + "dx = (mew_e - mew_o)*t; #Path difference between E-ray and O-ray(m)\n", + "dphi = (2*math.pi)/lamda*dx; #Phase retardation for quartz for given wavelength(rad)\n", + "dphi = dphi/math.pi;\n", + "\n", + "#Result\n", + "print \"The phase retardation for quartz for given wavelength is\",dphi, \"pi rad\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The phase retardation for quartz for given wavelength is 1.152 pi rad\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 5.6, Page number 114" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "C = 52; #Critical angle for total internal reflection(degrees)\n", + "\n", + "#Calculation\n", + "a = math.pi/180; #conversion factor from degrees to radians\n", + "C = C*a; #Critical angle for total internal reflection(rad)\n", + "#From Brewster's law, math.tan(i_B) = 1_mew_2\n", + "#Also math.sin(C) = 1_mew_2, so that math.tan(i_B) = math.sin(C), solving for i_B\n", + "i_B = math.atan(math.sin(C)); #Brewster angle at the boundary(rad)\n", + "b = 180/math.pi; #conversion factor from radians to degrees\n", + "i_B = i_B*b; #Brewster angle at the boundary(degrees)\n", + "\n", + "#Result\n", + "print \"The Brewster angle at the boundary between two materials is\",int(i_B), \"degrees\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The Brewster angle at the boundary between two materials is 38 degrees\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [], + "prompt_number": 10 + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter6_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter6_1.ipynb new file mode 100755 index 00000000..0de10069 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter6_1.ipynb @@ -0,0 +1,666 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:1812f754f8541ce5ac6b5aaa71f7eac9ff30ca728d742f618ea7c5d3873d8a96" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "6: Crystallography" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.1, Page number 134" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "M = 23+35.5; #Molecular weight of NaCl(kg/k-mole)\n", + "d = 2.18*10**3; #Density of rock salt(kg/m**3)\n", + "n = 4; #Number of atoms per unit cell for an fcc lattice of NaCl crystal\n", + "N = 6.02*10**26; #Avogadro's No., atoms/k-mol\n", + "\n", + "#Calculation\n", + "a = (n*M/(d*N))**(1/3); #Lattice constant of unit cell of NaCl(m)\n", + "a = a*10**9; ##Lattice constant of unit cell of NaCl(nm)\n", + "a = math.ceil(a*10**3)/10**3; #rounding off the value of a to 3 decimals\n", + "\n", + "#Result\n", + "print \"Lattice parameter for the NaCl crystal is\",a, \"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Lattice parameter for the NaCl crystal is 0.563 nm\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.2, Page number 134" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "m = 3;\n", + "n = 2; \n", + "p = 1; #Coefficients of intercepts along three axes\n", + "\n", + "#Calculation\n", + "#reciprocals of the intercepts are 1/m, 1/n, 1/p i.e 1/3, 1/2, 1\n", + "#multiplying by LCM the reciprocals become 2, 3, 6\n", + "\n", + "#Result\n", + "print \"The required miller indices are : (2, 3, 6)\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required miller indices are : (2, 3, 6)\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.3, Page number 135" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "\n", + "#Variable declaration\n", + "m = 2; #Coefficient of intercept along x-axis\n", + "#n = infinite Coefficient of intercept along y-axis\n", + "p = 3/2; #Coefficient of intercept along z-axis\n", + "\n", + "#Calculation\n", + "#reciprocals of the intercepts are 1/m, 1/n, 1/p i.e 1/2, 0, 2/3\n", + "#multiplying by LCM the reciprocals become 3, 0, 4\n", + "\n", + "#Result\n", + "print \"The required miller indices are : (3, 0, 4)\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The required miller indices are : (3, 0, 4)\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.4, Sketching not possible" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.5, Page number 136" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "#For (110) planes\n", + "h1 = 1;\n", + "k1 = 1;\n", + "l1 = 0; #Miller Indices for planes in a cubic crystal\n", + "a1 = 0.43; #Interatomic spacing(nm)\n", + "#For (212) planes\n", + "h2 = 2; \n", + "k2 = 1;\n", + "l2 = 2; #Miller Indices for planes in a cubic crystal\n", + "a2 = 0.43; #Interatomic spacing(nm)\n", + "\n", + "#Calculation\n", + "d1 = a1/(h1**2+k1**2+l1**2)**(1/2); #The interplanar spacing for cubic crystals(nm)\n", + "d1 = math.ceil(d1*10**4)/10**4; #rounding off the value of d1 to 4 decimals\n", + "d2 = a2/(h2**2+k2**2+l2**2)**(1/2); #The interplanar spacing for cubic crystals(nm)\n", + "d2 = math.ceil(d2*10**4)/10**4; #rounding off the value of d2 to 4 decimals\n", + "\n", + "#Result\n", + "print \"The interplanar spacing between consecutive (110) planes is\",d1, \"nm\";\n", + "print \"The interplanar spacing between consecutive (212) planes is\",d2, \"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The interplanar spacing between consecutive (110) planes is 0.3041 nm\n", + "The interplanar spacing between consecutive (212) planes is 0.1434 nm\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.6, Page number 136" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "h = 2;\n", + "k = 3;\n", + "l = 1; #Miller Indices for planes in a cubic crystal\n", + "r = 0.175; #Atomic radius of fcc lattice(nm)\n", + "\n", + "#Calculation\n", + "a = 2*math.sqrt(2)*r; #Interatomic spacing of fcc lattice(nm)\n", + "d = a/(h**2+k**2+l**2)**(1/2); #The interplanar spacing for cubic crystals(nm)\n", + "d = math.ceil(d*10**4)/10**4; #rounding off the value of d to 4 decimals\n", + "\n", + "#Result\n", + "print \"The interplanar spacing between consecutive (231) planes is\",d, \"nm\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The interplanar spacing between consecutive (231) planes is 0.1323 nm\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.7, Page number 136" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "lamda = 1.44; #Wavelength of X-rays(A)\n", + "d = 2.8; #Interplanar spacing of rocksalt crystal(A)\n", + "n1 = 1; #For 1st Order diffraction\n", + "n2 = 2; #For 2nd Order diffraction\n", + "\n", + "#Calculation\n", + "theta1 = math.asin(n1*lamda/(2*d)); #Angle of diffraction(radians)\n", + "theeta1 = theta1*57.2957795; #Angle of diffraction(degrees)\n", + "theeta1 = math.ceil(theeta1*10**2)/10**2; #rounding off the value of theeta1 to 2 decimals\n", + "theta2 = math.asin(n2*lamda/(2*d)); #Angle of diffraction(radians)\n", + "theeta2 = theta2*57.2957795; #Angle of diffraction(degrees)\n", + "theeta2 = math.ceil(theeta2*10**2)/10**2; #rounding off the value of theeta2 to 2 decimals\n", + "\n", + "#Result\n", + "print \"The angle of diffraction for first order maxima is\",theeta1, \"degrees\"\n", + "print \"The angle of diffraction for second order maxima is\",theeta2, \"degrees\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The angle of diffraction for first order maxima is 14.91 degrees\n", + "The angle of diffraction for second order maxima is 30.95 degrees\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.8, Page number 136" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "a = 1; #For convenience, assume interatomic spacing to be unity(m)\n", + "\n", + "#Calculation\n", + "N = 8*(1/8) + 6*(1/2); #total number of spheres in a unit cell\n", + "r = a/(2*math.sqrt(2)); #The atomic radius(m)\n", + "V_atom = N*(4/3)*math.pi*r**3; #Volume of atoms(m**3)\n", + "V_uc = a**3; #Volume of unit cell(m**3)\n", + "PV = (V_atom/V_uc)*100; #percentage of actual volume\n", + "PV = math.ceil(PV*10)/10; #rounding off the value of PV to 1 decimal\n", + "\n", + "#Result\n", + "print \"The percentage of actual volume occupied by the spheres in fcc structure is\",PV, \"percent\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The percentage of actual volume occupied by the spheres in fcc structure is 74.1 percent\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.9, Page number 137" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "#For (221) planes\n", + "h = 2; \n", + "k = 2; \n", + "l = 1; #Miller Indices for planes in a cubic crystal\n", + "a = 2.68; #Interatomic spacing(A)\n", + "n1 = 1; #First Order of diffraction \n", + "n2 = 2; #Second order of diffraction\n", + "theta1 = 8.5; #Glancing angle at which Bragg's reflection occurs(degrees)\n", + "\n", + "#Calculation\n", + "theta1 = theta1*0.0174532925; #Glancing angle at which Bragg's reflection occurs(radians)\n", + "a = a*10**-10; #Interatomic spacing(m)\n", + "d = a/(h**2+k**2+l**2)**(1/2); #The interplanar spacing for cubic crystal(m)\n", + "lamda = 2*d*math.sin(theta1)/n1; #Bragg's Law for wavelength of X-rays(m)\n", + "lamda_A = lamda*10**10; #Bragg's Law for wavelength of X-rays(A)\n", + "lamda_A = math.ceil(lamda_A*10**4)/10**4; #rounding off the value of lamda_A to 4 decimals\n", + "theta2 = math.asin(n2*lamda/(2*d)); #Angle at which second order Bragg reflection occurs(radians)\n", + "theta2 = theta2*57.2957795; #Angle at which second order Bragg reflection occurs(degrees)\n", + "theta2 = math.ceil(theta2*10)/10; #rounding off the value of theta2 to 1 decimal\n", + "\n", + "#Result\n", + "print \"The interplanar spacing between consecutive (221) planes is\",d, \"m\"\n", + "print \"The wavelength of X-rays is\",lamda_A, \"angstrom\"\n", + "print \"The angle at which second order Bragg reflection occurs is\",theta2, \"degrees\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The interplanar spacing between consecutive (221) planes is 8.93333333333e-11 m\n", + "The wavelength of X-rays is 0.2641 angstrom\n", + "The angle at which second order Bragg reflection occurs is 17.2 degrees\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.10, Page number 137" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "h = 1; \n", + "k = 1;\n", + "l = 0; #Miller Indices for planes in a cubic crystal\n", + "n = 1; #First Order of diffraction \n", + "theta = 25; #Glancing angle at which Bragg's reflection occurs(degrees)\n", + "lamda = 0.7; #Wavelength of X-rays(A)\n", + "\n", + "#Calculation\n", + "theta = theta*0.0174532925; #Glancing angle at which Bragg's reflection occurs(radians)\n", + "d = n*lamda/(2*math.sin(theta)); #Interplanar spacing of cubic crystal(A)\n", + "a = d*(h**2+k**2+l**2)**(1/2); #The lattice parameter for cubic crystal(A)\n", + "a = math.ceil(a*10**3)/10**3; #rounding off the value of a to 3 decimals\n", + "\n", + "#Result\n", + "print \"The lattice parameter for cubic crystal is\",a, \"angstrom\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The lattice parameter for cubic crystal is 1.172 angstrom\n" + ] + } + ], + "prompt_number": 10 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.11, Page number 138" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "d = 0.31; #Interplanar spacing(nm)\n", + "n = 1; #First Order of diffraction \n", + "theta = 9.25; #Glancing angle at which Bragg's reflection occurs(degrees)\n", + "theta_max = 90; #Maximum possible angle at which reflection can occur(degrees)\n", + "theta_max = theta_max*0.0174532925; #Maximum possible angle at which reflection can occur(radians)\n", + "\n", + "#Calculation\n", + "theta = theta*0.0174532925; #Glancing angle at which Bragg's reflection occurs(radians)\n", + "lamda = 2*d*math.sin(theta)/n; #Wavelength of X-rays(nm) (Bragg's Law)\n", + "lamda = math.ceil(lamda*10**5)/10**5; #rounding off the value of lamda to 5 decimals\n", + "n = 2*d*math.sin(theta_max)/lamda; #Maximum possible order of diffraction\n", + "\n", + "#Result\n", + "print \"The wavelength of X-rays is\",lamda, \"nm\"\n", + "print \"The Maximum possible order of diffraction is\",round(n)" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The wavelength of X-rays is 0.09967 nm\n", + "The Maximum possible order of diffraction is 6.0\n" + ] + } + ], + "prompt_number": 11 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.12, Page number 138" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "#For (110) planes\n", + "h1 = 1;\n", + "k1 = 1;\n", + "l1 = 0; #Miller indices for (110) planes\n", + "d_110 = 0.195; #Interplanar spacing between (110) planes(nm)\n", + "#For (210) planes\n", + "h2 = 2;\n", + "k2 = 1; \n", + "l2 = 0; #Miller indices for (110) planes\n", + "n = 2; #Second Order of diffraction \n", + "lamda = 0.071; #Wavelength of X-rays(nm)\n", + "\n", + "#Calculation\n", + "a = d_110*(h1**2 + k1**2 + l1**2)**(1/2); #Lattice parameter for bcc crystal(nm)\n", + "d_210 = a/(h2**2 + k2**2 + l2**2)**(1/2); #Interplanar spacing between (210) planes(nm)\n", + "theta = math.asin(n*lamda/(2*d_210)); #Bragg reflection angle for the second order diffraction(radians)\n", + "theeta = theta*57.2957795; #Bragg reflection angle for the second order diffraction(degrees)\n", + "theeta = math.ceil(theeta*10**3)/10**3; #rounding off the value of theeta to 3 decimals\n", + "\n", + "#Result\n", + "print \"Bragg reflection angle for the second order diffraction is\",theeta, \"degrees\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "Bragg reflection angle for the second order diffraction is 35.149 degrees\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.13, Page number 138" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "d = 2182; #Density of rock salt(kg/m**3)\n", + "n = 4; #Number of atoms per unit cell for an fcc lattice of NaCl crystal\n", + "N = 6.02*10**26; #Avogadro's number(atoms/k-mol)\n", + "\n", + "#Calculation\n", + "M = 23+35.5; #Molecular weight of NaCl(kg/k-mole)\n", + "#V = a^3 = M*n/(N*d)\n", + "a = (n*M/(d*N))**(1/3); #Lattice constant of unit cell of NaCl(m)\n", + "D = a/2; #distance between nearest neighbours(m)\n", + "D = D*10**9; #distance between nearest neighbours(nm)\n", + "D = math.ceil(D*10**4)/10**4; #rounding off the value of D to 4 decimals\n", + "\n", + "#Result\n", + "print \"The distance between nearest neighbours of NaCl structure is\",D, \"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The distance between nearest neighbours of NaCl structure is 0.2814 nm\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 6.14, Page number 139" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "r1 = 1.258; #Atomic radius of bcc structure of iron(A)\n", + "N1 = 2; #Number of atoms per unit cell in bcc structure\n", + "#For fcc structure\n", + "r2 = 1.292; #Atomic radius of fcc structure of iron(A)\n", + "N2 = 4; #Number of atoms per unit cell in fcc structure\n", + "\n", + "#Calculation\n", + "a1 = 4*r1/math.sqrt(3); #Lattice parameter of bcc structure of iron(A)\n", + "V1 = a1**3; #Volume of bcc unit cell(A)\n", + "V_atom_bcc = V1/N1; #Volume occupied by one atom(A)\n", + "a2 = 2*math.sqrt(2)*r2; #Lattice parameter of fcc structure of iron(A)\n", + "V2 = a2**3; #Volume of fcc unit cell(A)\n", + "V_atom_fcc = V2/N2; #Volume occupied by one atom(A)\n", + "delta_V = (V_atom_bcc-V_atom_fcc)/V_atom_bcc*100; #Percentage change in volume due to structural change of iron\n", + "delta_V = math.ceil(delta_V*10**3)/10**3; #rounding off the value of delta_V to 3 decimals\n", + "\n", + "#Result\n", + "print \"The percentage change in volume of iron is\",delta_V, \"percent\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The percentage change in volume of iron is 0.494 percent\n" + ] + } + ], + "prompt_number": 15 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter7_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter7_1.ipynb new file mode 100755 index 00000000..750a9700 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter7_1.ipynb @@ -0,0 +1,295 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:7388a73b9b3de996a0d87179cb12d51f5ad7f3cb764b14aa844019e8d2cdb4ea" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "7: Superconductivity" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.1, Page number 152" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "Tc=3.722; #critical temperature(K)\n", + "T=2; #temperature(K)\n", + "Bc_0=0.0305; #critical field(T)\n", + "\n", + "#Calculation\n", + "Bc_T=Bc_0*(1-(T/Tc)**2); #critical field at 2K(T)\n", + "Bc_T = math.ceil(Bc_T*10**4)/10**4; #rounding off the value of Bc_T to 4 decimals\n", + "\n", + "#Result\n", + "print \"The critical field at 2K is\",Bc_T, \"T\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The critical field at 2K is 0.0217 T\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.2, Page number 152" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "V = 1; #DC voltage applied across the Josephson junction(micro-volt)\n", + "e = 1.6*10**-19; #Charge on an electron(C)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "\n", + "#Calculation\n", + "V = V*10**-6; #DC voltage applied across the Josephson junction(V)\n", + "f = 2*e*V/h; #Frequency of Josephson current(Hz)\n", + "f = f*10**-6; #Frequency of Josephson current(MHz)\n", + "f = math.ceil(f*10**2)/10**2; #rounding off the value of f to 2 decimals\n", + "\n", + "#Result\n", + "print \"The frequency of Josephson current is\",f, \"MHz\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The frequency of Josephson current is 482.95 MHz\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.3, Page number 152" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "`\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "T_c = 0.517; #Critical temperature for cadmium(K)\n", + "k = 1.38*10**-23; #Boltzmann constant(J/K)\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "\n", + "#Calculation\n", + "E_g = 3.5*k*T_c/e; #Superconducting energy gap at absolute zero(eV)\n", + "E_g = E_g*10**4;\n", + "E_g = math.ceil(E_g*10**3)/10**3; #rounding off the value of E_g to 3 decimals\n", + "\n", + "#Result\n", + "print \"The superconducting energy gap for Cd at absolute zero is\",E_g,\"*10**-4 eV\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The superconducting energy gap for Cd at absolute zero is 1.561 *10**-4 eV\n" + ] + } + ], + "prompt_number": 8 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.4, Page number 152" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "c = 3*10**8; #Speed of light in free space(m/s)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "E_g = 1.5*10**-4; #Superconducting energy gap for a material(eV)\n", + "\n", + "#Calculation\n", + "#As E_g = h*new = h*c/lamda, solving for lambda\n", + "lamda = h*c/(E_g*e); #Wavelength of photon to break up a Cooper-pair(m)\n", + "lamda = lamda*10**3;\n", + "lamda = math.ceil(lamda*10**3)/10**3; #rounding off the value of lamda to 3 decimals\n", + "\n", + "#Result\n", + "print \"The wavelength of photon to break up a Cooper-pair is\",lamda,\"*10**-3 m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The wavelength of photon to break up a Cooper-pair is 8.283 *10**-3 m\n" + ] + } + ], + "prompt_number": 12 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.5, Page number 153" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "lambda_0 = 37; #Penetration depth of lead at 0 kelvin(nm)\n", + "T_c = 7.193; #Critical temperature of superconducting transition for lead(kelvin)\n", + "T = 5.2; #Temperature at which penetration depth for lead becomes lambda_T(kelvin) \n", + "\n", + "#Calculation\n", + "lambda_T = lambda_0*(1-(T/T_c)**4)**(-1/2); #Penetration depth of lead at 5.2 kelvin(nm)\n", + "lambda_T = math.ceil(lambda_T*10)/10; #rounding off the value of lamda_T to 1 decimal\n", + "\n", + "#Result\n", + "print \"The penetration depth of lead is\",lambda_T, \"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The penetration depth of lead is 43.4 nm\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 7.6, Page number 153" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "from __future__ import division\n", + "import math\n", + "\n", + "#Variable declaration\n", + "M1 = 199; #Mass of an isotope of mercury(amu)\n", + "T_C1 = 4.185; #Transition temperature of the isoptope of Hg(K)\n", + "T_C2 = 4.153; #Transition temperature of another isoptope of Hg(K)\n", + "alpha = 0.5; #Isotope coefficient\n", + "\n", + "#Calculation\n", + "M2 = M1*(T_C1/T_C2)**(1/alpha); #Mass of another isotope of mercury(amu)\n", + "M2 = math.ceil(M2*100)/100; #rounding off the value of M2 to 2 decimals\n", + "\n", + "#Result\n", + "print \"The mass of another isotope of mercury is\",M2, \"amu\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The mass of another isotope of mercury is 202.08 amu\n" + ] + } + ], + "prompt_number": 16 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter8_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter8_1.ipynb new file mode 100755 index 00000000..af1e48b4 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter8_1.ipynb @@ -0,0 +1,664 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:1888e774039c89bc21625752ef2171fa6b8e8f5f67497ebbdba82729676e8946" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "8: Special Theory of Relativity" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.1, Page number 171" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "L_0 = 1; #For simplicity, we assume classical length to be unity(m)\n", + "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", + "\n", + "#Calculation\n", + "L = (1-1/100)*L_0; #Relativistic length(m)\n", + "#Relativistic length contraction gives L = L_0*sqrt(1-v^2/c^2), solving for v\n", + "v = math.sqrt(1-(L/L_0)**2)*c; #Speed at which relativistic length is 1 percent of the classical length(m/s)\n", + "v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals\n", + "\n", + "#Result\n", + "print \"The speed at which relativistic length is 1 percent of the classical length is\",v, \"c\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The speed at which relativistic length is 1 percent of the classical length is 0.1411 c\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.2, Page number 171" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", + "delta_t = 5*10**-6; #Mean lifetime of particles as observed in the lab frame(s)\n", + "\n", + "#Calculation\n", + "v = 0.9*c; #Speed at which beam of particles travel(m/s)\n", + "delta_tau = delta_t*math.sqrt(1-(v/c)**2); #Proper lifetime of particle as per Time Dilation rule(s)\n", + "\n", + "#Result\n", + "print \"The proper lifetime of particle is\",delta_tau, \"s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The proper lifetime of particle is 2.17944947177e-06 s\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.3, Page number 171. theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.4, Page number 172" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", + "\n", + "#Calculation\n", + "v = 0.6*c; #Speed with which the rocket leaves the earth(m/s)\n", + "u_prime = 0.9*c; #Relative speed of second rocket w.r.t. the first rocket(m/s)\n", + "u1 = (u_prime+v)/(1+(u_prime*v)/c**2); #Speed of second rocket for same direction of firing as per Velocity Addition Rule(m/s)\n", + "u1 = math.ceil(u1*10**4)/10**4; #rounding off the value of u1 to 4 decimals\n", + "u2 = (-u_prime+v)/(1-(u_prime*v)/c**2); #Speed of second rocket for opposite direction of firing as per Velocity Addition Rule(m/s)\n", + "u2 = math.ceil(u2*10**4)/10**4; #rounding off the value of u2 to 4 decimals\n", + "\n", + "#Result\n", + "print \"The speed of second rocket for same direction of firing is\",u1,\"c\"\n", + "print \"The speed of second rocket for opposite direction of firing is\",u2,\"c\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The speed of second rocket for same direction of firing is 0.9741 c\n", + "The speed of second rocket for opposite direction of firing is -0.6521 c\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.5, Page number 172" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", + "L0 = 1; #For simplicity assume length in spaceship's frame to be unity(m)\n", + "tau = 1; #Unit time in the spaceship's frame(s)\n", + "\n", + "#Calculation\n", + "L = 1/2*L0; #Length as observed on earth(m)\n", + "#Relativistic length contraction gives L = L_0*sqrt(1-v^2/c^2), solving for v\n", + "v = math.sqrt(1-(L/L0)**2)*c; #Speed at which length of spaceship is observed as half from the earth frame(m/s)\n", + "t = tau/math.sqrt(1-(v/c)**2); #Time dilation of the spaceship's unit time(s)\n", + "v = math.ceil(v*10**4)/10**4; #rounding off the value of v to 4 decimals\n", + "\n", + "#Result\n", + "print \"The speed at which length of spaceship is observed as half from the earth frame is\",v, \"c\"\n", + "print \"The time dilation of the spaceship unit time is\",t,\"delta_tau\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The speed at which length of spaceship is observed as half from the earth frame is 0.8661 c\n", + "The time dilation of the spaceship unit time is 2.0 delta_tau\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.6, Page number 172" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 3*10**8; #Speed of light in vacuum(m/s)\n", + "t1 = 2*10**-7; #Time for which first event occurs(s)\n", + "t2 = 3*10**-7; #Time for which second event occurs(s)\n", + "x1 = 10; #Position at which first event occurs(m)\n", + "x2 = 40; #Position at which second event occurs(m)\n", + "\n", + "#Calculation\n", + "v = 0.6*c; #Velocity with which S2 frame moves relative to S1 frame(m/s)\n", + "L_factor = 1/math.sqrt(1-(v/c)**2); #Lorentz factor\n", + "delta_t = L_factor*(t2 - t1)+L_factor*v/c**2*(x1 - x2); #Time difference between the events(s)\n", + "delta_x = L_factor*(x2 - x1)-L_factor*v*(t2 - t1); #Distance between the events(m)\n", + "\n", + "#Result\n", + "print \"The time difference between the events is\",delta_t, \"s\" \n", + "print \"The distance between the events is\",delta_x, \"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The time difference between the events is 5e-08 s\n", + "The distance between the events is 15.0 m\n" + ] + } + ], + "prompt_number": 6 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.7, Page number 173" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 3*10**8; #Speed of light in vacuum(m/s)\n", + "tau = 2.6*10**-8; #Mean lifetime the particle in its own frame(s)\n", + "d = 20; #Distance which the unstable particle travels before decaying(m)\n", + "\n", + "#Calculation\n", + "#As t = d/v and also t = tau/sqrt(1-(v/c)^2), so that\n", + "#d/v = tau/sqrt(1-(v/c)^2), solving for v\n", + "v = math.sqrt(d**2/(tau**2+(d/c)**2)); #Speed of the unstable particle in lab frame(m/s)\n", + "v = v/10**8;\n", + "v = math.ceil(v*10)/10; #rounding off the value of v to 1 decimal\n", + "\n", + "#Result\n", + "print \"The speed of the unstable particle in lab frame is\",v,\"*10**8 m/s\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The speed of the unstable particle in lab frame is 2.8 *10**8 m/s\n" + ] + } + ], + "prompt_number": 9 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.8, Page number 174" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", + "me = 1; #For simplicity assume mass of electron to be unity(kg)\n", + "tau = 2.3*10**-6; #Average lifetime of mu-meson in rest frame(s)\n", + "t = 6.9*10**-6; #Average lifetime of mu-meson in laboratory frame(s)\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "C = 3*10**8; #Speed of light in vacuum(m/s)\n", + "m_e = 9.1*10**-31; #Mass of an electron(kg)\n", + "\n", + "#Calculation\n", + "#Fromm Time Dilation Rule, tau = t*sqrt(1-(v/c)^2), solving for v\n", + "v = c*math.sqrt(1-(tau/t)**2); #Speed of mu-meson in the laboratory frame(m/s)\n", + "v = math.ceil(v*10**5)/10**5; #rounding off the value of v to 5 decimals\n", + "m0 = 207*me; #Rest mass of mu-meson(kg)\n", + "m = m0/math.sqrt(1-(v/c)**2); #Relativistic variation of mass with velocity(kg)\n", + "m = math.ceil(m*10)/10; #rounding off the value of m to 1 decimal\n", + "T = (m*m_e*C**2 - m0*m_e*C**2)/e; #Kinetic energy of mu-meson(eV)\n", + "T = T*10**-6; #Kinetic energy of mu-meson(MeV)\n", + "T = math.ceil(T*100)/100; #rounding off the value of T to 2 decimals\n", + " \n", + "#Result\n", + "print \"The speed of mu-meson in the laboratory frame is\",v, \"c\"\n", + "print \"The effective mass of mu-meson is\",m, \"me\"\n", + "print \"The kinetic energy of mu-meson is\",T, \"MeV\"\n" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The speed of mu-meson in the laboratory frame is 0.94281 c\n", + "The effective mass of mu-meson is 621.1 me\n", + "The kinetic energy of mu-meson is 211.97 MeV\n" + ] + } + ], + "prompt_number": 13 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.9, Page number 174" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", + "m0 = 1; #For simplicity assume rest mass to be unity(kg)\n", + "\n", + "#Calculation\n", + "m = (20/100+1)*m0; #Mass in motion(kg)\n", + "#As m = m0/sqrt(1-(u/c)^2), solving for u\n", + "u = math.sqrt(1-(m0/m)**2)*c; #Speed of moving mass(m/s) \n", + "u = math.ceil(u*10**3)/10**3; #rounding off the value of u to 3 decimals\n", + "\n", + "#Result\n", + "print \"The speed of moving body is\",u, \"c\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The speed of moving body is 0.553 c\n" + ] + } + ], + "prompt_number": 14 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.10, Page number 175" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 3*10**8; #Speed of light in vacuum(m/s)\n", + "dE = 4*10**26; #Energy radiated per second my the sun(J/s)\n", + "\n", + "#Calculation\n", + "dm = dE/c**2; #Rate of decrease of mass of sun(kg/s)\n", + "dm = dm/10**9;\n", + "dm = math.ceil(dm*10**3)/10**3; #rounding off the value of dm to 3 decimals\n", + "\n", + "#Result\n", + "print \"The rate of decrease of mass of sun is\",dm,\"*10**9 kg/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The rate of decrease of mass of sun is 4.445 *10**9 kg/s\n" + ] + } + ], + "prompt_number": 18 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.11, Page number 175" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 1; #For simplicity assume speed of light to be unity(m/s)\n", + "m0 = 9.1*10**-31; #Mass of the electron(kg)\n", + "E0 = 0.512; #Rest energy of electron(MeV)\n", + "T = 10; #Kinetic energy of electron(MeV)\n", + "\n", + "#Calculation\n", + "E = T + E0; #Total energy of electron(MeV)\n", + "# From Relativistic mass-energy relation E^2 = c^2*p^2 + m0^2*c^4, solving for p\n", + "p = math.sqrt(E**2-m0**2*c**4)/c; #Momentum of the electron(MeV)\n", + "p = math.ceil(p*100)/100; #rounding off the value of p to 2 decimals\n", + "#As E = E0/sqrt(1-(u/c)^2), solving for u\n", + "u = math.sqrt(1-(E0/E)**2)*c; #Velocity of the electron(m/s)\n", + "u = math.ceil(u*10**4)/10**4; #rounding off the value of u to 4 decimals\n", + "\n", + "#Result\n", + "print \"The momentum of the electron is\",p,\"/c MeV\"\n", + "print \"The velocity of the electron is\",u, \"c\"\n", + "\n", + "#answer for velocity given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The momentum of the electron is 10.52 /c MeV\n", + "The velocity of the electron is 0.9989 c\n" + ] + } + ], + "prompt_number": 19 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.12, Page number 175. theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.13, Page number 176" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 3*10**8; #Speed of light in vacuum(m/s)\n", + "E = 4.5*10**17; #Total energy of object(J)\n", + "px = 3.8*10**8; #X-component of momentum(kg-m/s)\n", + "py = 3*10**8; #Y-component of momentum(kg-m/s)\n", + "pz = 3*10**8; #Z-component of momentum(kg-m/s)\n", + "\n", + "#Calculation\n", + "p = math.sqrt(px**2+py**2+pz**2); #Total momentum of the object(kg-m/s)\n", + "#From Relativistic mass-energy relation E^2 = c^2*p^2 + m0^2*c^4, solving for m0\n", + "m0 = math.sqrt(E**2/c**4 - p**2/c**2); #Rest mass of the body(kg)\n", + "m0 = math.ceil(m0*100)/100; #rounding off the value of m0 to 2 decimals\n", + "\n", + "#Result\n", + "print \"The rest mass of the body is\",m0, \"kg\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The rest mass of the body is 4.63 kg\n" + ] + } + ], + "prompt_number": 20 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.14, Page number 176" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 3*10**8; #Speed of light in vacuum(m/s)\n", + "m = 50000; #Mass of high speed probe(kg)\n", + "\n", + "#Calculation\n", + "u = 0.8*c; #Speed of the probe(m/s)\n", + "p = m*u/math.sqrt(1-(u/c)**2); #Momentum of the probe(kg-m/s)\n", + "\n", + "#Result\n", + "print \"The momentum of the high speed probe is\",p, \"kg-m/s\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The momentum of the high speed probe is 2e+13 kg-m/s\n" + ] + } + ], + "prompt_number": 21 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 8.15, Page number 177" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Electronic charge, C = Energy equivalent of 1 eV(J/eV)\n", + "m0 = 9.11*10**-31; #Rest mass of electron(kg)\n", + "c = 3*10**8; #Speed of light in vacuum(m/s)\n", + "\n", + "#Calculation\n", + "u1 = 0.98*c; #Inital speed of electron(m/s)\n", + "u2 = 0.99*c; #Final speed of electron(m/s)\n", + "m1 = m0/math.sqrt(1-(u1/c)**2); #Initial relativistic mass of electron(kg)\n", + "m2 = m0/math.sqrt(1-(u2/c)**2); #Final relativistic mass of electron(kg)\n", + "dm = m2 - m1; #Change in relativistic mass of the electron(kg)\n", + "W = dm*c**2/e; #Work done on the electron to change its velocity(eV)\n", + "W = W*10**-6; #Work done on the electron to change its velocity(MeV)\n", + "W = math.ceil(W*100)/100; #rounding off the value of W to 2 decimals\n", + "#As W = eV, V = accelerating potential, solving for V\n", + "V = W*10**6; #Accelerating potential(volt)\n", + "V = V/10**6;\n", + "\n", + "#Result\n", + "print \"The change in relativistic mass of the electron is\",dm, \"kg\"\n", + "print \"The work done on the electron to change its velocity is\",W, \"MeV\"\n", + "print \"The accelerating potential is\",V, \"*10**6 volt\"\n", + "\n", + "#answers given in the book are wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The change in relativistic mass of the electron is 1.87996052912e-30 kg\n", + "The work done on the electron to change its velocity is 1.06 MeV\n", + "The accelerating potential is 1.06 *10**6 volt\n" + ] + } + ], + "prompt_number": 24 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/Chapter9_1.ipynb b/Engineering_Physics_by_G._Aruldhas/Chapter9_1.ipynb new file mode 100755 index 00000000..af5adbcc --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/Chapter9_1.ipynb @@ -0,0 +1,363 @@ +{ + "metadata": { + "name": "", + "signature": "sha256:d58e11c98e937b7ff914fc9567035f99fc6ab344053f332f140829887d0ef6cc" + }, + "nbformat": 3, + "nbformat_minor": 0, + "worksheets": [ + { + "cells": [ + { + "cell_type": "heading", + "level": 1, + "metadata": {}, + "source": [ + "9: Quantum Mechanics" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.1, Page number 202" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "V = 100; #Accelerating potential for electron(volt)\n", + "\n", + "#Calculation\n", + "lamda = math.sqrt(150/V)*10**-10; #de-Broglie wavelength of electron(m)\n", + "\n", + "#Result\n", + "print \"The De-Broglie wavelength of electron is\",lamda, \"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The De-Broglie wavelength of electron is 1.22474487139e-10 m\n" + ] + } + ], + "prompt_number": 1 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.2, Page number 203" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "m = 9.11*10**-31; #Mass of the electron(kg)\n", + "Ek = 10; #Kinetic energy of electron(eV)\n", + "\n", + "#Calculation\n", + "p = math.sqrt(2*m*Ek*e); #Momentum of the electron(kg-m/s)\n", + "lamda = h/p ; #de-Broglie wavelength of electron from De-Broglie relation(m)\n", + "lamda = lamda*10**9; #de-Broglie wavelength of electron from De-Broglie relation(nm)\n", + "lamda = math.ceil(lamda*10**2)/10**2; #rounding off the value of lamda to 2 decimals\n", + "\n", + "#Result\n", + "print \"The de-Broglie wavelength of electron is\",lamda, \"nm\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The de-Broglie wavelength of electron is 0.39 nm\n" + ] + } + ], + "prompt_number": 2 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.3, Page number 203. theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.4, Page number 203" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "m = 9.11*10**-31; #Mass of the electron(kg)\n", + "v = 1.1*10**6; #Speed of the electron(m/s)\n", + "pr = 0.1; #precision in percent\n", + "\n", + "#Calculation\n", + "p = m*v; #Momentum of the electron(kg-m/s)\n", + "dp = pr/100*p; #Uncertainty in momentum(kg-m/s)\n", + "h_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\n", + "dx = h_bar/(2*dp); #Uncertainty in position(m)\n", + "\n", + "#Result\n", + "print \"The uncertainty in position of electron is\",dx, \"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The uncertainty in position of electron is 5.26175358211e-08 m\n" + ] + } + ], + "prompt_number": 3 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.5, Page number 203" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)\n", + "h = 6.626*10**-34; #Planck's constant(Js)\n", + "dt = 10**-8; #Uncertainty in time(s)\n", + "\n", + "#Calculation\n", + "h_bar = h/(2*math.pi); #Reduced Planck's constant(Js)\n", + "dE = h_bar/(2*dt*e); #Uncertainty in energy of the excited state(m)\n", + "\n", + "#Result\n", + "print \"The uncertainty in energy of the excited state is\",dE, \"eV\"\n", + "\n", + "#answer given in the book is wrong" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The uncertainty in energy of the excited state is 3.2955020404e-08 eV\n" + ] + } + ], + "prompt_number": 4 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.6, Page number 204" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "\n", + "#Variable declaration\n", + "c = 3*10**8; #Speed of light(m/s)\n", + "dt = 10**-8; #Average lifetime(s)\n", + "lamda = 400; #Wavelength of spectral line(nm)\n", + "\n", + "#Calculation\n", + "lamda = lamda*10**-9; #Wavelength of spectral line(m)\n", + "#From Heisenberg uncertainty principle,\n", + "#dE = h_bar/(2*dt) and also dE = h*c/lambda^2*d_lambda, which give\n", + "#h_bar/(2*dt) = h*c/lambda^2*d_lambda, solving for d_lambda\n", + "d_lamda = (lamda**2)/(4*math.pi*c*dt); #Width of spectral line(m)\n", + "\n", + "#Result\n", + "print \"The width of spectral line is\",d_lamda, \"m\"" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The width of spectral line is 4.24413181578e-15 m\n" + ] + } + ], + "prompt_number": 5 + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.7, Page number 204. theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.8, Page number 204. theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.9, Page number 205. theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.10, Page number 205. theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.11, Page number 205. theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.12, Page number 206. theoritical proof" + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.13, Page number 206. theoritical proof " + ] + }, + { + "cell_type": "heading", + "level": 2, + "metadata": {}, + "source": [ + "Example number 9.14, Page number 207" + ] + }, + { + "cell_type": "code", + "collapsed": false, + "input": [ + "\n", + "\n", + "#importing modules\n", + "import math\n", + "from __future__ import division\n", + "from scipy.integrate import quad\n", + "\n", + "#Variable declaration\n", + "a = 2*10**-10; # Width of 1D box(m)\n", + "x1=0; # Position of first extreme of the box(m)\n", + "x2=1*10**-10; # Position of second extreme of the box(m)\n", + "\n", + "#Calculation\n", + "def intg(x):\n", + " return ((2/a)*(math.sin(2*math.pi*x/a))**2)\n", + "S=quad(intg,x1,x2)[0]\n", + "\n", + "#Result\n", + "print \"The probability of finding the electron between x = 0 and x = 10**-10 is\",S" + ], + "language": "python", + "metadata": {}, + "outputs": [ + { + "output_type": "stream", + "stream": "stdout", + "text": [ + "The probability of finding the electron between x = 0 and x = 10**-10 is 0.5\n" + ] + } + ], + "prompt_number": 7 + }, + { + "cell_type": "code", + "collapsed": false, + "input": [], + "language": "python", + "metadata": {}, + "outputs": [] + } + ], + "metadata": {} + } + ] +}
\ No newline at end of file diff --git a/Engineering_Physics_by_G._Aruldhas/README.txt b/Engineering_Physics_by_G._Aruldhas/README.txt new file mode 100755 index 00000000..77c00324 --- /dev/null +++ b/Engineering_Physics_by_G._Aruldhas/README.txt @@ -0,0 +1,10 @@ +Contributed By: KRISHNA CHAITANYA +Course: btech +College/Institute/Organization: JNTUH +Department/Designation: Computer Science +Book Title: Engineering Physics +Author: G. Aruldhas +Publisher: PHI Learning ( New Delhi ) +Year of publication: 2012 +Isbn: 9788120339163 +Edition: 2
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