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Diffstat (limited to 'Engineering_Physics/Chapter3_1.ipynb')
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1 files changed, 13 insertions, 396 deletions
diff --git a/Engineering_Physics/Chapter3_1.ipynb b/Engineering_Physics/Chapter3_1.ipynb index 7f02f8be..9e2d3109 100755 --- a/Engineering_Physics/Chapter3_1.ipynb +++ b/Engineering_Physics/Chapter3_1.ipynb @@ -1,7 +1,6 @@ { "metadata": { - "name": "", - "signature": "sha256:366ab969956cd234404db0091b17960805856ec3ff44007e36b0efdbe1414f5e" + "name": "Chapter3" }, "nbformat": 3, "nbformat_minor": 0, @@ -12,452 +11,70 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": [ - "3: Interference" - ] + "source": "3: Fibre Optics and Applications" }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 3.1, Page number 71" - ] + "source": "Example number 3.1, Page number 84" }, { "cell_type": "code", "collapsed": false, - "input": [ - " \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", - "#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" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn1 = 1.5; #refractive index of core\nn2 = 1.47; #refractive index of cladding\nn0 = 1; #refractive index of air\na = 180/math.pi; #conversion factor of radian to degree\n\n#Calculation\nNA = math.sqrt((n1**2)-(n2**2)); #numerical aperture\nNA=math.ceil(NA*10)/10; #rounding off to 1 decimal\nalpha_m = math.asin(NA/n0); #acceptance angle(radian)\nalpha_m = alpha_m*a; #acceptance angle(degrees)\nalpha_m=math.ceil(alpha_m*10**2)/10**2; #rounding off to 2 decimals\nphi_m = math.asin(NA/n1); #phase angle(radian)\nphi_m = phi_m*a; #phase angle(degrees)\nphi_m=math.ceil(phi_m*10**2)/10**2; #rounding off to 2 decimals\ntheta_c = math.asin(n2/n1); #critical angle(radian)\ntheta_c = theta_c*a; #critical angle(degrees)\ntheta_c=math.ceil(theta_c*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint \"numerical aperture is\",NA\nprint \"acceptance angle is\",alpha_m,\"degrees\"\nprint \"phase angle is\",phi_m,\"degrees\"\nprint \"critical angle is\",theta_c,\"degrees\"", "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" - ] + "text": "numerical aperture is 0.3\nacceptance angle is 17.46 degrees\nphase angle is 11.54 degrees\ncritical angle is 78.522 degrees\n" } ], - "prompt_number": 5 + "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 3.3, Page number 71" - ] + "source": "Example number 3.2, Page number 85" }, { "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" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nn1 = 1.5; #refractive index of core\nn2 = 1.47; #refractive index of cladding\nc = 3*10**8; #velocity of light(m/sec)\n\n#Calculation\ndeltatbyL = (n1/n2)*((n1-n2)/c);\n\n#Result\nprint \"pulse broadening per unit length is\",deltatbyL,\"s/m\"", "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", - "text": [ - "The refractive index of the sheet of glass is 1.5642\n" - ] + "text": "pulse broadening per unit length is 1.02040816327e-10 s/m\n" } ], - "prompt_number": 6 + "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": [ - "Example number 3.4, Page number 72" - ] + "source": "Example number 3.3, Page number 85" }, { "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 = 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\"" - ], + "input": "#importing modules\nimport math\n\n#Variable declaration\nphi_m = 11.54; #phase angle(degrees)\na = 0.5*10**-4;\nx = math.pi/180; #conversion factor from degrees to radians\n\n#Calculation\nphi_m = phi_m*x; #phase angle(radian)\nL = a/math.tan(phi_m); #length(m)\nn = 1/(2*L); #total number of internal reflections(m-1)\n\n#Result\nprint \"alpha = 0 rays have no reflection. hence there are zero reflections for 1 metre.\"\nprint \"alpha = alpha_m rays have\",int(n),\"m-1 internal reflections\"\nprint \"answer given in the book is wrong\"", "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" - ] + "text": "alpha = 0 rays have no reflection. hence there are zero reflections for 1 metre.\nalpha = alpha_m rays have 2041 m-1 internal reflections\nanswer given in the book is wrong\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", - "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", - "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", - "#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", - "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": {} |