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Diffstat (limited to 'Engineering_Physics/Chapter5_1.ipynb')
| -rw-r--r-- | Engineering_Physics/Chapter5_1.ipynb | 182 |
1 files changed, 161 insertions, 21 deletions
diff --git a/Engineering_Physics/Chapter5_1.ipynb b/Engineering_Physics/Chapter5_1.ipynb index 3731e0ad..86db7d36 100644 --- a/Engineering_Physics/Chapter5_1.ipynb +++ b/Engineering_Physics/Chapter5_1.ipynb @@ -1,6 +1,7 @@ { "metadata": { - "name": "Chapter5" + "name": "", + "signature": "sha256:7539e2f35ea93dc5f143cbd45df18f4d6a1bee4d35a1729fab5d759b4b27d8ff" }, "nbformat": 3, "nbformat_minor": 0, @@ -11,25 +12,58 @@ "cell_type": "heading", "level": 1, "metadata": {}, - "source": "5: Polarization" + "source": [ + "5: Polarization" + ] }, { "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 5.1, Page number 113" + "source": [ + "Example number 5.1, Page number 113" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the angle of incidence for complete polarization\n\n#importing modules\nfrom __future__ import division\nimport math\n\n#Variable declaration\nmew_g = 1.72; #Refractive index of glass\nmew_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\ni_g = math.atan(mew_g/mew_w); #angle of incidence for complete polarization for flint glass(rad)\na = 180/math.pi; #conversion factor from radians to degrees\ni_g = i_g*a; #angle of incidence(degrees)\ni_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\ni_w = math.atan(mew_w/mew_g); #angle of incidence for complete polarization for water(rad)\ni_w = i_w*a; #angle of incidence(degrees)\ni_w = math.ceil(i_w*10**3)/10**3; #rounding off the value of i_w to 3 decimals\n\n#Result\nprint \"The angle of incidence for complete polarization to occur on flint glass is\",i_g, \"degrees\"\nprint \"The angle of incidence for complete polarization to occur on water is\",i_w, \"degrees\"", + "input": [ + " \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\nThe angle of incidence for complete polarization to occur on water is 37.783 degrees\n" + "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 @@ -38,19 +72,43 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 5.2, Page number 113" + "source": [ + "Example number 5.2, Page number 113" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the percentage transmission of incident light\n\n#importing modules\nfrom __future__ import division\nimport math\n\n#Variable declaration\nI0 = 1; #For simplicity, we assume the intensity of light falling on the second Nicol prism to be unity(W/m**2)\ntheta = 30; #Angle through which the crossed Nicol is rotated(degrees)\n\n#Calculation\ntheeta = 90-theta; #angle between the planes of transmission after rotating through 30 degrees\na = math.pi/180; #conversion factor from degrees to radians\ntheeta = theeta*a; ##angle between the planes of transmission(rad)\nI = I0*math.cos(theeta)**2; #Intensity of the emerging light from second Nicol(W/m**2)\nT = (I/(2*I0))*100; #Percentage transmission of incident light\nT = math.ceil(T*100)/100; #rounding off the value of T to 2 decimals\n\n#Result\nprint \"The percentage transmission of incident light after emerging through the Nicol prism is\",T, \"%\"", + "input": [ + " \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" + "text": [ + "The percentage transmission of incident light after emerging through the Nicol prism is 12.51 %\n" + ] } ], "prompt_number": 6 @@ -59,19 +117,40 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 5.3, Page number 113" + "source": [ + "Example number 5.3, Page number 113" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the thickness of Quarter Wave plate\n\n#importing modules\nfrom __future__ import division\nimport math\n\n#Variable declaration\nlamda = 6000; #Wavelength of incident light(A)\nmew_e = 1.55; #Refractive index of extraordinary ray\nmew_o = 1.54; #Refractive index of ordinary ray\n\n#Calculation\nlamda = lamda*10**-8; #Wavelength of incident light(cm)\nt = lamda/(4*(mew_e-mew_o)); #Thickness of Quarter Wave plate of positive crystal(cm)\n\n#Result\nprint \"The thickness of Quarter Wave plate is\",t, \"cm\"", + "input": [ + " \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" + "text": [ + "The thickness of Quarter Wave plate is 0.0015 cm\n" + ] } ], "prompt_number": 7 @@ -80,19 +159,31 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 5.4, Page number 114" + "source": [ + "Example number 5.4, Page number 114" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To show the behaviour of the plate\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\nprint \"The half wave plate for lamda will behave as a quarter wave plate for 2*lamda for negligible variation of refractive index with wavelength\"", + "input": [ + " \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" + "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 @@ -101,19 +192,45 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 5.5, Page number 114" + "source": [ + "Example number 5.5, Page number 114" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the phase retardation\n\n#importing modules\nfrom __future__ import division\nimport math\n\n#Variable declaration\nlamda = 500; #Wavelength of incident light(nm)\nmew_e = 1.5508; #Refractive index of extraordinary ray\nmew_o = 1.5418; #Refractive index of ordinary ray\nt = 0.032; #Thickness of quartz plate(mm)\n\n#Calculation\nlamda = lamda*10**-9; #Wavelength of incident light(m)\nt = t*10**-3; #Thickness of quartz plate(m)\ndx = (mew_e - mew_o)*t; #Path difference between E-ray and O-ray(m)\ndphi = (2*math.pi)/lamda*dx; #Phase retardation for quartz for given wavelength(rad)\ndphi = dphi/math.pi;\n\n#Result\nprint \"The phase retardation for quartz for given wavelength is\",dphi, \"pi rad\"", + "input": [ + " \n", + "\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" + "text": [ + "The phase retardation for quartz for given wavelength is 1.152 pi rad\n" + ] } ], "prompt_number": 9 @@ -122,19 +239,42 @@ "cell_type": "heading", "level": 2, "metadata": {}, - "source": "Example number 5.6, Page number 114" + "source": [ + "Example number 5.6, Page number 114" + ] }, { "cell_type": "code", "collapsed": false, - "input": "#To calculate the Brewster angle at the boundary\n\n#importing modules\nimport math\n\n#Variable declaration\nC = 52; #Critical angle for total internal reflection(degrees)\n\n#Calculation\na = math.pi/180; #conversion factor from degrees to radians\nC = 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\ni_B = math.atan(math.sin(C)); #Brewster angle at the boundary(rad)\nb = 180/math.pi; #conversion factor from radians to degrees\ni_B = i_B*b; #Brewster angle at the boundary(degrees)\n\n#Result\nprint \"The Brewster angle at the boundary between two materials is\",int(i_B), \"degrees\"", + "input": [ + " \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" + "text": [ + "The Brewster angle at the boundary between two materials is 38 degrees\n" + ] } ], "prompt_number": 13 @@ -142,7 +282,7 @@ { "cell_type": "code", "collapsed": false, - "input": "", + "input": [], "language": "python", "metadata": {}, "outputs": [], |