{
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"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": {}
}
]
}