# 5: Polarization¶

## Example number 5.1, Page number 113¶

In [5]:
#importing modules
from __future__ import division
import math

#Variable declaration
mew_g = 1.72;    #Refractive index of glass
mew_w = 4/3;      #Refractive index of water

#Calculation
#For polarization to occur on flint glass, tan(i) = mew_g/mew_w
#Solving for i
i_g = math.atan(mew_g/mew_w);      #angle of incidence for complete polarization for flint glass(rad)
a = 180/math.pi;       #conversion factor from radians to degrees
i_g = i_g*a;      #angle of incidence(degrees)
i_g = math.ceil(i_g*10**2)/10**2;     #rounding off the value of i_g to 2 decimals
#For polarization to occur on water, tan(i) = mew_w/mew_g
#Solving for i
i_w = math.atan(mew_w/mew_g);     #angle of incidence for complete polarization for water(rad)
i_w = i_w*a;       #angle of incidence(degrees)
i_w = math.ceil(i_w*10**3)/10**3;     #rounding off the value of i_w to 3 decimals

#Result
print "The angle of incidence for complete polarization to occur on flint glass is",i_g, "degrees"
print "The angle of incidence for complete polarization to occur on water is",i_w, "degrees"

The angle of incidence for complete polarization to occur on flint glass is 52.22 degrees
The angle of incidence for complete polarization to occur on water is 37.783 degrees


## Example number 5.2, Page number 113¶

In [6]:
#importing modules
from __future__ import division
import math

#Variable declaration
I0 = 1;    #For simplicity, we assume the intensity of light falling on the second Nicol prism to be unity(W/m**2)
theta = 30;    #Angle through which the crossed Nicol is rotated(degrees)

#Calculation
theeta = 90-theta;     #angle between the planes of transmission after rotating through 30 degrees
a = math.pi/180;           #conversion factor from degrees to radians
theeta = theeta*a;     ##angle between the planes of transmission(rad)
I = I0*math.cos(theeta)**2;    #Intensity of the emerging light from second Nicol(W/m**2)
T = (I/(2*I0))*100;    #Percentage transmission of incident light
T = math.ceil(T*100)/100;     #rounding off the value of T to 2 decimals

#Result
print "The percentage transmission of incident light after emerging through the Nicol prism is",T, "%"

The percentage transmission of incident light after emerging through the Nicol prism is 12.51 %


## Example number 5.3, Page number 113¶

In [7]:
#importing modules
from __future__ import division
import math

#Variable declaration
lamda = 6000;    #Wavelength of incident light(A)
mew_e = 1.55;    #Refractive index of extraordinary ray
mew_o = 1.54;     #Refractive index of ordinary ray

#Calculation
lamda = lamda*10**-8;      #Wavelength of incident light(cm)
t = lamda/(4*(mew_e-mew_o));    #Thickness of Quarter Wave plate of positive crystal(cm)

#Result
print "The thickness of Quarter Wave plate is",t, "cm"

The thickness of Quarter Wave plate is 0.0015 cm


## Example number 5.4, Page number 114¶

In [8]:
#Calculation
#the thickness of a half wave plate of calcite for wavelength lamda is
#t = lamda/(2*(mew_e - mew_o)) = (2*lamda)/(4*(mew_e - mew_o))

#Result
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"

The half wave plate for lamda will behave as a quarter wave plate for 2*lamda for negligible variation of refractive index with wavelength


## Example number 5.5, Page number 114¶

In [9]:
#importing modules
from __future__ import division
import math

#Variable declaration
lamda = 500;    #Wavelength of incident light(nm)
mew_e = 1.5508;    #Refractive index of extraordinary ray
mew_o = 1.5418;     #Refractive index of ordinary ray
t = 0.032;     #Thickness of quartz plate(mm)

#Calculation
lamda = lamda*10**-9;     #Wavelength of incident light(m)
t = t*10**-3;     #Thickness of quartz plate(m)
dx = (mew_e - mew_o)*t;    #Path difference between E-ray and O-ray(m)
dphi = (2*math.pi)/lamda*dx;    #Phase retardation for quartz for given wavelength(rad)
dphi = dphi/math.pi;

#Result
print "The phase retardation for quartz for given wavelength is",dphi, "pi rad"

The phase retardation for quartz for given wavelength is 1.152 pi rad


## Example number 5.6, Page number 114¶

In [13]:
#importing modules
import math

#Variable declaration
C = 52;    #Critical angle for total internal reflection(degrees)

#Calculation
a = math.pi/180;           #conversion factor from degrees to radians
C = C*a;      #Critical angle for total internal reflection(rad)
#From Brewster's law, math.tan(i_B) = 1_mew_2
#Also math.sin(C) = 1_mew_2, so that math.tan(i_B) = math.sin(C), solving for i_B
i_B = math.atan(math.sin(C));    #Brewster angle at the boundary(rad)
b = 180/math.pi;           #conversion factor from radians to degrees
i_B = i_B*b;     #Brewster angle at the boundary(degrees)

#Result
print "The Brewster angle at the boundary between two materials is",int(i_B), "degrees"

The Brewster angle at the boundary between two materials is 38 degrees

In [10]: