6: Polarisation

Example number 6.1, Page number 108

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
mew=1.63;              #refractive index of the glass plate

#Calculation                        
#tan ip=mew
ip=math.atan(mew);        #ip=polarising angle(radian)
ip=ip*180/math.pi;     #ip=polarising angle(degrees)
#ip+r=90
r=90-ip;              #angle of refraction(degrees)
rd=int(r);      #angle(degrees)
rm=round(60*(r-rd));     #angle(minutes)

#Result
print "The angle of refraction is",rd,"degrees",rm,"minutes"

The angle of refraction is 31 degrees 32.0 minutes

Example number 6.2, Page number 108

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

#Variable declaration
#I=I0(cos^2(teta))
theta=50;                #angle made between two principle planes(degrees)

#Calculation                        
theta=theta*math.pi/180;   #angle(radian)
I=(math.cos(theta))**2;         #incident unpolarized light
#percentage of incident unpolarised light is (I/I0)*100 where I0 is incident polarised light
p=I*100;      #percentage of incident unpolarized light(%)

#Result
print "The percentage of incident unpolarized light is",int(p),"%"

The percentage of incident unpolarized light is 41 %

Example number 6.3, Page number 108

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

#Variable declaration
#I=I0*cos^2(teta)
#cos^2(teta)=I/I0
a=0.08;                #a=I/I0;where I=incident unpolarized light & I0=incident polarized light

#Calculation                        
theta=math.acos(math.sqrt(a));    #angle between planes of transmission of analyser and polariser(radian)
theta=theta*180/math.pi;     #angle(degrees)
thetad=int(theta);     #angle(degrees)
thetam=round(60*(theta-thetad));     #angle(minutes)

#Result
print "The angle between the planes of transmission of analyser & polariser is +(or)- ",thetad,"degrees",thetam,"minutes"

The angle between the planes of transmission of analyser & polariser is +(or)-  73 degrees 34.0 minutes

Example number 6.4, Page number 108

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
#IE=A^2(cos^2(teta));IO=A^2(sin^2(teta))
#I0/IE=tan^2(teta)
theta=40;                    #angle made between incident beam & optic axis(degrees)

#Calculation                        
theta=theta*math.pi/180;   #angle(radian)
a=math.tan(theta)**2;                  #I0/IE

#Result
print "I0/IE=",round(a,1)

I0/IE= 0.7

Example number 6.5, Page number 108

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=589;                              #wavelength of light(nm)
mew0=1.54;                               #refractive index for ordinary wave
mewE=1.55;                               #refractive index for extraordinary wave

#Calculation                        
t=lamda/(4*(mewE-mew0))*10**-3;         #thickness(micro m)

#Result
print "The thickness of a quarter-wave plate is",t,"micro m"

The thickness of a quarter-wave plate is 14.725 micro m

Example number 6.6, Page number 109

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
ip=52;                               #angle of polarization(degrees)

#Calculation                        
ip=ip*math.pi/180;   #angle(radian)
mew=math.tan(ip);                    #refractive index of the material surface

#Result
print "The refractive index of the material surface is",round(mew,2)

The refractive index of the material surface is 1.28

Example number 6.7, Page number 109

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
r=33;                      #angle of refraction(degrees)

#Calculation                        
ip=90-r;                   #polarising angle(degrees)
ip=ip*math.pi/180;     #angle(radian)
mew=math.tan(ip);          #refractive index of quartz

#Result
print "The refractive index of quartz is",round(mew,2)

The refractive index of quartz is 1.54

Example number 6.8, Page number 109

In [20]:
#importing modules
import math
from __future__ import division

#Variable declaration
#IE=A^2*cos^2(teta);IO=A^2*sin^2(teta)
#I0/IE=tan^2(teta)=0.65
a=0.65;                        #ratio of intensities of ordinary & extraordinary light

#Calculation                        
theta=math.atan(math.sqrt(a));           #angle made by plane of vibration of the incident light with optic axis(radian)
theta=theta*180/math.pi;      #angle(degrees)
thetad=int(theta);     #angle(degrees)
thetam=int(60*(theta-thetad));

#Result
print "The angle made by the plane of vibration of incident light with the optic axis is",thetad,"degrees",thetam,"minutes"

The angle made by the plane of vibration of incident light with the optic axis is 38 degrees 52 minutes

Example number 6.9, Page number 109

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration
mew0=1.544;                                  #refractive index of ordinary waves
mewE=1.553;                                  #refractive index of extraordinary waves
lamda=550;                                  #wavelength(nm) 
t=9;

#Calculation                        
delta=((2*180)/(lamda*(10**-9)))*(mewE-mew0)*t*(10**-6);           #phase difference(degrees)

#Result
print "The phase difference between O and E rays is",int(delta),"degrees"

The phase difference between O and E rays is 53 degrees

Example number 6.10, Page number 109

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
delta=50;                                #phase difference(degrees)
mewE=1.544;                              #refractive index of extraordinary waves
mew0=1.553;                              #refractive index of ordinary waves
t=8;                                     #thickness(nm)

#Calculation                        
lamda=((2*180)/delta)*(mew0-mewE)*t*10**-6*10**9;              #wavelength of light incident(nm)

#Result
print "The wavelength of light incident is",lamda,"nm"

The wavelength of light incident is 518.4 nm