# 4: Wave Optics¶

## Example number 4.1, Page number 92¶

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

#Variable declaration
n=125;   #number of fingers cross the field of view
d=0.04*10**-3;   #distance of one of mirror moved(m)

#Calculation
w=2*d/n;     #wavelength of light used(m)

#Result
print "The wavelength of light used is",int(w*10**9),"nm"

The wavelength of light used is 640 nm


## Example number 4.2, Page number 92¶

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

#Variable declaration
Ri=1.5;      #refractive index of thin film of glass
n=30;     #number of fringes of sodium light is observed across the field of view
t=0.018*10**-3;    #thickness of glass film(m)

#Calculation
w=2*(Ri-1)*t/n;     #wavelength of the light used(m)

#Result
print "The wavelength of light used is",w*10**9,"nm"

The wavelength of light used is 600.0 nm


## Example number 4.3, Page number 92¶

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

#Variable declaration
n=200;     #number of fringes cross the field of view
d=0.0589*10**-3;     #distance of mirror displaced(m)

#Calculation
w=2*d/n;     #wavelength of the monochromatic source used(m)

#Result
print "The wavelength of the monochromatic source used is",w*10**9,"nm"

The wavelength of the monochromatic source used is 589.0 nm


## Example number 4.4, Page number 92¶

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

#Variable declaration
x=1.55;    #refractive index of transparent film of glass
w=480*10**-9;   #wavelength of light(m)
n=450;    #number of fringes to sweep across the field

#Calculation
t=n*w/(2*(x-1));    #thickness of the film(m)

#Result
print "The thickness of the film is",round(t*10**4,4),"*10**-4 m"

The thickness of the film is 1.9636 *10**-4 m


## Example number 4.5, Page number 93¶

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
t=0.004*10**-2;    #thickness of transparent sheet(m)
d=0.0027*10**-2;   #distance of mirror displaced(m)

#Calculation
X=(d/t)+1;    #refractive index of the material

#Result
print "The refractive index of material is",X

The refractive index of material is 1.675


## Example number 4.6, Page number 93¶

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=0.03205*10**-3;   #distance of movable mirror displaced(m)
w=580.9*10**-9;     #wavelength of light(m)

#Calculation
n=2*d/w;     #number of fringes shifted across the cross wire of eye piece of the telescope

#Result
print "The number of fringes shifted across the cross wire of eye piece of the telescope is",int(n)

The number of fringes shifted across the cross wire of eye piece of the telescope is 110


## Example number 4.7, Page number 101¶

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
w=5893*10**-10;   #wavelength of sodium light(m)
Re=1.5532;     #Refractive index of quartz for e ray
Ro=1.5332;     #Refractive index of quartz for o ray

#Calculation
t=w/(4*(Re-Ro));     #thickness of a quarter wave plate of quartz for sodium light(m)

#Result
print "The thickness of a quarter wave plate of quartz for sodium light is",t*10**6,"micro m"

The thickness of a quarter wave plate of quartz for sodium light is 7.36625 micro m


## Example number 4.8, Page number 102¶

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
w=6000*10**-10;    #wavelength(m)
Re=1.54;    #Refractive index of double refracting crystal for e ray
Ro=1.65;    #Refractive index of double refracting crystal for o ray

#Calculation
t=w/(2*(Ro-Re));     #thickness of a double refracting crystal required  at w/2(m)

#Result
print "The thickness of a double refracting crystal required at w/2 is",round(t*10**6,3),"micro m"

The thickness of a double refracting crystal required at w/2 is 2.727 micro m


## Example number 4.9, Page number 102¶

In [21]:
#importing modules
import math
from __future__ import division

#Variable declaration
w=5*10**-7;    #wavelength(m)
Re=1.5573;     #Refractive index for e ray when the emergent beam will be plane polarised
Ro=1.5442;     #Refractive index for o ray when the emergent beam will be plane polarised

#Calculation
t=w/(4*(Re-Ro));    #least thickness of a plate(m)

#Result
print "The least thickness of a plate when the emergent beam will be plane polarised is",round(t*10**6,2),"micro m"

The least thickness of a plate when the emergent beam will be plane polarised is 9.54 micro m


## Example number 4.10, Page number 102¶

In [24]:
#importing modules
import math
from __future__ import division

#Variable declaration
w=5893*10**-10;    #wavelength of sodium light(m)
Ro=1.658;       #Refractive index of calcite for o ray
Re=1.486;       #Refractive index of calcite for e ray

#Calculation
t=w/(2*(Ro-Re));      #thickness of the quarter wave plate for calcite(m)

#Result
print "The thickness of the quarter wave plate for calcite is",round(t*10**6,3),"*10**-6 m"
print "answer given in the book is wrong"

The thickness of the quarter wave plate for calcite is 1.713 *10**-6 m
answer given in the book is wrong


## Example number 4.11, Page number 102¶

In [26]:
#importing modules
import math
from __future__ import division

#Variable declaration
t=30*10**-6;     #thickness of wave plate(m)
Ro=1.55;      #Refractive index of wave plate for o ray
Re=1.54;      #Refractive index of wave plate for e ray

#Calculation
w=2*t*(Ro-Re);      #wavelength for which it can act as a half wave plate(m)

#Result
print "The wavelength for which it can act as a half wave plate is",w*10**9,"*10**-9 m"

The wavelength for which it can act as a half wave plate is 600.0 *10**-9 m


## Example number 4.12, Page number 102¶

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
w=546.1*10**-9;    #wavelength of light(m)
Re=1.592;      #Refractive index of mica for e ray
Ro=1.586;      #Refractive index of mica for o ray

#Calculation
t=w/(2*(Re-Ro));    #thickness of a mica sheet(m)

#Result
print "The thickness of a mica sheet required for making a half wave plate for a light is",round(t*10**5,4),"*10**-5 m"

The thickness of a mica sheet required for making a half wave plate for a light is 4.5508 *10**-5 m