4: Interference

Example number 4.1, Page number 69

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
i=40;                                    #angle of incidence(degrees)
mew=1.2;                                #refractive index
t=0.23;                                #thickness of the film(micro m)

#Calculation
i=i*math.pi/180;                     #angle of incidence(radian)
r=math.asin(math.sin(i)/mew);        #angle of refraction(radian)
lambda1=(2*mew*t*math.cos(r))*10**3;      #wavelength absent(nm) 
lambda2=lambda1/2;

#Result
print "The wavelength absent is",round(lambda1,1),"nm"

The wavelength absent is 466.1 nm

Example number 4.2, Page number 69

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

#Variable declaration
lambda1=400*10**-9;                #wavelength 1(m)
lambda2=600*10**-9;                #wavelength 2(m)
#2*t=n*lambda
n=150;    

#Calculation                        
t=((n*lambda2)/2)*10**6;     #thickness of the air film(micro meter)

#Result
print "The thickness of the air film is",t,"micro m"

The thickness of the air film is 45.0 micro m

Example number 4.3, Page number 70

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=600*10**-9;     #wavelength(m)
mew=2;
theta=0.025;      #wedge-angle(degrees)

#Calculation                        
theta=theta*math.pi/180;      #wedge-angle(radian)
x=(lamda/(2*mew*math.sin(theta)))*10**2;       #bandwidth(cm)

#Result
print "The bandwidth is",round(x,3),"cm"

The bandwidth is 0.034 cm

Example number 4.4, Page number 70

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

#Variable declaration
xair=0.15;                     #bandwidth of air(cm)
xliq=0.115;                    #bandwidth of liquid(cm)
mewair=1;                      #refractive index of air

#Calculation                        
mewliq=(xair*mewair)/xliq;      #refractive index of liquid

#Result
print "The refractive index of liquid is",round(mewliq,1)

The refractive index of liquid is 1.3

Example number 4.5, Page number 70

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

#Variable declaration
n=9;
lamda=589*10**-9;                   #wavelength of light used(m)
R=0.95;                             #radius of curvature of lens(m)
mew=1;

#Calculation                        
D=(math.sqrt((4*n*lamda*R)/mew))*10**2;   #diameter of the ninth dark ring(m)

#Result
print "The diameter of the ninth dark ring is",round(D,2),"cm"

The diameter of the ninth dark ring is 0.45 cm

Example number 4.6, Page number 70

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

#Variable declaration
x=0.055;                       #distance in fringe shift(mm)
n=200;                         #number of fringes

#Calculation                        
lamda=((2*x)/n)*10**6;          #wavelength(nm)

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

The wavelength of light used is 550.0 nm

Example number 4.7, Page number 70

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

#Variable declaration
n=50;                             #number of fringes
lamda=500*10**-9;                 #wavelength of light used(m)
mew=1.5;                          #refractive index of the plate

#Calculation                        
t=((n*lamda)/(2*(mew-1)))*10**6;    #thickness of the plate(micro meter)

#Result
print "The thickness of the plate is",t,"micro m"

The thickness of the plate is 25.0 micro m

Example number 4.8, Page number 70

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

#Variable declaration
lamda=550*10**-9;                   #wavelength(m)
mew=1.38;                            #refractive index

#Calculation                        
t=(lamda/(4*mew))*10**9;              #thickness(nm)

#Result
print "The minimum thickness of the plate for normal incidence of light is",round(t,3),"nm"

The minimum thickness of the plate for normal incidence of light is 99.638 nm

Example number 4.9, Page number 70

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

#Variable declaration
i=35;                                         #angle of incidence(degrees)
mew=1.4;                                      #refractive index
n=50;                                        
lamda=459*10**-9;       #wavelength(m)

#Calculation                        
i=i*math.pi/180;                     #angle of incidence(radian)
r=math.asin(math.sin(i)/mew);        #angle of refraction(radian)
#2*mew*cos(r)=n*lambda
#n(459)=(n+1)450
t=(n*lamda/(2*mew*math.cos(r)))*10**6;          #thickness of the film(micro meter)

#Result
print "The thickness of the film is",round(t,3),"micro m"

The thickness of the film is 8.985 micro m

Example number 4.10, Page number 71

In [31]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=500*10**-9;                      #wavelength(m)
x=0.07;                                 #observed band width(cm)
mew=1;                                  #refractive index

#Calculation                        
theta=(math.asin(lamda/(2*mew*x)))*10**2;     #wedge angle(radian)
theta=theta*180/math.pi;     #wedge angle(degrees)

#Result
print "The wedge angle is",round(theta,2),"degrees"

The wedge angle is 0.02 degrees

Example number 4.11, Page number 71

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration
dair=0.42;                   #diameter of certain rings(cm)
dliq=0.38;                   #diameter of rings when liquid is introduced(cm)

#Calculation                        
mew=dair**2/dliq**2;            #refractive index of liquid

#Result
print "The refravtive index of liquid is",round(mew,2)

The refravtive index of liquid is 1.22

Example number 4.12, Page number 71

In [39]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=8;                                           #eigth ring
n=3;                                           #third ring
dm=0.4;                                        #diameter of the eigth ring(cm)
dn=0.2;                                        #diameter of the third ring(cm)
R=101;                                         #Radius of curvature(cm)

#Calculation                        
lamda=(((dm**2)-(dn**2))/(4*R*(m-n)));      #wavelength of light(cm) 

#Result
print "The wavelength of light used is",round(lamda*10**5,4),"*10**-5 cm"

The wavelength of light used is 5.9406 *10**-5 cm

Example number 4.13, Page number 71

In [41]:
#importing modules
import math
from __future__ import division

#Variable declaration
mew=1.38;             #refractive index of magnesium floride
t=175;                #thickness of coating of magnesium fluoride(nm)

#Calculation                        
lamda=4*t*mew;        #wavelength(nm)

#Result
print "The wavelength which has high transmission is",lamda,"nm"

The wavelength which has high transmission is 966.0 nm