# 4: Interference¶

## Example number 4.1, Page number 69¶

In :
#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
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 :
#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 :
#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
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 :
#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 :
#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 :
#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 :
#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 :
#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 :
#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
#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 :
#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=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 :
#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 :
#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)

#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 :
#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