Chapter 1 : Wave Optics

Example number 1, Page Number 14

In [1]:
#importing modules 
import math
from __future__ import division

#Variable declaration
lamda=5890*10**-8    #wavelength
myu=1.6              #refractive index
m=12                 #order of the fringe

#Calculations
t=(lamda*m)/(myu-1)/10**-6

#Result
print"Thickness of sheet= %i*10**-8 cm" %t

Thickness of sheet= 1178*10**-8 cm

Example number 2, Page Number 15

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

#Variable declaration
lamda=5893*10**-8    #wavelength
myu=1.55             #refractive index
n=10                 #order of the fringe

#Calculations
t=(lamda*n)/(myu-1)/(10**-3)*10**3

#Result
print"Thickness of sheet= %0.2f*10**-8 cm" %t

Thickness of sheet= 1071.45*10**-8 cm

Example number 3, Page Number 15

In [3]:
#importing modules 
import math
from __future__ import division

#Variable declaration
lamda=5640*10**-8    #wavelength
d=0.01               #distnce between slits
n=0                  #first minimum

#Calculations
theta=(n+(1/2))*(lamda/d)

#Result
print"Angular position of first minima is= %0.2f" %math.degrees(theta)

Angular position of first minima is= 0.16

Example number 4, Page Number 16

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

#Variable declaration
lamda=5890*10**-8    #wavelength
myu=1.5              #refractive index of glass
n=1                  #first minimum
r=60                 #angle in degrees

#Calculations
t=(n*lamda)/(2*myu*0.5)/10**-5

#Result
print"minimum thickness of the film t= %1.3f*10**-5 cm" %t #The answer provided in the textbook is incorrect

minimum thickness of the film t= 3.927*10**-5 cm

Example number 5, Page Number 16

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

#Variable declaration
i=35                 #incident angle in degrees
myu=1.33             #refractive index 
n=1                  #first minimum
t=4*10**-5           #thickness

#Calculations
cos_r=0.90
lamda1=2*myu*t*cos_r/10**-5        #for first order n=1
lamda2=(2*myu*t*cos_r)/2/10**-5    #for second order n=2
lamda3=(2*myu*t*cos_r)/3/10**-5    #for third order n=3

#Result
print"(i)For the first order wavelength= %1.2f*10**-5 cm" %lamda1     #The answer provided in the textbook is incorrect
print"(ii)For the second order wavelength= %1.2f*10**-5 cm" %lamda2
print"(iii)For the third order wavelength= %1.2f*10**-5 cm" %lamda3

(i)For the first order wavelength= 9.58*10**-5 cm
(ii)For the second order wavelength= 4.79*10**-5 cm
(iii)For the third order wavelength= 3.19*10**-5 cm

Example number 6, Page Number 16

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

#Variable declaration
lamda=5890*10**-10   #wavelength
myu=1.5              #refractive index of glass
n=1                  #first minimum
r=60                 #angle in degrees

#Calculations
t=(n*lamda)/(2*myu*0.5)/10**-7

#Result
print"Thickness of the film t= %1.3f*10**-4 mm" %t 

Thickness of the film t= 3.927*10**-4 mm

Example number 7, Page Number 17

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

#Variable declaration
lamda=5890*10**-10   #wavelength
myu=1.33             #refractive index of glass
n=1                  #first minimum
r=45                 #angle in degrees
cos_r=0.707

#Calculations
t=(n*lamda)/(2*myu*cos_r)/10**-7

#Result
print"thickness of the film t= %1.3f*10**-4 mm" %t 

thickness of the film t= 3.132*10**-4 mm

Example number 8, Page Number 17

In [8]:
#importing modules 
import math
from __future__ import division

#Variable declaration
lamda=5.1*10**-7     #wavelength
myu=4/3              #refractive index of glass
r=45                 #angle in degrees
sin_i=4/5
n=50

#Calculations
sin_r=sin_i/myu
cos_r=(1-sin_r**2)**0.5
t=(n*lamda)/(2*myu*cos_r)/10**-5

#Result
print"thickness of the film t= %1.1f*10**-5 m" %t 

thickness of the film t= 1.2*10**-5 m

Example number 9, Page Number 18

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

#Variable declaration
n2=20                 #order of dark ring
lamda=5890*10**-8     #wavelenght

#Calculations
n1=n2*4

#Result
print"order of the dark ring n1= %i" %n1

order of the dark ring n1= 80

Example number 10 , Page Number 18

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

#Variable declaration
Dm=0.590              #diameter of ring 15
Dn=0.336              #diameter of ring 5
lamda=5890*10**-8
m=15
n=5

#Calculation
R=(Dm**2-Dn**2)/(4*lamda*(m-n))

#Result
print"Radius of curvature= %0.1f cm" %R

Radius of curvature= 99.8 cm

Example number 11 , Page Number 19

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

#Variable declaration
lamda1=6000*10**-8           
lamda2=4500*10**-8
R=90                 #Radius of curvature
n=3

#Calculation
dn=math.sqrt(4*n*lamda1*R)

#Result
print"diameter of the nth ring= %0.4f cm" %dn

diameter of the nth ring= 0.2546 cm

Example number 12, Page Number 19

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

#Variable declaration
Dm=0.50               #diameter of ring 1
lamda=5900*10**-8     #wavelenght
m=10

#Calculation
R=(Dm**2)/(4*lamda*m)/10**2*10**2

#Result
print"Radius of curvature= %0.2f cms" %R

Radius of curvature= 105.93 cms

Example number 13, Page Number 20

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

#Variable declaration
dn=0.3                #diameter of ring 5
lamda=5.895*10**-5    #wavelenght
R=100
n=5

#Calculation
myu=(4*R*n*lamda)/dn**2

#Result
print"Refractive index of liquid= %0.2f " %myu

Refractive index of liquid= 1.31

Example number 14, Page Number 20

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

#Variable declaration
D2=1.40                
D1=1.20                

#Calculation
myu=(D2/D1)**2

#Result
print"Refractive index of liquid= %1.3f " %myu

Refractive index of liquid= 1.361

Example number 15, Page Number 20

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

#Variable declaration
myu=4/3
Dn=0.5                 #diameter of 10th ring
lamda=6*10**-5
n=10

#Calculation
R=(myu*Dn**2)/(4*n*lamda)

#Result
print"Radius of curvature= %1.0f cm" %R

Radius of curvature= 139 cm

Example number 16, Page Number 21

In [16]:
#importing modules 
import math
from __future__ import division

#Variable declaration
myu=4/3
Dn=0.5                 #diameter of 10th ring
lamda=5895*10**-8
n=6
R=100
r=0.15

#Calculation
myu=(((2*n)-1)*lamda*R)/(2*r**2)

#Result
print"refractive index of liquid= %1.3f " %myu

refractive index of liquid= 1.441

Example number 17, Page Number 21

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

#Variable declaration
D15=5.90*10**-3        #diameter of 15th ring
D5=3.36*10**-3         #diameter of 5th ring
m=10
R=100

#Calculation
lamda=(D15**2-D5**2)/(4*m*R)/10**-9*10**3

#Result
print"wavelength of liquid used= %i Armstrong" %lamda

wavelength of liquid used= 5880 Armstrong

Example number 18, Page Number 21

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

#Variable declaration
D1=1.50
D2=1.30

#Calculation
myu=(D1/D2)**2

#Result
print"refractive index of liquid= %1.3f" %myu

refractive index of liquid= 1.331

Example number 19 , Page Number 22

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

#Variable declaration
lamda=5.9*10**-7
r=5.2*10**-3           #radius of ring
n=10

#Calculation
R=(r**2)/(n*lamda)
t=(n*lamda)/2/10**-6

#Result
print"(i)radius of curvature R= %f m" %R
print"(ii)Thickness of air film t= %1.2f*10**-6 m" %t

(i)radius of curvature R= 4.583051 m
(ii)Thickness of air film t= 2.95*10**-6 m