# 2: Interference and Diffraction¶

## Example number 2.1, Page number 75¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
t = 12*10**-5;         #thickness of mica sheet(cm)
lamda = 6000;          #wavelength(Angstrom)
n = 1;

#Calculation
lamda = lamda*10**-10;       #wavelength(m)
mew_1 = n*lamda/t;
mew = mew_1+1;            #refractive index of mica

#Result
print "refractive index of mica is",mew
print "answer given in the book is wrong"

refractive index of mica is 1.005
answer given in the book is wrong


## Example number 2.2, Page number 75¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
D = 0.53;       #distance of fringes from slit(m)
lamda = 5890;      #wavelength of light(angstrom)
two_d = 0.6*10**-3;     #separation of slits(m)

#Calculation
lamda = lamda*10**-10;          #wavelength(m)
beta = D*lamda/two_d;           #width of fringes(m)
beta = beta*10**3;
beta = math.ceil(beta*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "width of fringes is",beta,"*10**-3 m"

width of fringes is 0.521 *10**-3 m


## Example number 2.3, Page number 75¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
beta = 9*10**-4;       #width of fringes(m)
d1 = 75;          #distance of fringes from biprism(cm)
d2 = 5;           #distance of biprism from slit(cm)
lamda = 5890;      #wavelength of light(angstrom)
two_d = 0.6*10**-3;     #separation of slits(m)

#Calculation
lamda = lamda*10**-10;          #wavelength(m)
d1 = d1*10**-2;                 #distance of fringes from biprism(m)
d2 = d2*10**-2;                 #distance of biprism from slit(m)
D = d1+d2;                   #distance of fringes from slit(m)
two_d = D*lamda/beta;         #separation of slits(m)
two_d = two_d*10**4;
two_d = math.ceil(two_d*10**2)/10**2;   #rounding off to 2 decimals

#Result
print "distance between slits is",two_d,"*10**-4 m"

distance between slits is 5.24 *10**-4 m


## Example number 2.4, Page number 75¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
lamda = 6*10**-7;       #wavelength(m)
t = 7.2*10**-6;         #thickness(m)
n = 6;

#Calculation
mew_1 = n*lamda/t;
mew = mew_1+1;            #refractive index of sheet

#Result
print "refractive index of sheet is",mew

refractive index of sheet is 1.5


## Example number 2.5, Page number 76¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
beta = 3;        #fringe separation(mm)
mew = 1;         #refractive index
lamda = 6000;      #wavelength(angstrom)

#Calculation
lamda = lamda*10**-10;         #wavelength(m)
beta = beta*10**-3;         #fringe separation(m)
theta = lamda/(2*mew*beta);       #angle between plates(sec)
theeta = theta*180*3600/math.pi;     #angle between plates(sec ")
theta = theta*10**4;
theeta = math.ceil(theeta*10**3)/10**3;   #rounding off to 3 decimals

#Result
print "angle between plates is",theta,"*10**-4 sec or",theeta,"'"

angle between plates is 1.0 *10**-4 sec or 20.627 '


## Example number 2.6, Page number 76¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
lamda = 5900*10**-7;      #wavelength of light(m)
mew = 1;             #refractive index
n = 7.4;             #number of fringes

#Calculation
t2_t1 = n*lamda/(2*mew);       #difference of film thickness(m)
t2_t1 = t2_t1*10**2;

#Result
print "difference of film thickness is",t2_t1,"*10**-2 m"
print "answer given in the book is wrong"

difference of film thickness is 0.2183 *10**-2 m
answer given in the book is wrong


## Example number 2.7, Page number 77¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
lamda = 5.9*10**-7;          #wavelength of light(m)
n = 10;             #10th ring
D10 = 0.5;     #diameter of 10th ring(cm)

#Calculation
D10 = D10*10**-2;      #diameter of 10th ring(m)
R = D10**2/(4*n*lamda);        #radius of curvature of lens(m)
R = math.ceil(R*10**4)/10**4;   #rounding off to 4 decimals
t = D10**2/(8*R);           #thickness of the air film(m)

#Result
print "radius of curvature of lens is",R,"m"
print "thickness of the air film is",round(t/1e-6,2),"*10**-6 m"

radius of curvature of lens is 1.0594 m
thickness of the air film is 2.95 *10**-6 m


## Example number 2.8, Page number 77¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
n = 20;          #number of fringes
lamda = 5890;         #wavelength(angstrom)

#Calculation
lamda = lamda*10**-8;         #wavelength(cm)
t = n*lamda/2;                #thickness of wire(cm)
t = t*10**4;

#Result
print "thickness of wire is",t,"*10**-4 cm"

thickness of wire is 5.89 *10**-4 cm


## Example number 2.9, Page number 77¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
lamda = 5880;        #wavelength(angstrom)
n = 1;         #number of fringes
mew = 1.5;      #refractive index
r = 60;          #angle of refraction(degree)

#Calculation
r = r*math.pi/180;        #angle of refraction(radian)
lamda = lamda*10**-10;         #wavelength(m)
t = n*lamda/(2*mew*math.cos(r));       #smallest thickness of the plate(m)
t = t*10**10;          #smallest thickness of the plate(angstrom)

#Result
print "smallest thickness of the plate is",t,"angstrom"

smallest thickness of the plate is 3920.0 angstrom


## Example number 2.10, Page number 78¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
n1 = 4;          #fourth ring
n2 = 12;         #12th ring
n3 = 20;         #20th ring
D4 = 0.4;        #diameter of 4th ring(cm)
D12 = 0.7;       #diameter of 12th ring(cm)

#Calculation
p1 = n2-n1;
p2 = n3-n2;
#D12**2-D4**2 = 4*p1*lamda*R and D20**2-D12**2 = 4*p2*lamda*R
#therefore D12**2-D4**2 = D20**2-D12**2
D20 = math.sqrt((2*D12**2)-(D4**2));       #diameter of 20th ring(cm)
D20 = math.ceil(D20*100)/100;   #rounding off to 2 decimals

#Result
print "diameter of 20th ring is",D20,"cm"

diameter of 20th ring is 0.91 cm


## Example number 2.11, Page number 78¶

In :
#importing modules
import math
from __future__ import division

#Variable declaration
lamda1 = 6*10**-5;        #wavelength of light 1(cm)
lamda2 = 4.5*10**-5;      #wavelength of light 2(cm)
R = 90;          #radius of curvature(cm)

#Calculation
n = lamda2/(lamda1-lamda2);           #number of fringes
Dn = math.sqrt(4*n*lamda1*R);         #diameter of nth ring(cm)
Dn = math.ceil(Dn*10**4)/10**4;   #rounding off to 4 decimals

#Result
print "diameter of nth ring is",Dn,"cm"

diameter of nth ring is 0.2546 cm