3: Polarization, Laser and Holography

Example number 3.1, Page number 103

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

#Variable declaration
x = 5;        #distance of 1st minimum(mm)
D = 2;        #distance between lens and screen(m)
a = 0.2;      #width of slit(mm)

#Calculation
x = x*10**-3;        #distance of 1st minimum(m)
a = a*10**-3;        #width of slit(m)
lamda = a*x/D;         #wavelength of light(m)

#Result
print "wavelength of light is",lamda,"m"

wavelength of light is 5e-07 m

Example number 3.2, Page number 103

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

#Variable declaration
a = 0.2;       #width of slit(mm)
lamda = 5*10**-7;       #wavelength(m)
f = 50;        #focal length(cm)

#Calculation
a = a*10**-3;        #width of slit(m)
f = f*10**-2;        #focal length(m)
theta_1 = lamda/a;        #angular diffraction correcponding to 1st minima(radian)
theta_2 = 2*lamda/a;          #angular diffraction correcponding to 2nd minima(radian)
x = f*(theta_2-theta_1);       #separation between 1st and second minima(m)
x = x*10**2;

#Result
print "distance between first two minima on the screen is",x,"*10**-3 m"

distance between first two minima on the screen is 0.125 *10**-3 m

Example number 3.3, Page number 104

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

#Variable declaration
a = 0.16;       #1st slit width(mm)
b = 0.8;        #2nd slit width(mm)

#Calculation
nbym = (a+b)/a;       #condition for missing orders

#Result
print "n = ",nbym,"m"
print "n = ",nbym,",",2*nbym,",",3*nbym,"etc for m = 1,2,3..."

n =  6.0 m
n =  6.0 , 12.0 , 18.0 etc for m = 1,2,3...

Example number 3.4, Page number 104

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

#Variable declaration
n = 2;      #second order
theta = 30;     #angle of diffraction(degrees)
lamda = 5*10**-5;      #wavelength(cm)

#Calculation
theta = theta*math.pi/180;      #angle of diffraction(radian)
aplusb = n*lamda/math.sin(theta);
N = 1/aplusb;        #number of lines(per cm)

#Result
print "number of lines on the grating surface is",N,"per cm"

number of lines on the grating surface is 5000.0 per cm

Example number 3.5, Page number 105

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

#Variable declaration
aplusb = 1.5*10**-6;       #grating element(m)
lamda = 550;         #wavelength(nm)

#Calculation
lamda = lamda*10**-9;        #wavelength(m)
n = aplusb/lamda;         #maximum possible order
n = math.ceil(n*10**3)/10**3;   #rounding off to 3 decimals


#Result
print "maximum possible order is",n,". third and higher orders are not possible"

maximum possible order is 2.728 . third and higher orders are not possible

Example number 3.6, Page number 105

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

#Variable declaration
dlamda = 0.6;      #difference in wavelength(nm)
lamda = 589.3;     #wavelength(nm)
n = 1;         #first order

#Calculation
N = lamda/(n*dlamda);         #number of lines on grating

#Result
print "number of lines on grating is",int(N)

number of lines on grating is 982