In [3]:

```
from math import pi, atan
# Given
mu = 1.5 # refractive index of glass
#Calculations
Ip = atan(mu) * (180 / pi) # by brewster's law
r = 90 - Ip # calculation for angle of refraction
#Result
print "Brewster angle = %.f degree\nAngle of refraction = %.f degree"%(Ip,r)
```

In [2]:

```
from math import pi, atan
# Given
mu = 1.33 # refractive index of glass
#Calculations
Ip = atan(mu) * (180 / pi) # by Brewster's law
#Result
print "Angle of brewster = %.2f degree"%Ip
```

In [3]:

```
from math import pi, atan
# Given
mu_w = 1.33 # refractive index of water
mu_g = 1.54 # refractive index of glass
#Calculations
Ip_1 = atan(mu_g / mu_w) * (180 / pi)#calculation for polarizing angle for water
Ip_2 = atan(mu_w / mu_g) * (180 / pi) # calculation for polarizing angle for glass
#Result
print "Polarizing angle for water to glass = %.2f degree,\n Polarizing angle for glass to water = %.2f degree"%(Ip_1,Ip_2)
print "So polarizing angle is greater for a beam incident from water to glass"
```

In [47]:

```
from math import pi, asin, tan, sin
# Given
Ip = pi / 3 # polarizing angle of piece of glass for green light in radian
a = pi / 3 # angle of prism in radian
#Calculations
mu = tan(Ip) # calculation for refractive index
delta_m = 2 * (asin(mu * sin(a / 2)) - (a / 2)) * (180 / pi) # calculation for angle of minimum deviation
#Result
print "Angle of minimum deviation = %.f degree"%delta_m
```

In [4]:

```
from math import pi, atan
# Given
mu_w = 1.33 # refractive index of water
mu_g = 1.5 # refractive index of glass
#Calculations
Ip = atan(mu_g / mu_w) * (180 / pi) # calculation for Brewster angle
#Result
print "Brewster angle = %.1f degree"%Ip
```

In [5]:

```
from math import pi, atan
# Given
mu = 1.732 # refractive index of glass
#Calculations
Ip = atan(mu) * (180 / pi) # by Brewster's law
r = 90 - Ip# calculation for angle of refraction
#Result
print "Angle of incidence = %.f degree\nAngle of refraction = %.f degree"%(Ip,r)
```

In [9]:

```
from math import pi, cos
# Given
alpha = pi / 3 # angle between polarizer and analyzer
#Calculation
r = (cos(alpha))**2 # where r = transmitted intensity / incident intensity
#Result
print "Ratio between transmitted intensity to incident intensity = %.2f "%r
```

In [15]:

```
from math import sqrt,acos,degrees
#Given
r1 = 1./3 #ratio of intensity of transmitted light to the intensity of transmitted beam in first case
r2 = 1./3 #ratio of intensity of transmitted light to the intensity of incident beam in second case
p = 50 #percentage reduction in intensity of unpolarized light by the sheet
#Calculations
theta1 = degrees(acos(sqrt(r1))) #calculation for the angle between characteristics directions of the sheet in first case
theta2 = degrees(acos(sqrt(2*r2))) #calculation for the angle between characteristics directions of the sheet in second case
#Result
print "The angle between characteristics directions of the sheet in 1st case = %.2f degrees."%(theta1)
print "The angle between characteristics directions of the sheet in 2nd case = %.2f degrees."%(theta2)
```

In [45]:

```
from math import acos, sqrt, pi
# Given
r = 3. / 4 # ratio of intensity of transmitted light to the intensity of incident light
#Calculation
theta = acos(sqrt(r)) * (180 / pi) # calculation for angle between the nicol prisms
#Result
print "Angle between the nicol prisms = %.f degree"%theta
```

In [18]:

```
from math import pi, cos
# Given
theta1 = pi / 6 # angle between Nicole prisms in first case in radian
theta2 = pi / 4 # angle between Nicole prisms in second case in radian
theta3 = pi / 3 # angle between Nicole prisms in third case in radian
theta4 = pi / 2 # angle between Nicole prisms in fourth case in radian
#Calculations
I1 = (1 - (cos(theta1))**2) * 100
I2 = (1 - (cos(theta2))**2) * 100
I3 = (1 - (cos(theta3))**2) * 100
I4 = (1 - (cos(theta4))**2) * 100
#Result
print "Percentage reduction in intensity of light-\n(i)%.f %%\n(ii)%.f %%\n(iii)%.f %%\n(iv)%.f %%"%(I1,I2,I3,I4)
```

In [44]:

```
from math import pi, acos, sqrt
# Given
i1 = 1. / 2 # reduced intensity ratio in first case
i2 = 1. / 4 # reduced intensity ratio in second case
#Calculations
theta1 = acos(sqrt(i1)) * (180 / pi)# calculation for angle between nicols in first case
theta2 = acos(sqrt(i2)) * (180 / pi)# calculation for angle between nicols in second case
#Result
print "Angle between the Nicols in first case = %.f degree\nAnd in second case = %.f degree"%(theta1,theta2)
```

In [20]:

```
# Given
l = 5e-7 # wavelength of light in meter
mu_e = 1.553 # refractive index for extraordinary light
mu_o = 1.544 # refractive index for ordinary light
#Calculations
t = l / (2 * (mu_e - mu_o)) # calculation for thickness of half-wave plate of quartz
#Result
print "Thickness of half-wave plate of quartz = %.2e meter"%t
```

In [21]:

```
# Given
l = 5.893e-7 # wavelength of light in meter
mu_e = 1.533 # refractive index for extraordinary light
mu_o = 1.554 # refractive index for ordinary light
#Calculation
t = l / (4 * (mu_o - mu_e)) # calculation for thickness of quartz plate
#Result
print "Thickness of quartz plate = %.2e meter"%t
```

In [22]:

```
# Given
l = 5.89e-7 # wavelength of light in meter
mu_e1 = 1.5 # refractive index for extraordinary light in first case
mu_o1 = 1.55 # refractive index for ordinary light in first case
mu_e2 = 1.57 # refractive index for extraordinary light in second case
mu_o2 = 1.55 # refractive index for ordinary light in second case
#Calculations
t1 = l / (4 * (mu_o1 - mu_e1))
t2 = l / (4 * (mu_e2 - mu_o2))
# calculation for thickness of plate of quartz
#Result
print "Thickness of plate of quartz in first case = %.3e meter,\nAnd thickness of plate of quartz in second case = %.2e meter"%(t1,t2)
```

In [23]:

```
# Given
l = 5.89e-7 # wavelength of light in meter
mu_e = 1.486 # refractive index for extraordinary light
mu_o = 1.658 # refractive index for ordinary light
#Calculation
t = l / (4 * (mu_o - mu_e)) # calculation for thickness of calcite plate
#Result
print "Thickness of calcite plate = %.2e meter"%t
```

In [24]:

```
# Given
l = 5e-7 # wavelength of light in meter
mu_e = 1.5533 # refractive index for extraordinary light
mu_o = 1.5442 # refractive index for ordinary light
#Calculation
t = l / (4 * (mu_e - mu_o)) # calculation for thickness of quartz plate
#Result
print "Thickness of quartz plate = %.2e meter"%t
```

In [25]:

```
# Given
l = 5.89e-7 # wavelength of light in meter
mu_e = 1.54 # refractive index for extraordinary light
mu_o = 1.55 # refractive index for ordinary light
#Calculation
t = l / (4 * (mu_o - mu_e)) # calculation for thickness of quartz plate
#Result
print "Thickness of quartz plate = %.2e meter"%t
```

In [26]:

```
# Given
l = 5.89e-7 # wavelength of light in meter
mu_e = 1.553 # refractive index for extraordinary light
mu_o = 1.544 # refractive index for ordinary light
#Calculation
t = l / (4 * (mu_e - mu_o)) # calculation for thickness of quartz plate
#Result
print "Thickness of quartz plate = %.2e meter"%t
```

In [27]:

```
# Given
mu_e = 1.5442 # refractive index for extraordinary light
mu_o = 1.5533 # refractive index for ordinary light
l = 5e-7 # wavelength of plane polarized light in meter
#Calculation
t = l / (2 * (mu_o - mu_e))# calculation for thickness of quartz plate
#Result
print "Thickness of quartz plate = %.2e meter"%t
```

In [28]:

```
# Given
theta = 10 # rotation of plane of polarization in degree
s = 60 # specific rotation of sugar solution in degree per decimeter per unit concentration
l = 2.5 # length of Polari meter in decimeter
#Calculation
c = theta / (s * l) # calculation for concentration of sugar solution
#Result
print "Concentration of sugar solution = %.3f gm/cc"%c
```

In [43]:

```
# Given
theta = 26.4 # rotation of plane of polarization in degree
c = 0.2 # concentration of sugar solution in gm/cc
l = 2 # length of polarizing tube in decimeter
#Calculation
s = theta / (l * c)# calculation for specific rotation of sugar solution
#Result
print "Specific rotation of sugar solution = %.f degree/(dm-cc)"%s
```

In [42]:

```
# Given
theta = 6.5 # rotation of plane of polarization in degree
c = 0.05 # concentration of sugar solution in gm/cc
l = 2 # length of polarizing tube in decimeter
#Calculation
s = theta / (l * c) # calculation for specific rotation of sugar solution
#Result
print "Specific rotation of sugar solution = %.f degree/(dm-cc)"%s
```

In [29]:

```
# Given
w = 80 # weight of impure sugar in gm
theta = 9.9 # rotation of plane of polarization in degree
s = 66 # specific rotation of sugar solution in degree per decimeter per unit concentration
l = 2 # length of Polari meter in decimeter
#Calculations
c = theta / (s * l) * (1000) # in gm/l
per_c = (c * 100) / w # calculation for concentration of sugar solution
#Result
print "Concentration of sugar solution = %.2f percent"%per_c
```

In [30]:

```
# Given
theta = 11. # rotation of plane of polarization in degree
s = 66 # specific rotation of sugar solution in degree per decimeter per unit concentration
l = 2 # length of Polari meter in decimeter
#Calculation
c = theta / (s * l) # calculation for concentration of sugar solution
#Result
print "Concentration of sugar solution = %.4f gm/cc"%c
```

In [40]:

```
# Given
theta = 26.4 # rotation of plane of polarization in degree
c = 0.2 # concentration of sugar solution in gm/cc
l = 2 # length of polarizing tube in decimeter
#calculation
s = theta / (l * c) # calculation for specific rotation of sugar solution
#Result
print "Specific rotation of sugar solution = %.f degree/(dm-cc)"%s
```

In [39]:

```
# Given
theta = 13 # rotation of plane of polarization in degree
r = (1. / 3) # ratio of the final concentration to the initial solution
l = 2 # length of Polari meter in decimeter
l_ = 3 # length of second polarizing tube in decimeter
#Calculation
theta_ = (l_ * r * theta) / l# calculation for optical rotation of diluted solution
#Result
print "Optical rotation of diluted solution = %.1f degree"%theta_
```