# Chapter 3 Polarization of light¶

## Example 3.1 Page no 130¶

In :
#Given
u =1.54                                     #refrective index of glass

#Calculation
import math
i= math.atan(u)*180/3.14
r=90-i

#Result
print"Angle of refraction is",round(r,1),"degree"

Angle of refraction is 33.0 degree


## Example 3.2 Page no 130¶

In :
#Given
i= 60

#Calculation
import math
u= math.tan(i*3.14/180.0)

#Result
print"Refractive index of glass is",round(u,3)

Refractive index of glass is 1.73


## Example 3.3 Page no 130¶

In :
#Given
u=1.5697

#Calculation
import math
up=math.atan(u)*180/3.14

#Result
print"Angle is", round(up,1),"Degree"

Angle is 57.5 Degree


## Example 3.4 Page no 130¶

In :
#Given
u1=1.0
u2=1.54
u3=1.33

#Calculation
import math
u=u2/u1
a=math.atan(u)*180/3.14
U1=u1/u2
a2=math.atan(U1)*180/3.14
U2=u2/u3
a3=math.atan(U2)*180/3.14
U3=u3/u2
a4=math.atan(U3)*180/3.14
U4=u3/u1
a5=math.atan(U4)*180/3.14
U5=u1/u3
a6=math.atan(U5)*180/3.14

#Result
print"(i) Polarizing angle from air to glass is",round(a,0),"Degree"
print"(ii) Plolarizing angle from glass to air is",round(a2,0),"Degree"
print"(iii) Polarizing angle from water to glass is",round(a3,2),"Degree"
print"(iv) Polarizing angle from glass to water is",round(a4,2),"Degree"
print"(v) Polarizing angle from air to water is",round(a5,2),"Degree"
print"(vi) Polarizing angle from water to air is",round(a6,2),"Degree"

(i) Polarizing angle from air to glass is 57.0 Degree
(ii) Plolarizing angle from glass to air is 33.0 Degree
(iii) Polarizing angle from water to glass is 49.21 Degree
(iv) Polarizing angle from glass to water is 40.84 Degree
(v) Polarizing angle from air to water is 53.09 Degree
(vi) Polarizing angle from water to air is 36.96 Degree


## Example 3.5 Page no 131¶

In :
#Given
uglass=1.54
uwater=1.33

#Calculation
import math
u=uglass/uwater
i=math.atan(u)*180/3.14
u1=uwater/uglass
i1=math.atan(u1)*180/3.14

#Result
print"The polarizing angle for water to glass interface", round(i1,1),"degree is large"

The polarizing angle for water to glass interface 40.8 degree is large


## Example 3.6 Page no 131¶

In :
#Given
a=30                              #Degree
a1=45
a2=60

#Calculation
import math
I1=(math.cos(a*3.14/180.0))**2
I2=(math.cos(a1*3.14/180.0))**2
I3=(math.cos(a2*3.14/180.0))**2

#Result
print"(a) Intensity of light when analyser is rotated through 30 degree is", round(I1,2)
print"(b) Intensity of light when analyser is rotated through 45 degree is", round(I2,2)
print"(c) Intensity of light when analyser is rotated through 30 degree is", round(I3,2)

(a) Intensity of light when analyser is rotated through 30 degree is 0.75
(b) Intensity of light when analyser is rotated through 45 degree is 0.5
(c) Intensity of light when analyser is rotated through 30 degree is 0.25


## Example 3.7 Page no 132¶

In :
#Given
A=3.0

#Calculation
import math
x=1/(math.sqrt(A))
a=math.acos(x)*180/3.14

#Result
print"Angle is", round(a,2),"Degree"

Angle is 54.76 Degree


## Example 3.8 Page no 132¶

In :
#Given
a=30                         #Degree
b=60

#Calculation
import math
I=(math.cos(b*3.14/180.0)**2)/(math.cos(a*3.14/180.0)**2)

#Result
print"Intensity ratio is",round(I,2)

Intensity ratio is 0.33


## Example 3.9 Page no 132¶

In :
#Given
L=6000*10**-8
u0=1.55
ue=1.54

#Calculation
t=L/(2*(u0-ue))

#Result
print"Thickness is",t,"cm"

Thickness is 0.003 cm


## Example 3.10 Page no 133¶

In :
#Given
Uo =1.54
r =1.007
Ue=r*Uo
w =5893*10**-10

#Calculation
t=w /(2*( Uo -Ue))
t= abs (t)

print"Thickness of halfwave plate is",round(t*10**2,5),"cm"

Thickness of halfwave plate is 0.00273 cm


## Example 3.11 Page no 133¶

In :
#Given
Uo =1.652                         #refractive index for O ray
Ue =1.488
w =546*10**-9

#Calculation
p=w/2.0
t=w /(4.0*( Uo -Ue))
t1=t *100

#Result
print"Thickness of quarterwave plate is",round(t1*10**5,2)*10**-5,"cm"

Thickness of quarterwave plate is 8.32e-05 cm


## Example 3.12 Page no 133¶

In :
#Given
Uo =1.658
Ue =1.486
w =589*10**-9
n =1

#Calculation
t =(2*n -1)*w /(4.0*( Uo -Ue))
t1=t *100

#Result
print"Thickness of calcite plate is",round(t1*10**5,2)*10**-5,"cm"

Thickness of calcite plate is 8.56e-05 cm


## Example 3.13 Page no 134¶

In :
#Given
Ur =1.55810
Ul =1.55821
w=4*10**-7
d =0.002

#Calculation
R= 3.14*d*(Ul -Ur)/w
R1=R *180/3.14

#Result
print"Amount of optional rotation is",R1,"Degree"

Amount of optional rotation is 99.0 Degree


## Example 3.14 Page no 134¶

In :
#Given
Uo =1.5508
Ue =1.5418
w=5.0*10**-5
t =0.0032

#Calculation
p =2*3.14*(Uo -Ue)*t/w

#Result
print"Phase retardation is",round(p,2),"radian"

Phase retardation is 3.62 radian


## Example 3.15 Page no 134¶

In :
#Given
w=5892*10**-10
u=0.01
a=0.009

#Calculation
t=w/(2.0*a)
t1=w/(4.0*a)

#Result
print"Thickness of halfwave is", round(t*10**8,0),"*10**-8 m"
print"Thickness of quarter wave is",round(t1*10**8,0),"*10**-8 m"

Thickness of halfwave is 3273.0 *10**-8 m
Thickness of quarter wave is 1637.0 *10**-8 m


## Example 3.16 Page no 135¶

In :
#Given
ue=1.553
u0=1.544
w=5890*10**-10                   #m

#Calculation
t=w/(2*(ue-u0))

#Result
print"Thickness of halfwave plate is",round(t*10**7,0),"*10**-7 m"

Thickness of halfwave plate is 327.0 *10**-7 m


## Example 3.17 Page no 135¶

In :
#Given
theta =6.5
l =2
C =0.05

#Calculation
S= theta /(l*C)

#Result
print"Specific rotation of sugar solution is",S,"Degree"

Specific rotation of sugar solution is 65.0 Degree


## Example 3.18 Page no 135¶

In :
#Given
a=20
b=35
c1=5
c2=10.0

#Calculation
I2=b*c1/(a*c2)

#Result
print"Length of 10% solution is", I2

Length of 10% solution is 0.875


## Example 3.19 Page no 136¶

In :
#Given
l =2                                    #length of solution in decimeter
theta =12
S =60.0

#Calculation
C= theta /(S*l)

#Result
print"Strength of solution is",C,"gm/cc"

Strength of solution is 0.1 gm/cc


## Example 3.20 Page no 136¶

In :
#Given
a=20
l=3.5
s=60

#Calculation
C=a/(l*s)

#Result
print"Strength of sugar solution is",round(C*10**2,2),"%"

Strength of sugar solution is 9.52 %


## Example 3.21 Page no 136¶

In :
#Given
b =.172                              #bifringe of plate
w=6*10**-7

#Calculation
t=w /(4*( b))
t1=t *100

#Result
print"Thickness of quarterwave plate is",round(t1*10**5,2)*10**-5,"cm"

Thickness of quarterwave plate is 8.72e-05 cm