Chapter 3 Polarization of light

Example 3.1 Page no 130

In [10]:
#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 [14]:
#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 [18]:
#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 [38]:
#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 [43]:
#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 [51]:
#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 [60]:
#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 [64]:
#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 [66]:
#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 [77]:
#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 [23]:
#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 [27]:
#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 [29]:
#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 [81]:
#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 [97]:
#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 [102]:
#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 [103]:
#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 [105]:
#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 [34]:
#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 [111]:
#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 [39]:
#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