Chapter 18 Dispersion of light

Example 18.1 Page no 986

In [17]:
#Given
A=60                            #Degree

#Calculation
import math
a=math.sqrt(2)*math.sin(30*3.14/180.0)
b=math.asin(a)*180/3.14
c=(b*2)-A
i=(A+c)/2.0
r=A/2.0

#Result
print"(i) Angle of minimum deviation is", round(c,0),"Degree"
print"(ii) Angle of incidence is", round(i,0),"Degree"
print"(iii) The angle of refraction is", r,"Degree"

(i) Angle of minimum deviation is 30.0 Degree
(ii) Angle of incidence is 45.0 Degree
(iii) The angle of refraction is 30.0 Degree

Example 18.2 Page no 986

In [30]:
#Given
a=51                                   #Degree
A=60                                   #Degree

#Calculation
import math
b=(A+a)/2.0
c=A/2.0
u=(math.sin(b*3.14/180.0))/(math.sin(c*3.14/180.0))

#Result
print"(i) The refracting angle of the prism is", A,"Degree"
print"(ii) The refractive index of the material is",round(u,4)

(i) The refracting angle of the prism is 60 Degree
(ii) The refractive index of the material is 1.6485

Example 18.3 Page no 987

In [35]:
#Given
i1=48                         #Degree
A=60                          #Degree

#Calculation
import math
r=A/2.0
u=math.sin(i1*3.14/180.0)/math.sin(r*3.14/180.0)

#Result
print"Refractive index of the material is", round(u,2)

Refractive index of the material is 1.49

Example 18.4 Page no 987

In [42]:
#Given
a=2.0

#Calculation
import math
a=math.sqrt(a)/a
i=math.asin(a)*180/3.14

#Result
print"Angle of incidence is", round(i,0),"Degree"

Angle of incidence is 45.0 Degree

Example 18.5 Page no 987

In [45]:
#Given
u=1.5
a=6                          #Degree

#Calculation
A=a/(u-1)

#Result
print"Angle of the prism is", A,"Degree"

Angle of the prism is 12.0 Degree

Example 18.6 Page no 987

In [68]:
#Given
ug=1.5
r1=30                      #Degree
ua=1.0
A=60                       #Degree
A1=90                     #Degree

#Calculation
sin=(ug*math.sin(r1*3.14/180.0))/ua
i1=math.asin(sin)*180/3.14
a=(2*i1)-A
sin1=1/ug
r1=math.asin(sin1)*180/3.14
r2=A-r1
sin2=(ug*math.sin(r2*3.14/180.0))
i2=math.asin(sin2)*180/3.14
A3=A1+i2-A

#Result
print"(i) The angle of incidence for minimum deviation is", round(i1,0),"Degree"
print"(ii) The angle of minimum deviation is", round(a,0)
print"(iii) The angle of emergence of light at maximum deviation is", round(i2,0),"Degree"
print"(iv) Angle of maximum deviation is", round(A3,0)

(i) The angle of incidence for minimum deviation is 49.0 Degree
(ii) The angle of minimum deviation is 37.0
(iii) The angle of emergence of light at maximum deviation is 28.0 Degree
(iv) Angle of maximum deviation is 58.0

Example 18.7 Page no 991

In [71]:
#Given
uv=1.68
ur=1.56
A=18                         #degree

#Calculation
A1=A*(uv-ur)

#Result
print"Angular dispersion is", A1,"Degree"

Angular dispersion is 2.16 Degree

Example 18.8 Page no 991

In [74]:
#Given
av=3.32                              #Degree
ar=3.22                              #Degree
a=3.27                               #Degree

#Calculation
w=(av-ar)/a

#Result
print"Dispersive power of the flint glass is", round(w,4)

Dispersive power of the flint glass is 0.0306

Example 18.9 Page no 991

In [79]:
#Given
ur=1.5155
uv=1.5245

#Calculation
u=(ur+uv)/2.0
w=(uv-ur)/(u-1)

#Result
print"Dispersive power of the crown glass is", round(w,4)

Dispersive power of the crown glass is 0.0173

Example 18.10 Page no 991

In [83]:
#given
w=0.031
ur=1.645
ub=1.665

#Calculation
u=1+((ub-ur))/w

#Result
print"Refrective index for yellow colour is", round(u,3)

Refrective index for yellow colour is 1.645

Example 18.11 Page no 992

In [91]:
#Given
A=5                          #Degree
uv=1.523
ur=1.515
uv1=1.688
ur1=1.650

#Calculation
u=(uv+ur)/2.0
u1=(uv1+ur1)/2.0
A1=-((u-1)*A)/(u1-1)

#Result
print"Angle of flint line is",round(A1,2),"degree"

Angle of flint line is -3.88 degree

Example 18.12 Page no 992

In [95]:
#Given
w=0.021
u=1.53
w1=0.045
u1=1.65
A1=4.20                        #Degree

#Calculation
A=-(w1*A1*(u1-1))/(w*(u-1))

#Result
print"Angle of the prism is", round(A,2),"Degree"

Angle of the prism is -11.04 Degree

Example 18.13 Page no 992

In [122]:
#Given
A=72                          #Degree
ab=56.4                       #Degree
ar=53                          #Degree
ay=54.6                        #Degree
az=54
A11=60                         #Degree
ab1=52.8                       
A12=50.6
A13=51.9

#Calculation
import math
A1=(A+ay)/2.0
A2=A/2.0
ub=(math.sin(A1*3.14/180.0))/(math.sin(A2*3.14/180.0))
A3=(A+ar)/2.0
ur=(math.sin(A3*3.14/180.0))/(math.sin(A2*3.14/180.0))
A4=(A+az)/2.0
uy=(math.sin(A4*3.14/180.0))/(math.sin(A2*3.14/180.0))
w=(ub-ur)/(uy-1)

#For flint glass prism
A5=(A11+ab1)/2.0
A51=A11/2.0
ub1=(math.sin(A5*3.14/180.0))/(math.sin(A51*3.14/180.0))
A6=(A11+A12)/2.0
ur1=(math.sin(A6*3.14/180.0))/(math.sin(A51*3.14/180.0))
A7=(A11+A13)/2.0
uy1=(math.sin(A7*3.14/180.0))/(math.sin(A51*3.14/180.0))
w1=(ub1-ur1)/(uy1-1)
w2=w/w1

#Result
print"The ratio of dispersive power of crown glass and flint glass prism is", round(w2,3)

The ratio of dispersive power of crown glass and flint glass prism is 0.64