# Ch-2 : Ray Theory Transmission in Optical Fibers¶

## Ex:2_1 Pg: 54¶

In [3]:
from __future__ import division
from math import asin,pi,ceil,sqrt
n1=1.55## core refractive index
n2=1.50## cladding refractive index
x=asin(n2/n1)# # Critical angle in radians
x1=x*180/(pi)## Critical angle in degree
n_a=sqrt(n1**2-n2**2)## Numerical aperture
x_a=asin(n_a)*180/(pi)#
x_a1=ceil(x_a)## Acceptance angle in Degree
print "Critical angle in degree= %0.2f degree"%(x1)#
print "\n Numerical aperture= %0.2f "%(n_a)#
print "\n Acceptance angle in degree= %0.2f degree"%(x_a1)

Critical angle in degree= 75.41 degree

Numerical aperture= 0.39

Acceptance angle in degree= 23.00 degree


## Ex:2.2 Pg: 56¶

In [4]:
from __future__ import division
from math import sin,sqrt
c=3*10**8## speed of light in m/s
v=2*10**8## in m/s
n1=c/v#
x=75## in degree
n2=n1*sin((x*3.14/180))#
n_2=1.44#
n_a=sqrt(n1**2-n_2**2)## numerical aperture
print "Numerical aperture = %0.2f"%(n_a)

Numerical aperture = 0.42


## Ex:2.3 Pg: 57¶

In [5]:
from __future__ import division
from math import sqrt,asin,pi
n1=1.50## core refractive index
n2=1.47## cladding refractive index
dl=(n1-n2)/n1#
n_a=n1*(sqrt(2*dl))## numerical aperture
x_a=(asin(n_a))*180/pi## acceptance angle in degree
print "Numerical aperture = %0.2f"%(n_a)#
print "\n acceptance angle in degree = %0.2f degree"%(x_a)

Numerical aperture = 0.30

acceptance angle in degree = 17.46 degree


## Ex:2.4 Pg: 58¶

In [6]:
from __future__ import division
from math import sqrt,asin,pi
n1=1.50## core refractive index
n2=1.45## cladding refractive index
dl=(n1-n2)/n1#
n_a=n1*(sqrt(2*dl))## numerical aperture
x_a=(asin(n_a))*180/pi## acceptance angle in degree
x_c=(asin(n2/n1))*180/3.14## critical angle in degree
print "Numerical aperture = %0.2f"%(n_a)#
print "\n acceptance angle in degree = %0.2f degree"%(x_a)#
print "\n critical angle in degree = %0.2f degree"%(x_c)

Numerical aperture = 0.39

acceptance angle in degree = 22.79 degree

critical angle in degree = 75.20 degree


## Ex:2.5 Pg: 58¶

In [7]:
from __future__ import division
from math import sqrt
dl=0.012#
n_a=0.22## numerical aperture
n1=n_a/(sqrt(2*dl))## core refractive ondex
n2=n1-(dl*n1)## cladding refractive index
print "core refractive ondex = %0.2f"%(n1)#
print "\n cladding refractive index = %0.2f"%(n2)

core refractive ondex = 1.42

cladding refractive index = 1.40


## Ex:2.6 Pg: 59¶

In [8]:
from math import sqrt
from __future__ import division
dl=0.01#
n_a=0.35## numerical aperture
n1=n_a/(sqrt(2*dl))## core refractive ondex
n2=n1-(dl*n1)## cladding refractive index
print "core refractive ondex = %0.2f"%(n1)#
print "\n cladding refractive index = %0.2f"%(n2)

core refractive ondex = 2.47

cladding refractive index = 2.45


## Ex:2.7 Pg: 59¶

In [10]:
from math import sqrt,asin,pi,floor
from __future__ import division
n2=1.59## cladding refractive index
n_a=0.2## numerical aperture
n1=sqrt(n2**2+n_a**2)## core refractive index
n_1=1.60## core refractive index
n_o=1.33#
A=(sqrt(n_1**2-n2**2))/n_o#
x_a=(asin(A))*180/pi## acceptance angle in degree
x_c=(asin(n2/n1))*180/pi## critical angle in degree
y=1300*10**(-9)## in meter
a=25*10**(-6)## in meter
v=(2*pi*a*n_a)/y#
V=floor(v)#
M=V**2/2## number of modes transmitted
print "acceptance angle in degree = %0.2f degree"%(x_a)#
print "\n critical angle in degree = %0.2f degree"%(x_c)#
print "\n number of modes transmitted = %d"%(M)

acceptance angle in degree = 7.72 degree

critical angle in degree = 82.83 degree

number of modes transmitted = 288


## Ex:2.8 Pg: 60¶

In [11]:
from math import sqrt,pi,asin
from __future__ import division
n1=1.50## core refractive index
n2=1.47## cladding refractive index
dl=(n1-n2)/n1#
n_a=n1*(sqrt(2*dl))## numerical aperture
x_e=(asin(n_a))*180/pi## the maximum entrance angle in degree
print "Numerical aperture = %0.2f"%(n_a)#
print "\n the maximum entrance angle in degree = %0.2f degree"%(x_e)

Numerical aperture = 0.30

the maximum entrance angle in degree = 17.46 degree


## Ex:2.9 Pg: 61¶

In [12]:
from math import sqrt,pi,asin
from __future__ import division
n1=1.44## core refractive index
dl=0.02#
n_a=n1*sqrt(2*dl)#
n_a=n1*(sqrt(2*dl))## numerical aperture
x_a=(asin(n_a))*180/pi## acceptance angle in degree
print "Numerical aperture = %0.2f"%(n_a)#
print "\n acceptance angle in degree = %0.2f degree"%(x_a)

Numerical aperture = 0.29

acceptance angle in degree = 16.74 degree


## Ex:2.10 Pg: 61¶

In [13]:
from math import sqrt,pi,asin
from __future__ import division
n1=1.50## core refractive index
n2=(99/100)*1.50## cladding refractive index
x_c=(asin(n2/n1))*180/pi## critical angle in degree
n_m=sqrt(n1**2-n2**2)## numerical aperture
print "critical angle = %0.2f degree"%(x_c)#
print "\n numerical aperture = %0.2f"%(n_m)

critical angle = 81.89 degree

numerical aperture = 0.21


## Ex:2.11 Pg: 61¶

In [14]:
from math import sqrt,pi
from __future__ import division
n1=1.50## core refractive index
n2=1.45## cladding refractive index
n_m=sqrt(n1**2-n2**2)## numerical aperture
dl=(n1-n2)/n1## fractional difference
print "numerical aperture = %0.2f"%(n_m)#
print "\n fractional difference = %0.2f"%(dl)

numerical aperture = 0.38

fractional difference = 0.03


## Ex:2.12 Pg: 62¶

In [15]:
from math import sqrt,pi,asin
from __future__ import division
n1=1.46## core refractive index
n2=1.45## cladding refractive index
x_c=(asin(n2/n1))*180/pi## critical angle in degree
n_m=sqrt(n1**2-n2**2)## numerical aperture
x_a=(asin(n_m))*180/pi## acceptance angle in degree
print "critical angle = %0.2f degree"%(x_c)#
print "\n acceptance angle = %0.2f degree"%(x_a)#
print "\n numerical aperture = %0.2f"%(n_m)

critical angle = 83.29 degree

acceptance angle = 9.82 degree

numerical aperture = 0.17


## Ex:2.13 Pg: 62¶

In [16]:
from math import sqrt,pi
from __future__ import division
n_m=0.204## numerical aperture
dl=0.01## index difference
n1=n_m/(sqrt(2*dl))## core refractive index
n2=n1*(1-dl)## cladding refractive index
print "core refractive index = %0.2f"%(n1)#
print "\n cladding refractive index = %0.2f"%(n2)

core refractive index = 1.44

cladding refractive index = 1.43


## Ex:2.14 Pg: 62¶

In [17]:
from math import sqrt,pi,asin
from __future__ import division
n1=1.46## core refractive index
dl=0.01## index difference
n_2=n1-(n1*dl)## cladding refractive index
x_c=(asin(n_2/n1))*180/pi## critical angle in degree
n_m=sqrt(n1**2-n_2**2)## numerical aperture
print "critical angle = %0.2f degree"%(x_c)#
print "\n numerical aperture = %0.2f"%(n_m)

critical angle = 81.89 degree

numerical aperture = 0.21


## Ex:2.15 Pg: 62¶

In [18]:
from math import sqrt,pi,asin
from __future__ import division
n1=1.50## core refractive index
n2=1.45## cladding refractive index
x_c=(asin(n2/n1))*180/pi## critical angle in degree
n_m=sqrt(n1**2-n2**2)## numerical aperture
x_a=(asin(n_m))*180/pi## acceptance angle in degree
n_c=(n_m)**2*100## percentage of light
print "critical angle=%0.2f degree"%(x_c)#
print "\n acceptance angle=%0.2f degree"%(x_a)#
print "\n numerical aperture=%0.2f"%(n_m)#
print "\n percentage of light=%0.2f%%"%(n_c)

critical angle=75.16 degree

acceptance angle=22.59 degree

numerical aperture=0.38

percentage of light=14.75%


## Ex:2.16 Pg: 63¶

In [19]:
from math import sqrt,pi,asin
from __future__ import division
n1=1.50## core refractive index
dl=0.01## index difference
n_m=n1*(sqrt(2*dl))## numerical aperture
x_a=pi*(n_m)**2## acceptance angle in radian
n2_1=1-dl## the ratio of n2 to n1
x_c=(asin(n2_1))*180/pi## critical angle in degree
print "numerical aperture=%0.2f"%(n_m)#
print "\n acceptance angle=%0.2f radian"%(x_a)#
print "\n critical angle=%0.2f degree"%(x_c)

numerical aperture=0.21