6: Fiber Optics

Example number 6.1, Page number 146

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.545;    #refractive index of optical fibre core
n2=1.495;    #refractive index of cladding

#Calculation
CA=math.asin(n2/n1);    #critical angle(radian)
CA=CA*180/math.pi;      #critical angle(degree)
CAm=int(CA);
CAs=int(60*(CA-CAm));
AA=math.asin(math.sqrt(n1**2-n2**2));   #acceptance angle(radian)
AAd=AA*180/math.pi;      #acceptance angle(degree) 
AAm=int(AAd);
AAs=int(60*(AAd-AAm));
NA=math.sin(AA);    #numerical aperture

#Result
print "The critical angle is",CAm,"degrees",CAs,"minutes"
print "The acceptance angle is",AAm,"degrees",AAs,"minutes"
print "The numerical aperture is",round(NA,4)
print "answer varies due to rounding off errors"

The critical angle is 75 degrees 23 minutes
The acceptance angle is 22 degrees 56 minutes
The numerical aperture is 0.3899
answer varies due to rounding off errors

Example number 6.2, Page number 147

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.54;    #refractive index of optical fibre core
n2=1.5;     #refractive index of cladding

#Calculation
NA=math.sqrt(n1**2-n2**2);    #numerical aperture

#Result
print "The numerical aperture is",round(NA,4)

The numerical aperture is 0.3487

Example number 6.3, Page number 147

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.55;    #refractive index of optical fibre core
n2=1.47;    #refractive index of cladding

#Calculation
CA=math.asin(n2/n1);    #critical angle(radian)
CA=CA*180/math.pi;      #critical angle(degree) 
CAm=int(CA);
CAs=int(60*(CA-CAm));
NA=math.sqrt(n1**2-n2**2);    #numerical aperture 
AA=math.asin(NA);   #acceptance angle(radian)
AAd=AA*180/math.pi;      #acceptance angle(degree) 
AAm=int(AAd);
AAs=int(60*(AAd-AAm));

#Result
print "The critical angle is",CAm,"degrees",CAs,"minutes"
print "The acceptance angle is",AAm,"degrees",AAs,"minutes"
print "The numerical aperture is",round(NA,4)
print "answer for acceptance angle and numerical aperture given in the book is wrong"

The critical angle is 71 degrees 30 minutes
The acceptance angle is 29 degrees 26 minutes
The numerical aperture is 0.4915
answer for acceptance angle and numerical aperture given in the book is wrong

Example number 6.4, Page number 147

In [31]:
#importing modules
import math
from __future__ import division

#Variable declaration
n2=1.55;   #refractive index of cladding
no=1.33;   #refractive index of water
NA=0.20;   #numerical aperture of optical fibre

#Calculation
n1=math.sqrt(n2**2+NA**2);   #refractive index of optical fibre
NAW=math.sqrt(n1**2-n2**2)/no;   #numerical aperture when fibre is in water
AA=math.asin(NAW);    #Acceptance angle for the fibre in water(degrees)
AAd=AA*180/math.pi;      #acceptance angle(degree) 
AAm=int(AAd);
AAs=int(60*(AAd-AAm));

#Result
print "The refractive index of optical fibre is",round(n1,4)
print "The numerical aperture when fibre is in water is",round(NAW,2)
print "The Acceptance angle for the fibre in water is",AAm,"degrees",AAs,"minutes"
print "answer for minutes varies due to rounding off errors"

The refractive index of optical fibre is 1.5628
The numerical aperture when fibre is in water is 0.15
The Acceptance angle for the fibre in water is 8 degrees 38 minutes
answer for minutes varies due to rounding off errors

Example number 6.5, Page number 148

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration
NA=0.22;   #numerical aperture of optical fibre
no=0.012;  #refractive index difference

#Calculation
n1=NA/math.sqrt(2*no);    #The refractive index of the core of a fibre
n2=n1*(1-no);     #The refractive index of the cladding

#Result
print "The refractive index of the core of a fibre is",round(n1,2)
print "The refractive index of the cladding is",round(n2,3)
print "answer varies due to rounding off errors"

The refractive index of the core of a fibre is 1.42
The refractive index of the cladding is 1.403
answer varies due to rounding off errors