12: Fibre Optics

Example number 12.1, Page number 263

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
NA=0.39;    #numerical aperture
delta=0.05;     #refractive index of cladding

#Calculation
n1=NA/math.sqrt(2*delta);      #refractive index of core

#Result
print "refractive index of core is",round(n1,3)

refractive index of core is 1.233

Example number 12.2, Page number 264

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.563;          #Core refractive index
n2=1.498;          #Cladding refractive index

#Calculation
delta=(n1-n2)/n1;    #fractional index change

#Result
print "fractional index change is",round(delta,5)

fractional index change is 0.04159

Example number 12.3, Page number 264

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.55;          #Core refractive index
n2=1.50;          #Cladding refractive index

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

#Result
print "numerical aperture is",round(NA,2)

numerical aperture is 0.39

Example number 12.4, Page number 264

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.563;          #Core refractive index
n2=1.498;          #Cladding refractive index

#Calculation
NA=math.sqrt(n1**2-n2**2);    #numerical aperture
theta0=math.asin(NA);    #acceptance angle(radian)
theta0=theta0*180/math.pi;    #acceptance angle(degrees)

#Resul"
print "acceptance angle is",round(theta0,2),"degrees"

acceptance angle is 26.49 degrees

Example number 12.5, Page number 265

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.53;          #Core refractive index
n2=1.42;          #Cladding refractive index

#Calculation
thetac=math.asin(n2/n1);     #critical angle(radian)
thetac=thetac*180/math.pi;    #critical angle(degrees)

#Resul"
print "critical angle is",round(thetac,2),"degrees"

critical angle is 68.14 degrees

Example number 12.6, Page number 265

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.6;          #Core refractive index
n0=1.33;         #refractive index of air
n2=1.4;          #Cladding refractive index

#Calculation
NA=math.sqrt(n1**2-n2**2)/n0;    #numerical aperture
theta0=math.asin(NA);    #acceptance angle(radian)
theta0=theta0*180/math.pi;    #acceptance angle(degrees)

#Resul"
print "acceptance angle is",round(theta0,2),"degrees"
print "answer in the book varies due to rounding off errors"

acceptance angle is 35.62 degrees
answer in the book varies due to rounding off errors

Example number 12.7, Page number 265

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.5;          #Core refractive index
n2=1.3;          #Cladding refractive index

#Calculation
delta=(n1-n2)/n1;    #fractional index change

#Result
print "fractional index change is",round(delta,3)

fractional index change is 0.133

Example number 12.8, Page number 265

In [10]:
#importing modules
import math
from __future__ import division

#Variable declaration
n1=1.55;          #Core refractive index
n2=1.6;          #Cladding refractive index
theta1=60*math.pi/180;     #incident angle(degrees)

#Calculation
x=n1*math.sin(theta1)/n2;
theta2=math.asin(x);    #refraction angle(radian)
theta2=theta2*180/math.pi;    #refraction angle(degrees)

#Result
print "refraction angle is",round(theta2,2),"degrees"

refraction angle is 57.03 degrees

Example number 12.9, Page number 266

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
n2=1.3;          #Cladding refractive index
delta=0.140;    #fractional index change

#Calculation
n1=n2/(1-delta);     #Core refractive index

#Result
print "refractive index of core is",round(n1,2)

refractive index of core is 1.51

Example number 12.10, Page number 266

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
theta0=26.80*math.pi/180;    #acceptance angle(radian)

#Calculation
NA=math.sin(theta0);       #numerical aperture

#Result
print "numerical aperture is",round(NA,5)

numerical aperture is 0.45088