# Chapter24-Fibre Optics¶

## Ex1-pg701¶

In [1]:
import math
##Example 24.1
##Fiber optics

##given values
n=1.5;##refractive index
x=.0005;##fractional index difference

##calculation
u=n*(1-x);
alpha=math.asin(u/n)*180/math.pi;
print'%s %.2f %s'%('critical internal reflection angle(in degree) is',alpha,'');
theta=math.asin(math.sqrt(n**2-u**2))*180/math.pi;
print'%s %.2f %s'%('critical acceptance angle(in degree) is',theta,'');
N=n*math.sqrt(2.*x);
print'%s %.2f %s'%('numerical aperture is',N,'');

cladding index is 1.50
critical internal reflection angle(in degree) is 88.19
critical acceptance angle(in degree) is 2.72
numerical aperture is 0.05


## Ex2-pg701¶

In [2]:
import math
##Example 24.2
##calculation of acceptance angle

##given values
u=1.33;##refractive index of water
N=.20;##numerical aperture offibre
##calculation
x=math.sqrt(N**2+n**2.);##index of fibre
N1=math.sqrt(x**2-n**2.)/u;##numerical aperture when fibre is in water
alpha=math.asin(N1)*180./math.pi;
print'%s %.2f %s'%('acceptance angle in degree is',alpha,'');

acceptance angle in degree is 8.65


## Ex3-pg705¶

In [3]:
import math
##Example 24.3
##calculation of normalised frequency

##given values
n=1.45;##core refractive index
d=.6;##core diametre in m
N=.16;##numerical aperture of fibre
l=.9*10**-6.;##wavelength of light

##calculation
u=math.sqrt(n**2.+N**2.);##index of glass fibre
V=math.pi*d*math.sqrt(u**2.-n**2.)/l;
print'%s %.2f %s'%('normalised frequency is',V,'');

normalised frequency is 335103.22


## Ex4-pg705¶

In [4]:
import math
##Example 24.4
##calculation of normailsed frequency and no of modes

##given values
n=1.52;##core refractive index
d=29*10**-6.;##core diametre in m
l=1.3*10**-6.;##wavelength of light
x=.0007;##fractional refractive index

##calculation
u=n*(1.-x);##index of glass fibre
V=math.pi*d*math.sqrt(n**2-u**2)/l;
print'%s %.2f %s'%('normalised frequency is',V,'');
N=V**2./2.;
print'%s %.2f %s'%('no of modes is',N,'');

normalised frequency is 3.99
no of modes is 7.94


## Ex5-pg706¶

In [5]:
import math
##Example 24.5
##calculation of numerical aperture and maximum acceptance angle

##given values
n=1.480;##core refractive index
u=1.47;##index of glass
l=850*10**-9.;##wavelength of light
V=2.405;##V-number

##calculation
r=V*l/math.sqrt(n**2-u**2)/math.pi/2;##in m
print'%s %.2f %s'%('core radius in micrometre is',r*10**6,'');
N=math.sqrt(n**2-u**2);
print'%s %.2f %s'%('numerical aperture is',N,'');
alpha=math.asin(N)*180/math.pi;
print'%s %.2f %s'%('max acceptance angle is',alpha,'');

core radius in micrometre is 1.89
numerical aperture is 0.17
max acceptance angle is 9.89


## Ex6-pg712¶

In [6]:
import math
##Example 24.6
##calculation of power level

##given values
a=3.5;##attenuation in dB/km
Pi=.5*10**-3.;##initial power level in W
l=4.;##length of cable in km

##calculation
Po=Pi*10**6./(10**(a*l/10.));
print'%s %.2f %s'%('power level after km(in microwatt) is',Po,'');

power level after km(in microwatt) is 19.91


## Ex7-pg712¶

In [7]:
import math
##Example 24.7
##calculation of power loss

##given values
Pi=1*10**-3.;##initial power level in W
l=.5;##length of cable in km
Po=.85*Pi

##calculation
a=(10./l)*math.log10(Pi/Po);
print'%s %.2f %s'%('loss in dB/km is',a,'');

loss in dB/km is 1.41