Fibre Optics

Example number 3.1, Page number 98

In [4]:
#importing modules
import math

#Variable declaration
n1=1.6;    #refractive index of core
n2=1.5;    #refractive index of cladding

#Calculation
NA=math.sqrt((n1**2)-(n2**2));
NA=math.ceil(NA*10**4)/10**4;   #rounding off to 4 decimals

#Result
print("the numerical aperture of the fibre is",NA);

('the numerical aperture of the fibre is', 0.5568)

Example number 3.2, Page number 98

In [7]:
#importing modules
import math

#Variable declaration
n1=1.54;    #refractive index of core
n2=1.5;    #refractive index of cladding
n0=1;

#Calculation
NA=math.sqrt((n1**2)-(n2**2));         #numerical aperture of fibre
NA=math.ceil(NA*10**5)/10**5;   #rounding off to 5 decimals
alpha=math.asin(NA/n0);          #acceptance angle in radians
alpha=alpha*57.2957795;        #converting radians to degrees
alpha=math.ceil(alpha*10**5)/10**5;   #rounding off to 5 decimals
deg=int(alpha);        #converting to degrees
t=60*(alpha-deg);   
mi=int(t);     #converting to minutes
sec=60*(t-mi);    #converting to seconds
sec=math.ceil(sec*10**3)/10**3;   #rounding off to 3 decimals

#Result
print("the numerical aperture of the fibre is",NA);
print("the acceptance angle of the fibre in degrees is",alpha);
print("acceptance angle of the fibre is",deg,"degrees",mi,"minutes",sec,"seconds");

#answer for the angle given in the book is wrong

('the numerical aperture of the fibre is', 0.34872)
('the acceptance angle of the fibre in degrees is', 20.40905)
('acceptance angle of the fibre is', 20, 'degrees', 24, 'minutes', 32.581, 'seconds')

Example number 3.3, Page number 99

In [10]:
#importing modules
import math

#Variable declaration
n1=1.6;    #refractive index of core
n2=1.49;    #refractive index of cladding

#Calculation
thetac=math.asin(n2/n1);       #critical angle in radians
thetac=thetac*57.2957795;        #converting radians to degrees
theta_c=math.ceil(thetac*10**3)/10**3;   #rounding off to 3 decimals
deg=int(thetac);        #converting to degrees
t=60*(thetac-deg);   
mi=int(t);     #converting to minutes
sec=60*(t-mi);    #converting to seconds
sec=math.ceil(sec*10**2)/10**2;   #rounding off to 2 decimals

#Result
print("the critical angle of the fibre in degrees is",theta_c);
print("critical angle of the fibre is",deg,"degrees",mi,"minutes",sec,"seconds");

('the critical angle of the fibre in degrees is', 68.631)
('critical angle of the fibre is', 68, 'degrees', 37, 'minutes', 49.85, 'seconds')

Example number 3.4, Page number 99

In [13]:
#importing modules
import math

#Variable declaration
NA=0.15;     #numerical aperture
n2=1.55;    #refractive index of cladding
n0=1.33;    #refractive index of water

#Calculation
n1=math.sqrt((NA**2)+(n2**2));      #refractive index
n_1=math.ceil(n1*10**5)/10**5;   #rounding off to 5 decimals
alpha=math.asin(math.sqrt(n1**2-n2**2)/n0);     #acceptance angle in radians
alpha=alpha*57.2957795;        #converting radians to degrees
alphaa=math.ceil(alpha*10**3)/10**3;   #rounding off to 3 decimals
deg=int(alpha);        #converting to degrees
t=60*(alpha-deg);   
mi=int(t);     #converting to minutes
sec=60*(t-mi);    #converting to seconds
sec=math.ceil(sec*10**2)/10**2;   #rounding off to 2 decimals

#Result
print("refractive index of the core is",n_1);
print("the acceptance angle of the fibre in degrees is",alphaa);
print("acceptance angle of the fibre is",deg,"degrees",mi,"minutes",sec,"seconds");

#answer for acceptance angle given in the book is wrong

('refractive index of the core is', 1.55725)
('the acceptance angle of the fibre in degrees is', 6.476)
('acceptance angle of the fibre is', 6, 'degrees', 28, 'minutes', 32.55, 'seconds')

Example number 3.5, Page number 100

In [16]:
#importing modules
import math

#Variable declaration
NA=0.26;     #numerical aperture
n1=1.5;    #refractive index of core
d=100;     #core diameter in micro meter

#Calculation
d=100*(10**-6);    #core diameter in metre
n2=math.sqrt((n1**2)-(NA**2));
n2=math.ceil(n2*10**5)/10**5;   #rounding off to 5 decimals

#Result
print("refractive index of the cladding is",n2);

('refractive index of the cladding is', 1.4773)

Example number 3.6, Page number 100

In [19]:
#importing modules
import math

#Variable declaration
NA=0.26;     #numerical aperture
delta=0.015;   #refractive index difference

#Calculation
#NA=math.sqrt(n1**2-n2**2)
#let A=n1**2-n2**2
#therefore A=NA**2
A=NA**2;
#delta=(n1**2-n2**2)/2*(n1**2)
#let 2*(n1**2) be B
#therefore B=A/delta
B=A/delta;
n1=math.sqrt(B/2);
n1=math.ceil(n1*100)/100;   #rounding off to 2 decimals
n2=math.sqrt(n1**2-NA**2);
n2=math.ceil(n2*10**3)/10**3;   #rounding off to 4 decimals

#Result
print("refractive index of the core is",n1);
print("refractive index of the cladding is",n2);

#answer for refractive index of cladding given in the book is wrong

('refractive index of the core is', 1.51)
('refractive index of the cladding is', 1.488)
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