# Chapter 2- Optical Fiber¶

## Example 1: PgNo- 18¶

In [3]:
import math

# Variable declaration
n1=1.55 # core refractive index

# Calculations
x1=x*180/math.pi   #Critical angle in degree
n_a=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # Numerical aperture
x_a=math.asin(n_a)*180/math.pi
x_a1=math.ceil(x_a) # Acceptance angle in Degree

# Results
print ('%s %.2f %s' %(" Critical angle in degree= ", x1,"degree"))
print ('%s %.2f ' %("\n Numerical aperture= ",n_a))
print ('%s %.1f %s' %("\n Acceptance angle in degree= ",x_a1,"degree"))

 Critical angle in degree=  75.41 degree

Numerical aperture=  0.39

Acceptance angle in degree=  23.0 degree


## Example 2:PgNo-21¶

In [4]:
import math
# Variable declaration

c=3*math.pow(10,8) #speed of light in m/s
v=2*math.pow(10,8) # in m/s
# calculations
n1=c/v
x=75    # in degree
n2=n1*math.sin((x*math.pi/180))
n_2=1.44
n_a=math.sqrt(math.pow(n1,2)-math.pow(n_2,2)) # numerical aperture

# Results
print ('%s %.2f' %(" Numerical aperture = ",n_a))

 Numerical aperture =  0.42


## Example 3:PgNo-25¶

In [5]:
import math

# Variable declaration
n1=1.50 # core refractive index

# Calculations
dl=(n1-n2)/n1
n_a=n1*(math.sqrt(2*dl))# numerical aperture
x_a=(math.asin(n_a))*180/math.pi #acceptance angle in degree

# Results
print ('%s %.2f' %(" Numerical aperture = ",n_a))
print ('%s %.2f %s' %("\n Acceptance angle in degree = ",x_a,"degree"))

 Numerical aperture =  0.30

Acceptance angle in degree =  17.46 degree


## Example 4:PgNo-27¶

In [6]:
import math

# Variable declaration
n1=1.50 # core refractive index

# Calculations
dl=(n1-n2)/n1
n_a=n1*(math.sqrt(2*dl)) # numerical aperture
x_a=(math.asin(n_a))*180/math.pi # acceptance angle in degree
x_c=(math.asin(n2/n1))*180/math.pi # critical angle in degree

# Results
print ('%s %.2f' %(" Numerical aperture = ",n_a))
print ('%s %.2f %s' %("\n acceptance angle in degree = ",x_a,"degree"))
print ('%s %.2f %s' %("\n critical angle in degree = ",x_c,"degree"))

 Numerical aperture =  0.39

acceptance angle in degree =  22.79 degree

critical angle in degree =  75.16 degree


## Example 5:PgNo- 32¶

In [7]:
import math

# Variable declaration
dl=0.012
n_a=0.22  # numerical aperture

# Calculations
n1=n_a/(math.sqrt(2*dl)) # core refractive index

# Results
print ('%s %.2f' %(" core refractive index = ",n1))
print ('%s %.2f' %("\n cladding refractive index = ",n2))

 core refractive index =  1.42



## Example 6:PgNo-34¶

In [8]:
import math

# Variable declaration
dl=0.012
n_a=0.22 # numerical aperture

# Calculations
n1=n_a/(math.sqrt(2*dl)) # core refractive index

# Results
print ('%s %.2f' %(" core refractive index = ",n1))
print ('%s %.2f' %("\n cladding refractive index = ",n2))

 core refractive index =  1.42



## Example 7:PgNo-37¶

In [9]:
import math

# Variable declaration
n_a=0.2 # numerical aperture
n_1=1.60 # core refractive index
n_o=1.33

# Calculations
n1=math.sqrt(math.pow(n2,2)+math.pow(n_a,2)) # core refractive index
A=(math.sqrt(math.pow(n_1,2)-math.pow(n2,2)))/n_o
x_a=(math.asin(A))*180/math.pi        # acceptance angle in degree
x_c=(math.asin(n2/n1))*180/math.pi    #critical angle in degree
y=1300*math.pow(10,(-9))    # in meter
a=25*math.pow(10,(-6))      # in meter
v=(2*math.pi*a*n_a)/y
V=math.floor(v)
M=math.pow(V,2)/2 # number of modes transmitted

# Results
print ('%s %.2f %s' %(" acceptance angle in degree = ",x_a,"degree"))
print ('%s %.2f %s' %("\n critical angle in degree = ",x_c,"degree"))
print ('%s %d' %("\n number of modes transmitted = ",M))

 acceptance angle in degree =  7.72 degree

critical angle in degree =  82.83 degree

number of modes transmitted =  288


## Example 8:PgNo-42¶

In [10]:
import math

# Variable declaration
n1=1.50 # core refractive index

# Calculations
dl=(n1-n2)/n1
n_a=n1*(math.sqrt(2*dl)) # numerical aperture
x_e=(math.asin(n_a))*180/math.pi # the maximum entrance angle in degree

# Results
print ('%s %.1f' %(" Numerical aperture = ",n_a))
print ('%s %.2f %s' %("\n The maximum entrance angle in degree = ",x_e,"degree"))

 Numerical aperture =  0.3

The maximum entrance angle in degree =  17.46 degree


## Example 9:PgNo-47¶

In [11]:
import math

# Variable declaration
n1=1.44 # core refractive index
dl=0.02

# Calculations
n_a=n1*math.sqrt(2*dl)
n_a=n1*(math.sqrt(2*dl)) # numerical aperture
x_a=(math.asin(n_a))*180/math.pi # acceptance angle in degree

# Results
print " Numerical aperture = ",n_a
print ('%s %.2f %s'%("\n acceptance angle in degree = ",x_a,"degree"))

 Numerical aperture =  0.288

acceptance angle in degree =  16.74 degree


## Example 10:PgNo-53¶

In [12]:
import math

# Variable declaration
n1=1.50 # core refractive index

# Calculations
x_c=math.asin(n2/n1)*(180/math.pi) # critical angle in degree
n_m=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture

# Results
print ('%s %.2f %s' %(" critical angle = ",x_c,"degree"))
print ('%s %.2f' %("\n numerical aperture = ",n_m))

 critical angle =  81.89 degree

numerical aperture =  0.21


## Example 11: PgNo-58¶

In [13]:
import math

# Variable declaration
n1=1.50 # core refractive index

# Calculations
n_m=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
dl=(n1-n2)/n1 # fractional difference

# Results
print ('%s %.2f' %(" numerical aperture = ",n_m))
print ('%s %.2f' %("\n fractional difference = ",dl))

 numerical aperture =  0.38

fractional difference =  0.03


## Example 12: PgNo-65¶

In [14]:
import math

# Variable declaration
n1=1.46 # core refractive index

# Calculations
x_c=(math.asin(n2/n1))*180/math.pi # critical angle in degree
n_m=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
x_a=(math.asin(n_m))*180/math.pi # acceptance angle in degree

# Results
print ('%s %.2f %s' %(" critical angle = ",x_c,"degree"))
print ('%s %.2f %s' %("\n acceptance angle = ",x_a,"degree"))
print ('%s %.2f' %("\n numerical aperture = ",n_m))

 critical angle =  83.29 degree

acceptance angle =  9.82 degree

numerical aperture =  0.17


## Example 13: PgNo-67¶

In [15]:
import math
# Variable declaration
n_m=0.204 #numerical aperture
dl=0.01 # index difference

# Calculations
n1=n_m/(math.sqrt(2*dl)) # core refractive index

# Results
print ('%s %.2f' %(" core refractive index = ",n1))
print ('%s %.2f' %("\n cladding refractive index = ",n2))

 core refractive index =  1.44



## Example 14: PgNo-71¶

In [16]:
import math
# Variable declaration

n1=1.46 #core refractive index
dl=0.01 # index difference

# Calculations
x_c=(math.asin(n_2/n1))*180/math.pi #critical angle in degree
n_m=math.sqrt(math.pow(n1,2)-math.pow(n_2,2)) # numerical aperture

# Results
print ('%s %.2f %s' %(" critical angle = ",x_c,"degree"))
print ('%s %.2f' %("\n numerical aperture = ",n_m))

 critical angle =  81.89 degree

numerical aperture =  0.21


## Example 15: PgNo-76¶

In [17]:
import math
# Variable declaration
n1=1.50 # core refractive index

# Calculations
x_c=(math.asin(n2/n1))*180/math.pi # critical angle in degree
n_m=math.sqrt(math.pow(n1,2)-math.pow(n2,2)) # numerical aperture
x_a=(math.asin(n_m))*180/math.pi # acceptance angle in degree
n_c=math.pow((n_m),2)*100 # percentage of light

# Results
print ('%s %.2f %s' %(" critical angle= ",x_c,"degree"))
print ('%s %.2f %s' %("\n acceptance angle= ",x_a,"degree"))
print ('%s %.2f' %("\n numerical aperture= ",n_m))
print ('%s %.2f %s'%("\n percentage of light= ",n_c,"%"))

 critical angle=  75.16 degree

acceptance angle=  22.59 degree

numerical aperture=  0.38

percentage of light=  14.75 %


## Example 16: PgNo-81¶

In [18]:
import math

# Variable declaration
n1=1.50 # core refractive index
dl=0.01 # index difference

# Calculations
n_m=n1*(math.sqrt(2*dl)) # numerical aperture
x_a=math.pi*math.pow((n_m),2) # acceptance angle in radian
n2_1=(1-dl) # the ratio of n2 to n1
x_c=(math.asin(n2_1))*180/math.pi # critical angle in degree

# Results
print ('%s %.2f'%(" numerical aperture= ",n_m))
print ('%s %.2f %s' %("\n acceptance angle= ",x_a,"radian"))
print ('%s %.2f %s'%("\n critical angle= ",x_c,"degree"))

 numerical aperture=  0.21