Question

Consider the interface between the core of a fiber and its cladding that have refractive indices of n1 and n2, respectively. (a) If n2 is smaller than n1 by 1 % and if n1 = 1.450, show that n2 = 1.435. (b) Show that the critical angle is φc = 81.9°.

Answer 1

(a): Given ,

n1= 1.450

To show that n2= 1.435

1% of n1 is , =( 1.450 * 1 )/100 = 0.0145

Since n2 is smaller than n1 by 1% ,

n2= n1 - 0.0145

n2= 1.450-0.0145

n2=1.4355

So refractive index of cladding ,n2= 1.4355

(b): Formula for critical angle is given by ,

​​​c= n2 / n1

c=1.4355 /1.450

=0.99

c= 81.890

c= 81.9 degrees.

So the critical angle ,= 81.9 degrees.