a step index multi mode fibre along with

Question

A step index multi mode fibre along with numerical aperture of 0.2 supports approximately 1000 modes at an 850µm wavelength. Calculate

a) What is the diameter of the core?
b) How many modes this fibre supports at 1320nm?
c) How many modes this fibre supports at 1550nm?

Given, numerical aperture
Sinψ = (n₁2- n₂2)½=0.2

No. of modes, m=1000
Λ=850nm

For a multi mode fibre
m= V2 /4
V= (4 x No. of modes) ^½
= (4 x 1000) ^½
=63.24
Take V=63

a) We know that

V= Πd (n₁2- n₂2)^½ / λ
where d is the diameter.

Substituting the values of V, n₁, n₂, d and solving for Λ, we get
d= 85.227µm

b) At Λ=1320nm,

From
V= Πd (n₁2- n₂2)^½ / λ
Substituting Λ=1320nm, we get
V=40.5679
Take V=40
No. of modes= V²/2 =402/2 = 400

c) At Λ=1550nm,

From
V= Πd (n₁2- n₂2)^½ / λ
Substituting Λ=1550nm, we get
V=34.548
Take V=35
No. of modes= V²/4 =35²/4 = 298