a multimode step index fibre along with a core

Question

A multimode step index fibre along with a core diameter of 80µm and a associative refractive index difference of 1.5% is operating at a wavelength of 0.85µm. If the core refractive index is 1.48, calculate the V number and the number of guided modes.

Given, core diameter, d=80µm
Δ=1.5%=0.015
Λ=0.85µm
n1=1.48
We know that Numerical Aperture,
Sinψ = n₁ (2Δ)^½
=1.48 (2 x 0.015)^½
=0.2563
i.e. (n12- n22)^½ =0.2563
(1.482- n22)^½ =0.2563
Squaring,
1.482- n22 =0.0657
i.e. n2=1.4576
We know that V number is given through
V= Πd (n12- n22)^½ / Λ

Substituting the values for d, n₁, n₂ and Λ, we get
V=75.78
Take V=76

Number of modes= V2 /2= 762 /2 = 2888