Given: Core diameter $= 45µm$

Core radius $(a) = 22.5µm$

$NA = 0.22 \\ λ = 1.2µm$

To find: Total number of guided modes $(M_g)= ?$

Solution: For graded index fiber,

$M_g= \dfrac {V^2}4 \\ V= \dfrac {2π}λ ∙a∙NA \\ V= \dfrac { 2π}{1.2×10^{-6}} ∙22.5× 10 ^{-6}∙0.22 \\ ∴V=25.918 \\ M_g= \dfrac {25.918^2}4 \\ ∴ M_g=167.93 ≈168 $

Ans: The number of guided modes $M_g=168$