Question

Difference between step index and graded index fibre.
An optical fibre has a numerical aperture of 0.20 and refractive index of cladding is 1.59. Determine the core refractive index and the acceptance angle for the fibre in water which has a refractive index of 1.33.

Answer 1

Sr.no.	Step index fibre	Graded index fibre.
1	The refractive index of the core of step index fiber is constant throughout the core.	The refractive index of the core of the graded index fiber is maximum at center,core and then it decreases towards core-cladding interface.
2	Step index fiber is of two types viz; mono mode fiber and multi mode fiber.	Graded index fiber is of only one type,that is multi mode fiber.
3	The light rays propagate in zig-zag manner inside the core.	The light rays,propagate in the form of skew rays or helical rays.
4	The rays cross the fiber axis for every reflection.	The rays will not cross the,fiber axis.
5	They can be manufactured easily.	They manufacturing process is complex.

Solution of problem :

`N.A = sqrt(μ_1^2− μ_2^2)/(μ_0)`
In air μ₀ = 1 
`N.A = sqrt( μ_1^2− μ_2^2 = 0.2`
`μ1 = sqrt( 0.2^2+1.59^2)`
μ1 = 1.6025
In water μ₀ = 1.33 

`N.A = sqrt( 1.6025^2− 1.59^2) /1.33`
= 0.15

sin θ_max = N.A

θ_{max = sin}^-1(0.15)

θ_max = 8.6^o  
Core refractive index = 1.6025
Acceptance angle for the fibre in water = 8.6^o