Problems on Numerical Aperture, Acceptance angle & Fractional Index Change

1. In an optical fiber the refractive indexes of core and cladding are 1.46 and 1.45 respectively. Find:

1. the critical angle 𝜃𝑐 at the core-cladding interface
2. the numerical aperture N.A. of the optical fiber
3. the angle of acceptance αmax of the optical fiber system

2. An optical fiber has a core material of refractive index of 1.55 and cladding material refractive index of 1.50. The light is launched into it in air. Calculate the numerical aperture?

3. Calculate the fractional index change for a given optical fiber if the refractive indices of the core and cladding are 1.563 and 1.498, respectively