Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index `n_1` surrounded by a medium of lower refractive index `n_2`. The light guidance in the structure takes place due to successive total internal reflectrions at the interface of the media `n_1` and `n_2` as shown in the fugure. All rays with the angle of incidence i less than a particular value `i_m` are confined in the medium of refractive index `n_1`. The numerical aprture (NA) of the structure is defined as `sini_m`
For two structure namely `S_1` with `n_1=(sqrt45)/(4)` and `n_2=(3)/(2)`, and `S_2` with `n_1=(8)/(5)` and `n_2=(7)/(5)` and taking the refractive index of water to be `(4)/(3)` and that of air to be 1, the correct option (s) is (are) ? `

Options

A. a.`NA` of `S_(1)` immersed in liquid of refractive index `(6)/(sqrt15)` is same as that of `S_(2)` immersed in water
B. b.`NA` of `S_(1)` immersed in liquid of refractive index `(6)/(sqrt15)` is same as that of `S_(2)` immersed in water
C. c.`NA` of `S_(1)` placed in air is the same as that of `S_(2)` immersed in liquid of refractive index `(4)/(sqrt15)`
D. b.`NA` of `S_(1)` placed in air is the same as that of `S_(2)` placed in water

Answer

D

Explanation

N//a