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`
If two structure of same cross-sectional area, but different numerical apertures `NA_1`and `NA_2(NA_2ltNA_1)` are joined longitudinally, the numerical aperture of the combined structure is `

Options

A. NA of `S_(1)` immersed in water is the same as that of `S_(2)` immersed in a liquid of refractive index `16/(3sqrt(15))`
B. NA of `S_(1)` immersed in liquid of refractive index `16/sqrt(15)` is the same as that of `S_(2)` immersed in water
C. NA of `S_(1)` placed in air is the same as that of `S_(2)` immersed in liquid of refractive index `4/sqrt(15)`
D. NA of `S_(1)` placed in air is the same as that of `S_(2)` placed in water

Answer

A, C