Light guidance in an optical fiber can be understood by considering a sturcture comprising of thin solid glass cylinderof 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 reflection at the interface of the media `n_(1)` and `n_(2)` as shown in the figure. All reys with the angle of incedence `i` less than a particular value `i_(m)` are confined in the medium of refractive index `n_(1)`. The numerical aperture `(NA)` of the structure is defined as `sin i_(m)`

If two structures of same cross-sectional area, but different numerical apertures `NA_(1)` and `NA_(2)` `(NA_(2)ltNA_(1))` are joined longitudinally, the numerical aperture of the combined structure is

Answer

D

Explanation

It is given that
`implies i_(m2) lt i_(m1)`
Hence if the combination can be placed both ways i.e., `1^(st)` structure & then `2^(nd)` structure and then reversed also , then the condition of TIR is satisfied for lower `i_(m)` then it can satisfied for all other less angler as well.
Hence `NA_(2)` will be the numerical aperture of the combined structure .