Light guidance in an optical fiber 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 reflections at the interface of the media `n_(1)` and `n_(2)` as shown in the figure . all rays with the angle of incidence i less than a particular value of `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)`
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If two structures of same cross - sectional area, but different numerical apertures `NA_(1)` and `NA_(2)(NA_(2) lt NA_(1))` are joined longitudinally , the number 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 .