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_(1) NA_(2))/(NA_(1) + NA_(2))`
B. `NA_(1) + NA_(2)`
C. `NA_(1)`
D. `NA_(2)`

Answer

D

Explanation

The numerical aperture is limited by second slab.
`:. Sin i_(2) lt NA_(2)` [smaller `NA`]
`sin i_(1) gt sin i_(2)`
`:. NA` of combination `=` smaller `NA = NA_(2)`