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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 $$i_m$$ are confined in the medium of refractive index $$n_1$$. The numerical aperture (NA) of the structureis defined as sin $$i_m$$.

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