Physics - Geometrical Optics Question with Solution | TestHub

Paragraph: 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 structure is defined as $\sin i_m$.

Question: If two structures of same cross-sectional area, but different numerical apertures $N{A}_1$ and $N{A}_2\left(N{A}_2<N{A}_1\right)$ are joined longitudinally, the numerical aperture of the combined structure is