Paragraph: Light guidance in an optical fiber can be understood by...

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