Question

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 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 $\sin i_m$.

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

• A. $\frac{N{A}_{1}N{A}_2}{N{A}_1+N_2}$
• B. $N{A}_1+N{A}_2$
• C. $N{A}_1$
• D. $N{A}_2$

Answer 1

The correct option is D $N{A}_2$

$N{A}_2<N{A}_1$

$\Rightarrow i_{m2}<i_{m1}$

If the combination is placed in any order, Total internal Reflection if satisfied for lower $i_m$, it can be satisfied for any lower angles as well.

$\therefore$ $N{A}_2$ will be the numerical aperture of the combined structure.