For two structures namely $S_1$ with $n_1=\frac{\sqrt{45}}{4}$ and $n_2=\frac{3}{2}$, and $S_2$ with $n_1=\frac{8}{5}$ and $n_2=\frac{7}{5}$ and taking the refractive index of water to be $\frac{4}{3}$ and that of air to be $1$, the correct option(s) is (are)

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 $\sin i_m$.

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

A ray of light originates from inside a glass slab and is incident on its inner surface at an angle $\mathrm{\theta }$ as shown,

In this experiment the location $x$ of the spot where they ray hits the screen is recorded. Which of the following correctly shown the plot of variation of $x$ with the angle $\mathrm{\theta }$ ?

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 $\sin i_m$.

For two structures namely $S_1$ with $n_1=\frac{\sqrt{45}}{4}$ and $n_2=\frac{3}{2}$ , and $S_2$ with $n_1=\frac{8}{5}$ and $n_2=\frac{7}{5}$ and taking the refractive index of water to be $\frac{4}{3}$ and that of air to be 1, the correct option(s) is (are)