How far can fish see?

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)

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 rectangular glass slab ABCD of refractive index $n_1$ is immersed in water of refractive index $n_2\left(n_1>n_2\right)$. A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence ${\alpha }_{\text{max'}}$ such that the ray comes out only from the surface CD, is given by

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$