Total internal reflection can happen when light enters from rarer medium to denser medium.

A small coin is fixed at the center of the base of an empty cylindrical steel container having radius $R=1 \mathrm{m}$ and height $d=4 \mathrm{m}$. At time $t=0 \mathrm{s}$, the container starts getting filled with water at a flowrate of $Q=0.1 {\mathrm{m}}^3/\mathrm{s}$ without disturbing the coin. Find the approximate time when the coin will first be seen by the observer "$O$" from the height of $H=5.75 \mathrm{m}$ above and $L=1.5 \mathrm{m}$ radially away from the coin as shown in the figure. Refractive index of water is $n=1.33$.

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

If the refractive index of water with respect to air (${}_{a }\mu _w$)  is $\frac{5}{3}$.  Calculate the refractive index of air with respect to water (${}_{w }\mu _a$).

What is the relation between the refractive index of water with respect to air $\left({}_{a }\mu _w\right)$, and the refractive index of air with respect to water $\left({}_{w }\mu _a\right)$.

The diagram below shows a light source P embedded in a rectangular glass block ABCD of critical angle 42°. Complete the path of the ray PQ till it emerges out of the block. Write necessary angles.
 

A diver, $30 \mathrm{m}$ below water surface is trying to shine a torch light towards the point O which is horizontally $30 \mathrm{m}$ away. The amount and direction in which diver has to swim (in the figure) so that the light can not travel outside the surface of water is (Refractive index of water $=\frac{4}{3}$)