A travelling microscope is used during the experiment

The path of a light ray inside a transparent slab of variable refractive index is $y\mathit{=}4x^2\mathit{.}$ A light ray travelling in air falls on the surface of the slab at an angle $30°$ as shown in the figure. The refractive index of the slab at $y=0.5 \mathrm{m}$ is

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 $n=1.33$.

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 $=\frac{4}{3}$)

A cubical vessel has opaque walls. An observer (dark circle in the figure below) is located, such that she can see only the wall, $CD$, but not the bottom. Nearly to what height should water be poured, so that she can see an object placed at the bottom at a distance of, $10 \mathrm{cm}$, from the corner, $C$? Refractive index of water is, $1.33$.