The absolute refractive indices of water and glycerine are $1.33$ and $1.46$ respectively. Find the critical angle for a ray travelling from glycerine into water.

A small bulb is placed at the bottom of a tank containing water to a depth of $80 \mathrm{cm}$. What is the area of the surface of water through which light of the bulb can emerge out? Refractive index of water is $1.33$. Consider the bulb to be a point-source.

A point-source of light is placed at the centre of the bottom of a jar having a liquid of refractive index $\raisebox{1ex}{$5$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$. An opaque disc of radius $1.0 \mathrm{cm}$ is placed on the liquid surface with its centre vertically above the source. What is the maximum height of the liquid for which the source is not visible from above?

An observer can see the top end $B$ of a thin rod of height $h$, through a pin-hole. The height of the beaker is $3h$, and the radius is $h$. When the beaker is filled with a liquid up to a height $2h$, the observer can see the lower end $A$ of the rod. The refractive index of the liquid is:

An air bubble in a glass slab with refractive index $1.5$ (near normal incidence) is $5 \mathrm{cm}$ deep when viewed from one surface and $3 \mathrm{cm}$ deep when viewed from the opposite face. The thickness (in $\mathrm{cm}$) of the slab is:

A container is filled with water ($n=1.33$) up to a height of $33.25 \mathrm{cm}$. A concave mirror is held $15 \mathrm{cm}$ above the water level, and the image $I$ of an object $O$ placed at the bottom is formed $25 \mathrm{cm}$ below the water level. The focal length of the mirror is roughly:

A ball is dropped from a height of $20 \mathrm{cm}$ above the surface of water in a lake. The refractive index of water is $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$. A fish inside the lake, in line of fall of the ball, is looking at the ball. At an instant, when the ball is $12.8 \mathrm{m}$ above the water surface, the fish sees the speed of the ball as:

A point source $S$ is placed at the bottom of a transparent block of height $10 \mathrm{mm}$ and refractive index $2.72$. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter $11.54 \mathrm{mm}$ on the top of the block. The refractive index of the liquid is: