An observer can see the top of a thin rod of height $h$ through a pinhole. The height of the container is $3h$ and its radius is $2h$. When the container is filled with a liquid up to a height of $2h$,the observer can see the bottom end of the rod. Find the refractive index of the liquid.

$A$ glass cube of length $24 \ cm$ has a small air bubble trapped inside. When viewed normally from one face,it is $10 \ cm$ below the surface. When viewed normally from the opposite face,its apparent distance is $6 \ cm$. The refractive index of glass is:

Which of the following ray diagrams shows physically possible refraction?

$A$,$B$ and $C$ are parallel-sided transparent media of refractive indices $n_{1}$,$n_{2}$ and $n_{3}$ respectively. They are arranged as shown in the figure. $A$ ray is incident at an angle $i$ on the surface of separation of $A$ and $B$. After refraction into medium $B$,the ray grazes the surface of separation of media $B$ and $C$. Then,$\sin i$ equals to

Time taken by light to travel in two different materials $A$ and $B$ of refractive indices $\mu_{A}$ and $\mu_{B}$ of the same thickness is $t_{1}$ and $t_{2}$ respectively. If $t_{2}-t_{1}=5 \times 10^{-10} \text{ s}$ and the ratio of $\mu_{A}$ to $\mu_{B}$ is $1:2$. Then the thickness of the material,in meters,is: (Given $v_{A}$ and $v_{B}$ are velocities of light in $A$ and $B$ materials respectively).

Explain rarer and denser medium.