$A$ ray of light is incident on a transparent sphere at an angle of $\pi / 4$ and is refracted at an angle $r$. The ray emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is

$A$ monochromatic light is travelling in a medium of refractive index $n=1.6$. It enters a stack of glass layers from the bottom side at an angle $\theta=30^{\circ}$. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as $n_m=n-m \Delta n$,where $n_m$ is the refractive index of the $m^{\text{th}}$ slab and $\Delta n=0.1$ (see the figure). The ray is refracted out parallel to the interface between the $(m-1)^{\text{th}}$ and $m^{\text{th}}$ slabs from the right side of the stack. What is the value of $m$?

$A$ tank is filled with water to a height of $12.5 \, cm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \, cm$. If water is replaced by a liquid of refractive index $1.63$ up to the same height,what will be the apparent depth of the needle in $cm$?

The refractive index of water is $1.33$. The direction in which a man under water should look to see the setting sun is

The refractive index of air with respect to vacuum is . . . . . . .

What is refraction of light?