A light ray incident along vector $2\widehat{i}+4\widehat{j}+\sqrt{5}\widehat{k}$ strikes on the $x-z$ plane from medium of refractive index $\sqrt{3}$ and enters into medium $\mathrm{I}\mathrm{I}$ of refractive index is ${\mu }_2$ . The value of ${\mu }_2$ for which the value of angle of refraction becomes ${90}^o$ , is

Electromagnetic waves emanating from a point $A$ (in air) are incident on a rectangular block of material $M$ and emerge from the other side as shown below. The angles $i$ and $r$ are angles of incidence and refraction when the wave travels from air to the medium. Such paths for the rays are possible,

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, $1.33$.

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