Let the $XY$-plane be the boundary between two transparent media. Medium $1$ in $Z\ge 0$ has a refractive index of $\sqrt{2}$ and medium $2$ with $Z<0$ has a refractive index of $\sqrt{3}$. A ray of light in medium $1$ given by the vector $\overrightarrow{A}=6\sqrt{3}\hat{i}+8\sqrt{3}\hat{j}-10\hat{k}$ is incident on the plane of separation. The angle of refraction in medium $2$ is

In a pond of water, a flame is held $2 \mathrm{m}$ above the surface of water. A fish is at depth of $4 \mathrm{m}$ from water surface. Refractive index of water is $\frac{4}{3}.$ The apparent height of the flame from the eyes of fish is

A ray $OP$ of monochromatic light is incident on the face $AB$ of prism $ABCD$ near vertex $B$ at an incident angle of $60$, Fig. $13.90$. If the refractive index of the material of the prism is $\sqrt{3}$, which of the following is (are) correct?