$A$ bird is flying at $12 \ m$ height above the water surface and a fish is swimming $16 \ m$ below the water surface $(\mu_{\text{water}} = 4/3)$. Find the distance of the bird with respect to the fish as seen by the fish. (in $m$)

When light is incident on a medium at an angle $i$ and refracted into a second medium at an angle $r$,the graph of $\sin i$ vs $\sin r$ is as shown. From this,one can conclude that:

Let the $x-z$ 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 $\overrightarrow{A} = 6\sqrt{3} \widehat{i} + 8\sqrt{3} \widehat{j} - 10\widehat{k}$ is incident on the plane of separation. The angle of refraction in medium $2$ is ......$^o$.

If the wavelength of light in vacuum is $\lambda$,the wavelength in a medium of refractive index $n$ will be

An infinitely long cylinder of radius $R$ is made of an unusual exotic material with refractive index $-1$ (See figure). The cylinder is placed between two planes whose normals are along the $y$-direction. The center of the cylinder $O$ lies along the $y$-axis. $A$ narrow laser beam is directed along the $y$-direction from the lower plate. The laser source is at a horizontal distance $x$ from the diameter in the $y$-direction. Find the range of $x$ such that light emitted from the lower plane does not reach the upper plane.

When light travels from glass to air,the incident angle is ${\theta _1}$ and the refracted angle is ${\theta _2}$. The true relation is: