A small bulb is placed at the bottom of a tank containing water to a depth of $\sqrt{7} \mathrm{m}$. The refractive index of water is $\frac{4}{3}$. The area of the surface of water through which light from the bulb can emerge out is $x\pi {\mathrm{m}}^2$. The value of $x$ is _____ .

A light ray is incident, at an incident angle ${\theta }_1$, on the system of two plane mirrors $M_1$ and $M_2$ having an inclination angle $75°$ between them (as shown in figure). After reflecting from mirror $M_1$ it gets reflected back by the mirror $M_2$ with an angle of reflection $30°$. The total deviation of the ray will be _____ degree.

A convex lens has power $P$. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.

The speed of light in media $A$ and $B$ are $2.0\times {10}^{10} \mathrm{cm} {\mathrm{s}}^{-1}$ and $1.5\times {10}^{10} \mathrm{cm} {\mathrm{s}}^{-1}$ respectively. A ray of light enters from the medium $B$ to $A$ at an incident angle $\theta$. If the ray suffers total internal reflection, then