An object of height $15 \mathrm{cm}$ is placed $20 \mathrm{cm}$ from a mirror and an erect image of size $5 \mathrm{cm}$ is obtained. The mirror is

A point object is moving with speed $4 \mathrm{cm}{ \mathrm{s}}^{-1}$ in front of a combination of two plane mirrors (see figure). Velocity of image of the object formed by mirror $M_1$ relative to image formed by mirror $M_2$ is

A concave lens of radius of curvature $15 \mathrm{cm}$ and $\mu =1.5$ is placed in water $\left(\mu =\frac{4}{3}\right).$ If one surface is silvered, then image distance from lens when an object is placed at distance of $14 \mathrm{cm}$ from the lens is

A ray of ligand is incident perpendicularly on a prism and it follows the path as shown in figure. The minimum refractive index of the prism can be

A ray of light, moving parallel to $x$-axis is incident on a parabolic mirror at point $P$ as shown in figure. If angle of deviation suffered by the ray after reflection is $120°$, the $y$-coordinate of point $P$ is

An equiconvex lens of $\mu =1.5$ and radius of curvature $R=20 \mathrm{cm}$ is placed in front of a convex mirror of radius of curvature $20 \mathrm{cm}$ as shown. An object is placed as indicated. The possible value of $x$ so that the image coincides with the object is

The refractive index of a slab of length $21$ changes as $\mu =\left\{\begin{array}{l}{\mu }_0\frac{x}{1},0\le x\le 1\\ {\mu }_0\frac{x^2}{1^2},I\le x\le 2I\end{array}\right.$where $x$ is measured from left and the equivalent refractive index of the slab would be