A convex lens of focal length $20 \mathrm{cm}$ and another convex lens of focal length $40 \mathrm{cm}$ are placed co-axially. What should be the distance $d$ (in $\mathrm{cm}$) between lenses so that final image of object $O$ is formed on $O$ itself?

A plane mirror in $y$-$z$ plane is moving with $-2 \hat{\mathrm{i}} {\mathrm{ms}}^{-1}$ as shown. The object shown now starts moving with $(3\hat{\mathrm{i}}+\hat{\mathrm{j}}-4\hat{\mathrm{k}}) \mathrm{m} {\mathrm{s}}^{-1}$. What is the velocity of the image?

Consider a ray of light incident on a vertical plane mirror as shown. By what amount and in what sense should the mirror be rotated so that the ray becomes horizontal after reflection?

A person of height $h$ is standing in front of a plane mirror.

(a) What is the minimum size of the mirror so that complete image of the person is formed?

(b) What is the minimum size of the mirror so that the person can see his complete image ?

(c) Where should the top edge of the mirror be placed relative to the eyes and the head of the person, so that the person sees his complete image.