For the system shown, if the speed of image formed by the plane mirror is minimum then speed, $v$ of the plane mirror is

A rod of length $5 \mathrm{cm}$ is placed longitudinally on the optical axis of concave mirror of focal length, $f=20 \mathrm{cm}$ such that image of one end coincides with itself and the image is diminished. The axial magnification produced by mirror is

A cylindrical parallel beam of light of radius $r$ falls on a thin convex lens of focal length $40 \mathrm{cm}$ and then on a concave lens of focal length $10 \mathrm{cm}$ as shown. Area illuminated by beam on the screen is

A right-angled glass prism $(\mu =\sqrt{3})$ is kept on a horizontal surface in contact with a vertical plane mirror as shown. A ray of light travelling horizontally retraces its path when transparent liquid of refractive index $\mu$ is filled in the space between prism and mirror. Refractive index, $\mu$ of the liquid is

Consider the situation shown in the figure. The minimum angle by which the plane mirror $M$ should be rotated about the point of incidence $O$ such that the reflected ray is horizontal is

The concave mirror shown in the figure has focal length of $20 \mathrm{cm}.$ The $y$ coordinate of image of object $O$ will be

A plane mirror whose reflecting surface is parallel to the $y-z$ plane is moving with velocity $4\hat{\mathrm{i}} \mathrm{m} {\mathrm{s}}^{–1}.$ If the velocity of the object is $\left(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+2\hat{\mathrm{k}}\right) \mathrm{m} {\mathrm{s}}^{–1}$, then the velocity of the image is