A spherical surface of radius of curvature $R=20 \mathrm{cm}$ separates two media as shown in figure. Two particles $A$ and $B$ are moving with equal speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ as indicated. At a certain instant, the two particles are at equal distances of $20 \mathrm{cm}$ from the spherical interface. At this instant relative velocity of $A$ as seen from $B$ is

In the arrangement shown in the figure, the distance of final image from the lens is

A quarter of a cylinder of $\mu =\sqrt{3}$ and radius $R=2 \mathrm{cm}$ is placed as shown. The surface $OB$ is silvered. A ray of light making angle $30°$ is incident on cylinder as shown in figure. If the ray retraces its path back, the $x$-coordinate of point $P$ is

A bulb is at the centre of base of a hollow cube of side length $a.$ It is half filled with water $\left(\mu =\frac{4}{3}\right).$ The area on the ceiling illuminated by light is

A concave mirror of radius of curvature $R=40 \mathrm{cm}$ is placed inside water $\left(\mu =\frac{4}{3}\right)$ of depth $30 \mathrm{cm}.$ A parallel beam of light is incident on water surface as shown. The distance of final image is