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

A point object is placed in the arrangement shown. The distance of image formed by lens-$2$ from its optical centre is