A plane mirror and a concave mirror of radius of curvature $60 \mathrm{cm}$ are placed facing each other, with a point object at the center of them. If the image formed by first reflection at the spherical mirror and then at the plane mirror coincides with the object then the separation (in $\mathrm{cm}$) between two mirrors will be _____ .

A ray of light is incident on a glass sphere of refractive index $\sqrt{3}$ at an angle of incidence $60°$ as shown in figure. The total deviation (in degree) suffered by the ray is _____ .

Figure shows a graph of angle of deviation $\delta$ versus angle of incidence, $i$ for a light ray striking a prism. Angle of prism is _____ degree.

A glass cube of side length $\text{'}a\text{'}$ and $\mu =1.5$ is placed on a surface. A small light bulb is at the centre of base of cube. What minimum area of side wall of the cube should be painted so that no light comes out of the side walls of the cube? (Consider only single reflection or refraction)

A beam of light of diameter $2R$ is incident on flat surface of hemispherical glass of $\mu =\frac{2}{\sqrt{3}}$ and radius $R,$ placed on surface of table as shown in figure. The area on table illuminated by light is

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