A convex lens $A$ of focal length $f_1=30 \mathrm{cm}$ and a concave lens $B$ of focal length $f_2=10 \mathrm{cm}$ are kept along the same axis with a distance $d$(in $\mathrm{cm}$) between them. For what value of $d$ does a parallel beam of light incident on $A$ leave $B$ as a parallel beam?

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