The diameter of the Sun is $1.4 \times 10^9 \, m$ and its distance from the Earth is $10^{11} \, m$. What is the diameter of the image (in $cm$) formed by a convex lens of focal length $2 \, m$?

$A$ glass concave lens is placed in a liquid in which it behaves like a convergent lens. If the refractive indices of glass and liquid with respect to air are $_a \mu_g$ and $_a \mu_l$ respectively,then

$A$ magnifying glass is to be used at a fixed object distance of $1 \text{ inch}$. If it is to produce an erect image magnified $5$ times,its focal length should be ........ $\text{inch}$.

If the refractive index from air to glass is $\frac{3}{2}$ and that from air to water is $\frac{4}{3}$,then the ratio of focal lengths of a glass lens in water and in air is

The refractive index of the material of a concave lens is $\mu$. It is immersed in a medium of refractive index $\mu_1$. $A$ parallel beam of light is incident on the lens. The path of the emergent rays when $\mu_1 > \mu$ is

The light gathering power of a camera lens depends on: