$A$ film projector magnifies a film onto a screen of area $100 \, cm^2$. If the linear magnification is $4$,what will be the area of the image on the screen in $cm^2$?

$A$ particle executes linear $S.H.M.$ along the principal axis of a convex lens of focal length $8 \,cm$. The mean position of oscillation is at $14 \,cm$ from the lens with amplitude $1 \,cm$. The amplitude of the oscillating image of the particle is nearly: (in $\,cm$)

Two point light sources are $24 \, cm$ apart. Where should a convex lens of focal length $9 \, cm$ be placed between them from one source so that the images of both the sources are formed at the same place (in $, cm$)?

The focal lengths for violet,green,and red light rays are ${f_V}$,${f_G}$,and ${f_R}$ respectively. Which of the following is the true relationship?

The two surfaces of a concave lens, made of glass of refractive index $1.5$, have the same radii of curvature $R$. It is now immersed in a medium of refractive index $1.75$. Then the lens:

The light gathering power of a camera lens depends on: