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 focal length of a plano-convex lens is equal to its radius of curvature. Find the refractive index of its material.

$A$ diminished image of an object is to be obtained on a large screen $1\, m$ from it. This can be achieved by

An object is placed at a distance of $5 \, cm$ from the first principal focus of a convex lens of focal length $10 \, cm$. If a real image is formed,find its distance from the lens in $cm$.

The focal length of a thin converging lens in air is $20 \ cm$. When the lens is immersed in a liquid,it behaves like a concave lens of power $1 \ D$. If the refractive index of the material of the lens is $1.5$,the refractive index of the liquid is

$A$ concave lens made of material of refractive index $1.6$ is immersed in a medium of refractive index $2.0$. The two surfaces of the concave lens have the same radius of curvature $0.2 \, m$. The lens will behave as a