The graph between the lateral magnification $(m)$ produced by a lens and the distance of the image $(v)$ is given by

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

An object is placed at a distance of $f/2$ from a convex lens. The image will be

The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 \,cm$. If the radii of curvature are equal, the value of the radius of curvature (in $cm$) is

An object and a screen are fixed on the uprights of an optical bench. The distance between them is $100 \, cm$. $A$ convex lens is placed in between the object and the screen and the position of the lens is so adjusted that the image of the object is formed on the screen at two conjugate positions of the lens. The distance between these conjugate positions of the lens is $40 \, cm$. What is the focal length of the lens in $cm$?

$A$ parallel beam of light is incident on a converging lens parallel to its principal axis. As one moves away from the lens on the other side along the principal axis,the intensity of light