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

$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a convex lens of focal length $20 \, cm$ (in $, cm$)?

The focal length of a lens is $10 \ cm$. What is the power of the lens in dioptre (in $D$)?

$A$ biconvex lens with equal radii of curvature has a refractive index of $1.6$ and a focal length of $10 \ cm$. Its radius of curvature will be.......$cm$.

$A$ convex lens of focal length $0.15 \,m$ is made of a material of refractive index $\frac{3}{2}$. When it is placed in a liquid, its focal length is increased by $0.225 \,m$. The refractive index of the liquid is

An object is placed at a certain distance to the left of a convex lens of focal length $20 \,cm$. Find the distance of the object if the image obtained is magnified by $4$ times.