One end of a cylindrical rod of glass $(n = 1.5)$ shown in the figure is given a spherical shape of the radius

$2.0 \mathrm{cm}$. On the left side of this end is placed an object $O$ at a distance of $12 \mathrm{cm}$. Find out the distance ($v$) of the image.

The radii of curvature of a double convex lens are $15 \mathrm{cm}$ and $30 \mathrm{cm}$ and the refractive index of its glass is $1.5$. Calculate the focal length of the lens.

The radii of curvature of a double concave lens are $30 \mathrm{cm}$ and $60 \mathrm{cm}$ and the refractive index of its glass is $1.5$. Calculate the focal length of the lens.

The radius of curvature of each face of a biconcave lens made of glass of refractive index $1.5$ is $30 \mathrm{cm}$. Calculate the focal length of the lens in air.

Calculate the focal length of a convex lens whose radii of curvature of two surfaces is $10 \mathrm{cm}$ and $15 \mathrm{cm}$ respectively and its refractive index is $1.5$.

The radius of curvature of the convex face of a plano-convex lens is $55 \mathrm{cm}$ and the refractive index of its material is $1.55$. Find the focal length of the lens.

The radii of curvature of the two faces of a convex lens are $0.10 \mathrm{m}$ and $0.15 \mathrm{m}$ respectively. If the focal length of the lens is $0.12 \mathrm{m}$, find the refractive index of the material of the lens.

The radii of curvature of the two surfaces of a convexo-concave lens are $15 \mathrm{cm}$ and $30 \mathrm{cm}$. Find the focal length of the lens. Take refractive index of the lens material to be $1.5$.

A bi-convex spherical lens A has a focal length of $20 \mathrm{cm}$. If it is split along a plane $AB$ into two halves to form two plano convex lenses,then what will be the focal length of each plano-convex lens?