If in a plano-convex lens,the radius of curvature of the convex surface is $10 \ cm$ and the focal length of the lens is $30 \ cm,$ then the refractive index of the material of the lens will be

An achromatic telescope objective is to be made by combining the lenses of flint and crown glasses. This proper choice is

Double-convex lenses are to be manufactured from a glass of refractive index $1.55$,with both faces of the same radius of curvature. What is the radius of curvature (in $cm$) required if the focal length is to be $20\;cm$?

The refractive index of a converging lens is $1.4$. What will be the focal length of this lens if it is placed in a medium of the same refractive index? (Assume the radii of curvature of the faces of the lens are $R_{1}$ and $R_{2}$ respectively)

$A$ candle placed $25 \ cm$ from a lens forms an image on a screen placed $75 \ cm$ on the other side of the lens. The focal length and type of the lens should be

The refractive index of a material of a plano-concave lens is $5/3$, and the radius of curvature is $0.3 \,m$. The focal length of the lens in air is (in $\,m$)