The radius of curvature of a convex lens is $40 \,cm$ for each surface. Its refractive index is $1.5$. Its focal length is: (in $\,cm$)

The dispersive powers of crown and flint glasses are $0.02$ and $0.04$ respectively. In an achromatic combination of lenses,the focal length of the flint glass lens is $40 \ cm$. The focal length of the crown glass lens will be $....... \ cm$.

For an object placed at a distance $2.4\,m$ from a lens,a sharp focused image is observed on a screen placed at a distance $12\,cm$ from the lens. $A$ glass plate of refractive index $1.5$ and thickness $1\,cm$ is introduced between the lens and the screen such that the glass plate faces are parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen (in $,m$)?

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.

$A$ luminous object is separated from a screen by a distance $d$. $A$ convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

The distance between the object and the screen is $100 \, cm$. $A$ lens produces an image on the screen when it is placed at either of two positions $40 \, cm$ apart. The power of the lens is (approximately): (in $, D$)