$A$ convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is $2/3$. Their equivalent focal length is $30 \ cm$. What are their individual focal lengths?

Two similar plano-convex lenses are combined together in three different ways as shown in the adjoining figure. The ratio of the focal lengths in three cases will be

An optician makes spectacles having a combination of a convex lens of focal length $40 \ cm$ in contact with a concave lens of focal length $25 \ cm$. The power of this combination of lenses in dioptre is:

The size of the image of an object, which is at infinity, as formed by a convex lens of focal length $30\,cm$ is $2\,cm$. If a concave lens of focal length $20\,cm$ is placed between the convex lens and the image at a distance of $26\,cm$ from the convex lens, calculate the new size of the image. (in $cm$)

An achromatic convergent doublet of two lenses in contact has a power of $+2 \ D$. The convex lens has a power of $+5 \ D$. What is the ratio of the dispersive powers of the convergent and divergent lenses?

$A$ convex lens and a concave lens,each having the same focal length of $25\, cm$,are put in contact to form a combination of lenses. The power in diopters of the combination is: