Two thin lenses have a combined power of $+9 D$. When they are separated by a distance of $20 \,cm$, their equivalent power becomes $+\frac{27}{5} D$. Their individual powers (in diopters) are respectively:

Two lenses having focal lengths in the ratio $f_1:f_2 = 2:3$ are combined to produce no net dispersion. Find the ratio of the dispersive powers of the glasses used.

An object is placed $30 \ cm$ away from a convex lens of focal length $10 \ cm$ and a sharp image is formed on a screen. Now,a concave lens is placed in contact with the convex lens. The screen now has to be moved by $45 \ cm$ to get a sharp image again. The magnitude of the focal length of the concave lens is (in $cm$):

Find the equivalent focal length of a combination of two convex lenses in contact,each having a focal length of $30 \ cm$. (in $cm$)

Two thin convex lenses are kept in contact coaxially. If the focal length of the combination of the lenses is $4 \ cm$ and the sum of the focal lengths of the two lenses is $18 \ cm$,then the focal length of the lens of lower power is (in $cm$)

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