Two lenses of power $-15 D$ and $+5 D$ are in contact with each other. The focal length of the combination is

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.

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

If two lenses of $+5$ diopters are mounted at some distance apart,the equivalent power will always be negative if the distance is

Two thin lenses,one of focal length $+ 60 \ cm$ and the other of focal length $-20 \ cm$ are put in contact. The combined focal length is........$cm$.

An object $AB$ is placed $15 \text{ cm}$ on the left of a convex lens $P$ of focal length $10 \text{ cm}$. Another convex lens $Q$ is now placed $15 \text{ cm}$ to the right of lens $P$. If the focal length of lens $Q$ is $15 \text{ cm}$, the final image is . . . . . . .