The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal lengths $10 \,cm$ and $15 \,cm$ respectively. The distance between $L_1$ and $L_2$ is: (in $\,cm$)

$A$ convex lens of focal length $A$ and a concave lens of focal length $B$ are placed in contact with each other. The focal length of this combination is ......

The focal length (in $cm$) of a lens with dispersive power $0.45$ that should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to form an achromatic combination is:

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

$A$ convex and a concave lens separated by a distance are then put in contact. How does the focal length of the combination change?

$A$ convex lens of focal length $40 \; cm$ is in contact with a concave lens of focal length $25 \; cm$. The power of the combination is: