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

$A$ convex lens of focal length $10 \, cm$ is placed in contact with a concave lens. The focal length of the combination is numerically equal to that of the concave lens. The focal length of the concave lens is ............ $cm$.

The focal length of a lens of dispersive power $0.45$ which should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to make the achromatic combination from the two lenses,in $cm$ is

$A$ convex lens $A$ of focal length $20 \,cm$ and a concave lens $B$ of focal length $56 \,cm$ are kept along the same axis with a distance $d$ between them. If a parallel beam of light falling on $A$ leaves $B$ as a parallel beam, then the magnitude of distance $d$ (in $cm$) is

$A$ combination of two thin lenses of the same material with focal lengths $f_1$ and $f_2$,arranged on a common axis,minimizes chromatic aberration if the distance between them is:

The focal length of a combination of lenses formed with lenses having powers of $+2.50 \ D$ and $-3.75 \ D$ will be .... $cm$.