Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact. The focal length of this combination is

Two convex lenses of focal lengths $20 \,cm$ and $30 \,cm$ are placed in contact with each other co-axially. The focal length of the combination 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

Two thin lenses whose powers are $+2 \ D$ and $-4 \ D$ respectively are combined. The power of the combination is:

The focal length of the field lens (which is an achromatic combination of two lenses) of a telescope is $90 \ cm$. The dispersive powers of the two lenses in the combination are $0.024$ and $0.036$. The focal lengths of the two lenses are:

The given lens is broken into four parts and rearranged as shown. If the initial focal length is $f$,then after rearrangement,the equivalent focal length is