Find the distance of the final image from the object $O$,formed by the combination of lenses shown in the figure (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 lenses of power $+10D$ and $-5D$ are placed in contact. At what distance (in $cm$) should an object be held from the lens combination to obtain a virtual image of magnification $2$?

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 $cm$)

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

An achromatic combination of lenses is formed by joining