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 lens and a concave lens, each with a focal length of $4 \,cm$, are separated by a distance of $6 \,cm$ along their axis. An object is placed $8 \,cm$ before the convex lens. The distance between the object and its final image is (in $\,cm$)

The plane faces of two identical plano-convex lenses,each with focal length $f$,are pressed against each other using an optical glue to form a convex lens. The distance from the optical centre at which an object must be placed to obtain an image of the same size as the object is

Two lenses of power $-15 \, D$ and $5 \, D$ are placed in contact with each other. The focal length of this combination will be ....... $cm$.

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.

Find the position of the final image formed by the combination of the three lenses shown in the figure. The focal lengths are $f_1 = 10 \ cm$,$f_2 = -10 \ cm$,and $f_3 = 30 \ cm$.