An optician makes spectacles having a combination of a convex lens of focal length $40 \ cm$ in contact with a concave lens of focal length $25 \ cm$. The power of this combination of lenses in dioptre is:

$A$ 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 $\,cm$)

An object is placed $12 \ cm$ to the left of a converging lens of focal length $8 \ cm$. Another converging lens of $6 \ cm$ focal length is placed at a distance of $30 \ cm$ to the right of the first lens. The second lens will produce

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.

Two lenses of power $+12 \ D$ and $-2 \ D$ are placed in contact. What will be the focal length of the combination in $cm$?

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 $\,cm$)