Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact and coaxial. The combination is equivalent to a single lens of power:

What is the focal length of a convex lens of focal length $30 \ cm$ in contact with a concave lens of focal length $10 \ cm$? (Ignore the thickness of the lenses.)

An achromatic combination of lenses produces

$A$ 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 diagram below shows an object placed at a distance $2f$ in front of a convex lens of focal length $f$. Which of the following represents the positions of the image when $(i)$ a parallel-sided glass block,or $(ii)$ a converging lens of long focal length is inserted between the object and the convex lens?

$A$ convex lens of focal length $A$ and a concave lens of focal length $B$ are placed in contact with each other. The focal length of this combination is ......