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.)

If a convex lens of focal length $80 \;cm$ and a concave lens of focal length $50 \;cm$ are combined together,what will be their resulting power?

The size of the image of an object at infinity, formed by a convex lens of focal length $30 \,cm$, is $2 \,cm$. If a concave lens of focal length $20 \,cm$ is placed between the convex lens and the image at a distance of $26 \,cm$ from the convex lens, what is the new size of the image (in $\,cm$)?

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?

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.

$A$ lens of power $+2$ diopters is placed in contact with a lens of power $-1$ diopter. The combination will behave like