$A$ convex lens of focal length $0.5 \ m$ and a concave lens of focal length $1 \ m$ are combined. The power of the resulting lens will be: (in $D$)

Two thin lenses have a combined power of $+9 D$. When they are separated by a distance of $20 \,cm$, their equivalent power becomes $+\frac{27}{5} D$. Their individual powers (in diopters) are respectively:

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 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

The dispersive powers of the materials of two lenses forming an achromatic combination are in the ratio of $4:3$. If the effective focal length of the combination is $+60 \ cm$, then the focal lengths of the lenses should be:

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.