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.

The lens combination consists of two lenses, $L_1$ and $L_2$, of focal lengths $+10 \text{ cm}$ and $-10 \text{ cm}$, respectively. The object is placed at a distance of $30 \text{ cm}$ from the first lens $L_1$. The distance between the two lenses is $3 \text{ cm}$. Find the position of the final image formed.

$A$ thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses?

$A$ lens of power $3.5 \, D$ is placed in contact with a lens of power $-2.5 \, D$. The combination behaves as:

Two thin convex lenses are kept in contact coaxially. If the focal length of the combination of the lenses is $4 \ cm$ and the sum of the focal lengths of the two lenses is $18 \ cm$,then the focal length of the lens of lower power is (in $cm$)

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: