$A$ convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is $2/3$. Their equivalent focal length is $30 \ cm$. What are their individual focal lengths?

Curved surfaces of a plano-convex lens of refractive index $\mu_{1}$ and a plano-concave lens of refractive index $\mu_{2}$ have equal radius of curvature as shown in the figure. Find the ratio of the radius of curvature to the focal length of the combined lenses.

An achromatic convergent doublet of two lenses in contact has a power $+2 \text{ D}$. The convex lens has power $+5 \text{ D}$. The ratio of the dispersive powers of the convergent and divergent lenses is (in magnitude)

$A$ parallel beam of light is incident on a system of two convex lenses with focal lengths $f_1 = 20 \, cm$ and $f_2 = 10 \, cm$. What should be the distance between the two lenses so that the rays,after refraction from both lenses,emerge as a parallel beam? (in $cm$)

Two thin lenses of focal lengths $f_1$ and $f_2$ are in contact. The focal length of this combination is

$A$ real image of an object is formed at a distance of $20 \, cm$ from a lens. On putting another identical lens in contact with it,the image is shifted $10 \, cm$ towards the combination. The power of the lens is (in $, D$)