Two thin lenses in contact form an achromatic doublet of power $+2 \text{ D}$. The power of the convex lens is $+5 \text{ D}$. What is the ratio of the dispersive powers of the converging and diverging lenses?

$A$ convex lens of focal length $20 \, cm$ is cut into two equal parts. This results in two plano-convex lenses as shown in the figure. These two parts are then placed in contact with each other as shown in the figure. What will be the focal length of the system in $cm$?

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 $cm$)

$A$ plano-convex lens of refractive index $\mu_1$ fits exactly into a plano-concave lens of refractive index $\mu_2$. Their plane surfaces are parallel to each other. $R$ is the radius of curvature of the curved surface of the lenses. The focal length of the combination is:

Two thin equiconvex lenses each of focal length $0.2 \,m$ are placed coaxially with their optic centres $0.5 \,m$ apart. Then the focal length of the combination is (in $\,m$)

An achromatic combination of lenses produces