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.

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)

The given lens is broken into four parts and rearranged as shown. If the initial focal length is $f$,then after rearrangement,the equivalent focal length is

$A$ biconvex lens is formed by using two thin planoconvex lenses,as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in the figure. When an object is placed on the left side of the lens at a distance of $30 \ cm$ from the biconvex lens,the magnification of the image will be:

$A$ convex lens of focal length $25 \ cm$ and a concave lens of focal length $10 \ cm$ are joined together. The power of the combination will be

Concave and convex lenses are placed touching each other. The ratio of the magnitudes of their power is $2:3$. The focal length of the system is $30 \ cm$. Then the focal lengths of the individual lenses are: