An effective power of a combination of $5$ identical convex lenses which are kept in contact along the principal axis is $25 \ D$. Focal length of each of the convex lens is: (in $cm$)

$A$ plano-convex lens (focal length $f_2,$ refractive index $\mu_2,$ radius of curvature $R$) fits exactly into a plano-concave lens (focal length $f_1,$ refractive index $\mu_1,$ radius of curvature $R$). Their plane surfaces are parallel to each other. Then,the focal length of the combination will be

$A$ convex and a concave lens separated by a distance are then put in contact. How does the focal length of the combination change?

$A$ convex lens $A$ of focal length $20 \, cm$ and a concave lens $B$ of focal length $5 \, cm$ are kept along the same axis with a distance $d$ between them. If a parallel beam of light falling on $A$ leaves $B$ as a parallel beam,then the distance $d$ in $cm$ will be:

The two lenses of an achromatic doublet should have:

Two lenses have focal lengths $f_1$ and $f_2$ and their dispersive powers are $\omega_1$ and $\omega_2$ respectively. They will together form an achromatic combination if