$A$ 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:

$A$ convex lens of focal length $40 \, cm$ and a concave lens of focal length $25 \, cm$ are placed in contact. The power of the combination is .......... $D$.

An achromatic convergent doublet of two lenses in contact has a power of $+2 \ D$. The convex lens has a power of $+5 \ D$. What is the ratio of the dispersive powers of the convergent and divergent lenses?

$A$ plano-convex lens of material of refractive index $\mu_1$ exactly fits into a plano-concave lens of material of refractive index $\mu_2$. If $R$ is the radius of curvature of the curved surfaces of the lenses and the plane surfaces of the lenses are parallel,the focal length of the combination is:

$A$ lens of power $+2$ diopters is placed in contact with a lens of power $-1$ diopter. The combination will behave like

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?