$A$ 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:

An achromatic combination of lenses is formed by joining

$A$ convex lens of focal length $40 \ cm$ is in contact with a concave lens of focal length $25 \ cm$. The power of the combination is:

Obtain the equivalent focal length of a combination of thin lenses placed in contact.

An object is placed $12 \ cm$ to the left of a converging lens of focal length $8 \ cm$. Another converging lens of $6 \ cm$ focal length is placed at a distance of $30 \ cm$ to the right of the first lens. The second lens will produce

$A$ plano-convex lens of refractive index ${\mu _1}$ and focal length $f_1$ is kept in contact with another plano-concave lens of refractive index ${\mu _2}$ and focal length $f_2$. If the radius of curvature of their spherical faces is $R$ each and $f_1 = 2f_2$,then ${\mu _1}$ and ${\mu _2}$ are related as: