$A$ 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

$A$ point object,$O$ is placed in front of two thin symmetrical coaxial convex lenses $L_1$ and $L_2$ with focal lengths $24\,cm$ and $9\,cm$ respectively. The distance between the two lenses is $10\,cm$ and the object is placed $6\,cm$ away from lens $L_1$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is .........$cm$.

$A$ 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:

The dispersive powers of two lenses are $0.01$ and $0.02.$ If the focal length of one lens is $+10\, cm$,what should be the focal length of the second lens so that they form an achromatic combination?

$A$ convex lens of focal length $30 \ cm$ is placed in contact with a concave lens of focal length $20 \ cm$. An object is placed at $20 \ cm$ to the left of this lens system. The distance of the image from the lens in $cm$ is . . . . . .