Two lenses of power $+10 \, D$ and $-5 \, D$ are placed in contact. Where should an object be held from the lens so as to obtain a virtual image of magnification $2$ (in $, cm$)?

$A$ 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 two lenses of an achromatic doublet should have:

Three lenses of focal lengths $+10 \ cm, -10 \ cm$ and $+30 \ cm$ are placed at distances of $30 \ cm, 35 \ cm$ and $45 \ cm$ respectively from an object. The distance between the object and the final image formed is: (in $cm$)

The focal length of the field lens (which is an achromatic combination of two lenses) of a telescope is $90 \ cm$. The dispersive powers of the two lenses in the combination are $0.024$ and $0.036$. The focal lengths of the two lenses are:

In which optical instruments is a combination of lenses used?