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 $, cm$)?

The size of the image of an object at infinity, formed by a convex lens of focal length $30 \,cm$, is $2 \,cm$. If a concave lens of focal length $20 \,cm$ is placed between the convex lens and the image at a distance of $26 \,cm$ from the convex lens, what is the new size of the image (in $\,cm$)?

Two thin lenses whose powers are $+2 \ D$ and $-4 \ D$ respectively are combined. The power of the combination is:

Two thin convex lenses of focal length $f_1$ and $f_2$ are placed in contact with each other. The equivalent power of the lens combination is . . . . . . .

$A$ plano-convex lens of refractive index $\mu_1$ fits exactly into a plano-concave lens of refractive index $\mu_2$. Their plane surfaces are parallel to each other. $R$ is the radius of curvature of the curved surface of the lenses. The focal length of the combination is:

Two convex lenses of focal lengths $20 \,cm$ and $30 \,cm$ are placed in contact with each other co-axially. The focal length of the combination is (in $\,cm$)