$A$ convex lens of focal length $30 \ cm$ is placed in contact with a concave mirror of focal length $20 \ cm$. What is the focal length of the system in $cm$?

In the diagram given below,there are three lenses formed. Considering the negligible thickness of each of them as compared to $|R_1|$ and $|R_2|$,i.e.,the radii of curvature for the upper and lower surfaces of the glass lens,the power of the combination is:

When a thin convex lens is placed in contact with a concave mirror of the same focal length,the resultant focal length of the system is ......

An upright object is placed at a distance of $40\, cm$ in front of a convergent lens of focal length $20\, cm$. $A$ convergent mirror of focal length $10\, cm$ is placed at a distance of $60\, cm$ on the other side of the lens. The position and size of the final image will be

The distance between a convex lens and a plane mirror is $10 \, cm$. The parallel rays incident on the convex lens after reflection from the mirror form an image at the optical centre of the lens. The focal length of the lens will be.....$cm$.

$A$ plano-convex lens $(f=20 \,cm)$ is silvered at its plane surface. What will be its new focal length (in $\,cm$)?