$A$ plano-convex lens has a focal length of $20\,cm$. If its plane surface is silvered,it behaves as a converging mirror. What will be its focal length in $cm$?

$A$ point object is placed at a distance of $20 \, cm$ from a thin plano-convex lens of focal length $15 \, cm$. If the plane surface is silvered,where will the image form?

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:

The radius of curvature of a lens is $20\,cm$ and its refractive index is $1.5$. If the refractive index of the surrounding liquid is $1.6$,then the focal length of the system is .......... $cm$.

$A$ convex lens of focal length $15 \,cm$ is placed in front of a plane mirror at a distance of $25 \,cm$ from the mirror. Where on the optical axis and from the centre of the lens should a small object be placed such that the final image coincides with the object?

$A$ pin is placed at a distance of $10 \, cm$ in front of a convex lens of focal length $20 \, cm$. The lens is made of a material with a refractive index of $1.5$. The surface of the lens farther from the pin is silvered,and its radius of curvature is $22 \, cm$. Find the position of the final image in $cm$.