$A$ 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 $cm$?

$A$ thin equiconvex lens has a focal length of $10\; cm$ and a refractive index of $1.5$. One of its faces is now silvered,and for an object placed at a distance $u$ in front of the lens,the image coincides with the object. The value of $u$ is: (in $; cm$)

An object is placed at a distance of $30\,cm$ from a convex lens of focal length $20\,cm$. At what distance (in $cm$) from the lens on the other side should a convex mirror of radius of curvature $10\,cm$ be placed so that the images formed by the lens and the mirror coincide?

The diagram shows a silvered equiconvex lens. An object of length $1\,cm$ is placed at a distance of $30\,cm$ in front of the lens. What will be the final image properties? The refractive index of the lens is $\mu$ and the refractive index of the medium in which the lens has been placed is $2\mu$. Both surfaces have a radius of curvature $R$.

$A$ convex lens has a focal length $f$. It is cut into two parts along the dotted line as shown in the figure. The focal length of each part will be

$A$ convex lens forms a real image of a point object at a distance of $50 \, cm$ from the convex lens. $A$ concave lens is placed $10 \, cm$ behind the convex lens on the image side. On placing a plane mirror on the image side and facing the concave lens,it is observed that the final image now coincides with the object itself. The focal length of the concave lens is .............. $cm$.