$A$ 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 $cm$?

$A$ luminous object is placed at a distance of $30 \,cm$ from a convex lens of focal length $20 \,cm$. On the other side of the lens,at what distance from the lens should a convex mirror of radius of curvature $10 \,cm$ be placed in order to have an upright image of the object coincident with it (in $,cm$)?

$A$ 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 .............. $cm$.

$A$ plano-convex lens of focal length $30\,cm$ has its plane surface silvered. An object is placed $40\,cm$ from the lens on the convex side. The distance of the image from the lens is.......$cm$

$A$ point object is held above a thin equiconvex lens at its focus. The focal length is $0.1 \ m$ and the lens rests on a horizontal thin plane mirror. The final image will be formed at

$A$ plano-convex lens,when silvered at its plane surface,is equivalent to a concave mirror of focal length $28 \, cm$. When its curved surface is silvered and the plane surface is not silvered,it is equivalent to a concave mirror of focal length $10 \, cm$. Find the refractive index of the material of the lens.