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

$A$ plano-convex lens,when silvered on the plane side,behaves like a concave mirror of focal length $30 \ cm$. However,when silvered on the convex side,it behaves like a concave mirror of focal length $10 \ cm$. The refractive index of its material is:

$A$ bi-convex lens of focal length $10\,cm$ is cut into two identical parts along a plane perpendicular to the principal axis. The power of each lens after the cut is $...........\,D$.

$A$ glass slab of thickness $6 \, cm$ is silvered at one surface. An object is placed at a distance of $8 \, cm$ from the first surface. The image is formed at a distance of $12 \, cm$ behind the silvered surface. Find the refractive index of the glass.

$A$ converging mirror is placed on the right-hand side of a converging lens as shown in the figure. The focal length of the lens and the mirror are $15 \ cm$ and $20 \ cm$ respectively. The separation between the lens and the mirror is $40 \ cm$ and their principal axes coincide. $A$ point source is placed on the principal axis at a distance $d$ to the left of the lens. If the final beam comes out parallel to the principal axis,then the value of $d$ is: (in $cm$)

$A$ lens is placed on a plane mirror. An object needle and its image coincide at $15 \, cm$. The focal length of the lens is......$cm$.