The figure shows an equiconvex lens of focal length $f$. If the lens is cut along $AB$,the focal length of each half will be

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?

$A$ plano-convex lens $(\mu = 1.5)$ has a radius of curvature of $10 \; cm$. It is silvered on its plane surface. Find the focal length after silvering. (in $; cm$)

$A$ concave mirror is placed on a horizontal table with its axis pointing vertically upwards. Let $O$ be the pole of the mirror and $C$ be its center of curvature. $A$ point object is placed at $C$. It forms a real image at $C$. If the mirror is now filled with water,the image will be formed . . . . . .

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 .......... $cm$.