The plane surface of a plano convex lens having radius of curvature 20 cm is silvered. If this silvered lens is equivalent to a concave mirror, the radius of curvature of the mirror is (Refractive index of glass is 1.5)

Focal length of a silvered lens is given by 

$\frac{1}{\mathrm{F}}=-\frac{2}{{\mathrm{f}}_{\mathrm{l}}}+\frac{1}{{\mathrm{f}}_{\mathrm{m}}}$

The silvered surface behaves like a plane mirror, therefore ${\mathrm{f}}_{\mathrm{m}}=\infty$. Also $\frac{1}{{\mathrm{f}}_{\mathrm{l}}}=\frac{\mathrm{\mu }-1}{\mathrm{R}}=\frac{1.5-1}{20}=\frac{1}{40}$

$\therefore \frac{1}{\mathrm{F}}=-2\times \frac{1}{40}\Rightarrow \mathrm{F}=-20\mathrm{cm}$

So focal length of the concave mirror is 20 cm. Hence radius of curvature $=2\times 20\mathrm{cm}=40\mathrm{cm}$