The radius of curvature of a thin plano-convex lens is 10cm (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then it behaves like a concave mirror of focal length (in cm )

$\begin{array}{l}\text{ The silvered plano convex lens behaves as a concave }\\ \text{ mirror; whose focal length is given by }\\ \frac{1}{ \text{F}}=\frac{2}{{\text{f}}_1}+\frac{1}{{\text{f}}_{\text{m}}}\\ \text{ If plane surface is silvered ,}{f}_m=\frac{R_2}{2}=\frac{\infty }{2}=\infty \\ \frac{1}{{\text{f}}_1}=(\mu -1)(\frac{1}{{\text{R}}_1}-\frac{1}{{\text{R}}_2})=(\mu -1)(\frac{1}{\text{R}}-\frac{1}{\infty })=\frac{\mu -1}{\text{R}}\\ \\ \therefore \frac{1}{ \text{F}}=\frac{2(\mu -1)}{\text{R}}+\frac{1}{\infty }=\frac{2(\mu -1)}{\text{R}}\\ \Rightarrow \text{F}=\frac{\text{R}}{2(\mu -1)}\\ \text{ Here R}=20 \text{cm},\mu =1.5\\ \therefore \text{F}=\frac{20}{2(1.5-1)}=20 \text{cm}\end{array}$