• question_answer 40) The radius of curvature of a thin plano-convex lens is 10 cm (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 A)  $10\,cm$                    B)  $15\,cm$C)  $20\,cm$                    D)  $5\,cm$

The silvered piano convex lens behaves as a concave mirror; whose focal length is given by $\frac{1}{F}=\frac{2}{{{f}_{1}}}+\frac{1}{{{f}_{m}}}$ If plane surface is silvered ${{f}_{m}}=\frac{{{R}_{2}}}{2}=\frac{\infty }{2}=\infty$ $\therefore$ $\frac{1}{{{f}_{1}}}=(\mu -1)\left( \frac{1}{{{R}_{1}}}-\frac{1}{{{R}_{2}}} \right)=(\mu -1)\left( \frac{1}{R}-\frac{1}{\infty } \right)=\frac{\mu -1}{R}$ $\therefore$ $\frac{1}{F}=\frac{2(\mu -1)}{R}+\frac{1}{\infty }=\frac{2(\mu -1)}{R}\Rightarrow F=\frac{R}{2(\mu -1)}$ Here $R=20\,cm,\,\mu =1.5$ $\therefore$ $F=\frac{20}{2(1.5-1)}=20\,cm$