Question

A thin plano-convex lens acts like concave mirror of focal length $0.2m$ when silvered at its plane surface. Refractive index of the material of lens is $1.5$. Radius of curvature of convex surface of the lens is

• A. $0.1m$
• B. $0.2m$
• C. $0.4m$
• D. $0.8m$

Answer 1

The correct option is B $0.2m$

$\begin{array}{c}{f}_L=\text{focal length of lens}\\ f_m=\text{focal length of mirror.}\\ f=20cm\end{array}$

$\begin{array}{c}\Rightarrow \frac{1}{f}=\frac{2}{f_L}+\frac{1}{f_m}\\ \therefore \frac{1}{20}=\frac{2}{F_L}\pm \frac{1}{\alpha }\\ +⟩f_L=40cm\end{array}$

$\begin{array}{cc}\text{Now,}\frac{1}{f}=& (u-1)(\frac{1}{R_1}-\frac{1}{R_m})\\ \therefore \frac{1}{40}& =(1.5-1)(\frac{1}{R}-\frac{1}{\alpha })\\ \therefore & R=20cm=0.2m\end{array}$

$\text{Hence, option (B) is trur or correct}$