Question

The focal length of a plano convex lens when curved surface is silvered and the object is in front of plane surface is

• A. $-\frac{R}{2\mu }$
• B. $\frac{2R}{\mu }$
• C. $-\frac{R}{\mu }$
• D. $-\frac{2R}{\mu }$

Answer 1

The correct option is A $-\frac{R}{2\mu }$

In this case
$\frac{1}{f_L}=(\mu -1)[\frac{1}{\infty }-\frac{1}{-R}]=\frac{(\mu -1)}{R}And{F}_M=\frac{(\mu -1)}{R}So{P}_L=\frac{1}{f_L}=\frac{(\mu -1)}{R}And{P}_m=-\frac{1}{fM}=\frac{2}{R}$
And hence power of system
$P=P_L+P_M+P_L=2P_L+P_M\Rightarrow P=\frac{2(\mu -1)}{R}+\frac{2}{R}=\frac{2\mu }{R}\therefore F=-\frac{1}{P}=-\frac{R}{2\mu }$
i.e. the lens will be equivalent to a converging mirror of focal length $\left(R/2\mu \right)$