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# The focal length of a Plano convex lens when curved surface is silvered and object is in front of plane surface is :-

$(a)\;\frac{R}{\mu} \\ (b)\;\frac{R}{2\mu} \\ (c)\;\frac{R}{3\mu} \\ (d)\;\frac{3R}{\mu}$

In this case
$\large\frac{1}{f_L}=(\mu-1) \bigg[ \large\frac{1}{\infty}-\frac{1}{-R} \bigg]$
$\qquad= \large\frac{\mu-1}{R}$ and $f_m =\large\frac{(-R)}{2}$
So, $P_L= \large\frac{1}{f_L}=\frac{(\mu-1)}{R}$
and $P_M=\large\frac{-1}{f_m} =\frac{2}{R}$
and hence power of system
$P=P_L+P_m+P_L$
$\quad=2P_L +P_M$
$P= \large\frac{2( \mu-1)}{R} +\frac{2}{R}$
$\quad= \large\frac{2 \mu}{R}$
$\therefore F= \large\frac{-1}{P}=\large\frac{-R}{2\mu}$
ie the lens will be equivalent to a converging mirror of focal length $\bigg( \large\frac{R}{2y}\bigg)$
Hence b is the correct answer.

edited Jul 22, 2014