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

$(a)\;\frac{R}{2 (y-1)} \\ (b)\;\frac{3R}{2(\mu-1)} \\ (c)\;\frac{R}{(\mu-1)} \\ (d)\;\frac{2R}{(\mu-1)}$

Can you answer this question?

In this situation
$\large\frac {1}{f_L}=(\mu-1) \bigg( \large\frac{1}{R}-\frac{1}{\infty}\bigg)$
and $F_m =\large\frac{\infty}{2}$$=\infty So, P_L =\large\frac{1}{f_L}=\frac{(\mu-1)}{R} and P_M=\large\frac{-1}{f_M} \qquad= \large\frac{1}{\infty} \qquad= 0 and hence power of system P= P_l+P_M+P_L \quad= 2PL+P_M ie p=2 \large\frac{(\mu-1)}{R}$$+0$
$\qquad= \large\frac{2(\mu-1)}{R}$
$\therefore F=\large\frac{1}{P}$
$\qquad= \large\frac{R}{2(\mu-1)}$
ie lens will behave as a concave mirror of focal length $\large\frac{R}{2 (\mu-1)}$
Hence a is the correct answer.

answered Feb 13, 2014 by
edited Jul 22, 2014