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Two mirror one concave of radius of curvature $0.4\;m$ and another convex mirror of radius of curvature $0.2 \;m$ are kept facing each other which are $0.5\;m$ apart. An object is placed between two mirrors, $0.25\;m$ from concave mirror. Where is the image formed after two reflections.

(a) 0.5 m behind concave mirror

(b) 0.5 m behind convex mirror

(c) 0.125 m behind concave mirror

(d) 0.125 m behind convex mirror

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The first reflection at concave mirror.
$u = -0.25 m$
$f= \large\frac{r}{2} $$=-0.2\;m$
$\large\frac{1}{f} =\frac{1}{u}+\frac{1}{v}$
$\large\frac{-1}{.2} =\frac{-1}{.25}+\frac{1}{v}$
$v= -1 m$
ie the image forms 1 m in front of the concave mirror ie 0.5 m behind convex mirror.(virtual image ) for reflection at convex mirror
$u= +0.5$
$f =\large\frac{r}{2}$$=+0.1$
$\therefore u= \large\frac{1}{0.1} =\frac{1}{0.5}+\frac{1}{v}$
$v= +0.125\;m$
ie $0.125$ behind convex mirror
Hence d is the correct answer.
answered Jan 17, 2014 by meena.p

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