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A thin convex lens of focal length ‘f’ is put on a plane mirror as shown in the figure. When an object is kept at a distance ‘a’from the lens-mirror combination, its image is formed at a distance a/3 in front of the combination. The value of ‘a’ is

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$\frac{3}{2} f$

answer is D.

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Detailed Solution

$\frac{1}{f_{eq}} = \frac{1}{f_{l}} + \frac{1}{f_{m}} + \frac{1}{f_{l}} = \frac{2}{f}$

Acts as a concave mirror

$\frac{1}{f_{eq}} = \frac{1}{v} + \frac{1}{u}$

$\frac{2}{f} = \frac{3}{a} + \frac{1}{a}$

$a = 2 f$ as concave mirror

act as concave mirror

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