A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of:

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TestHub · Accepted Answer

From lens formula for convex lens, we have
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\Rightarrow \frac{1}{30} = \frac{1}{v} + \frac{1}{60}$
$\Rightarrow \frac{1}{60} = \frac{1}{v}$

Applying lens formula to concave lens, we have
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\Rightarrow \frac{1}{- 120} = \frac{1}{v} - \frac{1}{40}, (∵ u = + 40 cm)$
$\Rightarrow v = 60 cm$

Virtual object 10 cm behind plane mirror.
Hence real image 10 cm in front of mirror.
Hence 60 cm from convex lens.

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