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.

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The final image formed by the combination is real at distance of 60 cm from convex lens

Virtual object 10 cm behind the plane mirror

Real image 10 cm infront of plane mirror

The final image formed by the combination is real at distance of 70 cm from convex lens

answer is A, B, C.

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Detailed Solution

Len’s formula is given by $\frac{1}{f} = \frac{1}{V} - \frac{1}{u}$

For convex lens:

$\frac{1}{30} = \frac{1}{v} + \frac{1}{60} \Rightarrow \frac{1}{60} = \frac{1}{v}$

Similarly for concave lens:

$\frac{1}{- 120} = \frac{1}{v} - \frac{1}{40} \Rightarrow \frac{1}{v} = \frac{1}{60}$

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

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