Ray Optics

JEE Main level, single correct, medium

204 of 295

Question 204 of 295

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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Answer: (A) 60 cm from the convex lens

From lens formula for convex lens, we have
1f=1v−1u\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}
⇒130=1v+160\Rightarrow \dfrac{1}{30}=\dfrac{1}{v}+\dfrac{1}{60}
⇒160=1v\Rightarrow \dfrac{1}{60}=\dfrac{1}{v}

Applying lens formula to concave lens, we have
1f=1v−1u\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}
⇒1−120=1v−140,(∵u=+40cm)\Rightarrow \dfrac{1}{-120}=\dfrac{1}{v}-\dfrac{1}{40},\left(∵u=+40cm\right)
⇒v=60cm\Rightarrow v=60cm

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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