A point like object is placed at a distance of 1 m in front of a… | JEE Main 2020 (6 Sep, Shift 1)

Q50JEE Main 2020 · 6 SEP · SHIFT 1Difficult

Combination of Lenses

A point like object is placed at a distance of 1 m in front of a convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2 m behind the lens. The position and nature of the final image formed by the system is:

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Answer: (a)

Lens: $\frac{1}{v} = \frac{1}{0.5} - \frac{1}{1} \Rightarrow v = 1\text{ m}$ , i.e. 1 m in front of the mirror.
Plane mirror image: 1 m behind the mirror, 3 m from the lens; it is a real object for the lens on the return path.
$\frac{1}{v'} = \frac{1}{0.5} - \frac{1}{3} = \frac{5}{3} \Rightarrow v' = 0.6\text{ m}$ on the object side, real.
Distance from mirror $= 2 + 0.6 = 2.6\text{ m}$ .
So the answer is (a) 2.6 m from the mirror, real.

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Combination of Lenses question from JEE Main 2020 (6 Sep, Shift 1)

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