An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be: (a) 20 cm from the convergent mirror, same size as the object (b) 40 cm from the convergent mirror, same size as the object (c) 40 cm from the convergent lens, same size as the object (d) 20 cm from the convergent mirror, twice the size of the object

Answer: (c). Lens: u = 2f = 40 ⇒ v = 40 cm, inverted, same size; it is 20 cm in front of the mirror. Mirror: object at 2f = 20 cm, image at 20 cm, same size, i.e. 40 cm from the lens. Back through the lens: object at 2f, image 40 cm from the lens on the object side, same size. So the answer is (c) 40 cm from the convergent lens, same size as the object.

An upright object is placed at a distance of 40 cm in front of a… | JEE Main 2019 (8 Apr, Shift 1)

Q62JEE Main 2019 · 8 APR · SHIFT 1Difficult

Combination of Lenses

An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be:

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Answer: (c)

Lens: $u = 2f = 40 \Rightarrow v = 40\text{ cm}$ , inverted, same size; it is 20 cm in front of the mirror.
Mirror: object at $2f = 20\text{ cm}$ , image at 20 cm, same size, i.e. 40 cm from the lens.
Back through the lens: object at $2f$ , image 40 cm from the lens on the object side, same size.
So the answer is (c) 40 cm from the convergent lens, same size as the object.

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