A convex lens (of focal length 20 cm) and a concave mirror, having… | JEE Main 2019 (8 Apr, Shift 2)

Q61JEE Main 2019 · 8 APR · SHIFT 2Difficult

Combination of Lenses

A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be :-

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Answer: (b)

Lens: $\frac{1}{v} = \frac{1}{20} - \frac{1}{30} \Rightarrow v = 60\text{ cm}$ , i.e. 20 cm in front of the mirror.
Image unchanged by the mirror means the mirror images this point onto itself: it is at the centre of curvature, $R = 20\text{ cm}$ , $f = 10\text{ cm}$ .
A concave mirror forms a virtual image only when the object is within $f$ .
So the answer is (b) 10 cm.

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