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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 -

1. 20 cm
2. 10 cm
3. 25 cm
4. 30 cm

Correct answer: 10 cm

Solution

The correct option is 10 cm because the concave mirror can only produce a virtual image when the object is placed within its focal length. Since the focal length of the concave mirror is equal to the distance from the mirror to the image formed by the lens, which is 10 cm, any object placed beyond this distance will not yield a virtual image.

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