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Question

A teacher gives a convex lens and a concave mirror of focal length of about 20 cm each to his student and ask him to find their focal lengths by obtaining the image of a distant object. The student uses a distant tree as the object and obtains its sharp image, one by one, on a screen. The distance d1 and d2 between the lens/mirror and the screen in the two cases and the nature of their respective sharp images are likely to be:
(1) (20 cm, 40 cm) and (erect, erect)
(2) (20 cm, 40 cm) and (inverted, erect)
(3) (20 cm, 20 cm) and (inverted, inverted)
(4) (20 cm, 20 cm) and (erect, inverted)

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Solution

A convex lens and a concave mirror both converges the rays coming from a distant object to their focal point to form an inverted image. If images formed by them are obtained on a screen, then the distance of the screen from the lens or the mirror would be the focal length of the lens or the mirror respectively.

Similarly, in the given case, the distances d1 and d2 are the focal lengths of the given convex lens and concave mirror respectively and the nature of the image would be inverted for both lens and the mirror.

Hence, the correct answer is option 3.

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