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A 5 cm tall object is placed 20 cm in front of a convex lens of focal length 10 cm, forming an image at v = +20 cm. What are the magnification and image height?
AM = −1, height −5 cm (inverted, same size)
BM = +1, height +5 cm (erect, same size)
CM = −2, height −10 cm (inverted, larger)
DM = −0.5, height −2.5 cm (inverted, smaller)
Answer & Solution
Correct answer: A. M = −1, height −5 cm (inverted, same size)
1. Magnification $M = \frac{v}{u} = \frac{+20}{-20} = -1$.
2. Image height $h_2 = M \times h_1 = (-1)(5) = -5$ cm.
3. The negative sign shows the image is real and inverted, and its magnitude equals the object, so same size. A positive M would wrongly imply an erect image.
_Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 7 "Lenses", p.95_
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