A converging lens with focal length f = 10 cm forms an image of an object placed at do = 15 cm. What is di and the magnification?

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Multiple Choice

A converging lens with focal length f = 10 cm forms an image of an object placed at do = 15 cm. What is di and the magnification?

Explanation:
The key idea is how a thin lens relates distances through 1/f = 1/do + 1/di. With a converging lens, f is positive. Plug in f = 10 cm and do = 15 cm: 1/di = 1/f − 1/do = 1/10 − 1/15 = 1/30, so di = 30 cm. A positive image distance means a real image forms on the opposite side of the lens from the object. The magnification is m = −di/do = −30/15 = −2, so the image is inverted and twice the size of the object. Therefore di = 30 cm and magnification = −2.

The key idea is how a thin lens relates distances through 1/f = 1/do + 1/di. With a converging lens, f is positive. Plug in f = 10 cm and do = 15 cm: 1/di = 1/f − 1/do = 1/10 − 1/15 = 1/30, so di = 30 cm. A positive image distance means a real image forms on the opposite side of the lens from the object. The magnification is m = −di/do = −30/15 = −2, so the image is inverted and twice the size of the object. Therefore di = 30 cm and magnification = −2.

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