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A converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point 15 cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is

1. −10 cm
2. 20 cm
3. −30 cm
4. 5 cm

Correct answer: −10 cm

Solution

When the lens is removed, the rays converge 5 cm closer, so the object distance for the lens is -10 cm (virtual object). Using the lens formula, 1/f = 1/v - 1/u, with v = 15 cm and u = -10 cm, we find f = -10 cm.

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