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 is 5 cm closer to the lens. The focal length of the lens is:
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Question

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 is 5 cm closer to the lens. The focal length of the lens is:

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G1 Physics · Accepted Answer

Step 1: Incident converging rays have a virtual object at u = +10 cm on image side (without lens rays converge 5 cm closer than 15 cm). Step 2: With diverging lens, image at v = +15 cm. Step 3: Thin lens formula 1/f = 1/v − 1/u = 1/15 − 1/10 = −1/30 cm⁻¹. Final answer: (C) f = −30 cm.