A convex lens of focal length +30 cm is in contact with a concave lens of focal length -20 cm. An object is placed 20 cm to the left of the combination. The magnitude of the image distance is:
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Question

A convex lens of focal length +30 cm is in contact with a concave lens of focal length -20 cm. An object is placed 20 cm to the left of the combination. The magnitude of the image distance is:

G1 Physics · Accepted Answer

Equivalent focal length: 1/f = 1/f₁ + 1/f₂ = 1/30 - 1/20 = (2-3)/60 = -1/60. Hence, f = -60 cm. Using the lens formula 1/v - 1/u = 1/f, with u = -20 cm, f = -60 cm: 1/v - (-1/20) = -1/60 ⇒ 1/v + 1/20 = -1/60 ⇒ 1/v = -1/60 - 3/60 = -4/60 = -1/15. Thus, v = -15 cm. The magnitude of image distance is 15 cm. Correct option: D.