JAMB 2011 Physics · Question 25

An image in a convex lens is upright and magnified 3 times. If the focal length of the lens is 15 cm, what is the object distance?

Options

A.10 cm
B.25 cm
C.16 cm
D.14 cm

Answer: A. 10 cm

Explanation written with AI and checked against the answer key

Analyze the question A convex lens forms an upright, magnified image only when it acts as a magnifying glass, so the object is placed inside the focal length. The image is virtual and on the same side as the object. Magnification is m = 3, and f = 15 cm. Concept Use the lens formula with the real-is-positive convention: 1/f = 1/u + 1/v Magnification: m = v/u, with v negative for a virtual image. Solution The image is upright and virtual, so v = −3u. 1/f = 1/u + 1/v 1/15 = 1/u − 1/(3u) 1/15 = (3 − 1)/(3u) = 2/(3u) Cross-multiplying: 3u = 30 u = 10 cm Check v = −3(10) = −30 cm, so the image is virtual and 30 cm from the lens. 1/10 − 1/30 = 3/30 − 1/30 = 2/30 = 1/15 ✓ The object distance of 10 cm is also less than f = 15 cm, as expected for a magnifier. Answer: A (10 cm) Tip For an upright (virtual) image from a convex lens, the object must be inside the focal length. A quick shortcut for a magnifier is u = f(m − 1)/m = 15 × 2/3 = 10 cm. Only option A is less than 15 cm and fits, though C and D (16 and 14) are close distractors, so always check by calculation.

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