WAEC 2015 Physics · Question 45

An object is placed 20cm from a concave mirror of focal length 15cm. Calculate the linear magnification of the image formed

Options

A.0.5
B.1.5
C.2.0
D.3.0

Answer: D. 3.0

Explanation written with AI and checked against the answer key

Analyze the question: A concave mirror has f = 15 cm and the object distance is u = 20 cm. We need the linear magnification m. Concept: Use the mirror formula: 1/f = 1/u + 1/v and the magnification formula: m = v/u (magnitude) Here the object is between f and 2f (15 cm < 20 cm < 30 cm), so the image will be real, inverted, and magnified. Solution: 1/v = 1/f − 1/u 1/v = 1/15 − 1/20 1/v = (4 − 3)/60 = 1/60 v = 60 cm m = v/u = 60/20 = 3 So the magnification has a magnitude of 3.0. The image is real and inverted, so by sign convention m = −3, but the exam option gives the magnitude. Check with the shortcut: m = f/(f − u) = 15/(15 − 20) = −3, with magnitude 3. ✔ Answer: D. 3.0 Tip: For a concave mirror, use m = f/(u − f) to get the magnitude quickly: 15/(20 − 15) = 3. Always check that the object lies between f and 2f. If so, the image is magnified and real, so your answer should be greater than 1.

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