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A concave mirror produces a magnification m1 when an object is placed 25 cm from it. The object is then moved 15 cm farther away from its original position, and the magnification becomes m2. If m1/m2 = 4, what is the focal length of the mirror (in cm)?

1. 10
2. 15
3. 20
4. 25

Correct answer: 20

Solution

With u1 = -25 cm and u2 = -40 cm and f = -|f| for a concave mirror, the ratio m1/m2 = (40 - |f|)/(25 - |f|) = 4 gives |f| = 20 cm. Verification: m1 = -20/5 = -4, m2 = -20/20 = -1, ratio = 4.

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