Where should a person stand, measured straight out from the pole of a convex mirror of focal length 2.0 m on its axis, so that the image formed becomes half of his original height?

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Accepted Answer

(4) -2.0 m. Given: convex mirror, f = +2.0 m. A convex mirror always makes an erect, diminished, virtual image, so half height means m = +1/2. Idea: m = -v/u, so v = -u/2. Put that into 1/v+1/u = 1/f: -2/u+1/u = 1/f, i.e. -1/u = 1/f. So u = -f = -2.0 m: the person stands at a distance equal to the focal length. Check: u = -2.0 m gives 1/v = 1/(2.0)+1/(2.0) = 1, v = +1.0 m, and m = -(1.0)/(-2.0) = +0.5. So he should stand 2.0 m in front of the mirror, u = -2.0 m.

Where should a person stand, measured straight out from the pole of a convex mirror of focal length 2.0 m on its axis, so that the image formed becomes half of his original height?

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