A 1.76 m tall man looks at his reflection in a plane mirror. He stands 4.2 m away from the mirror. How far from his eyes are the images of his feet? Assume his eyes are 5 cm below the top of his head.
A) 8.4 m
B) 11.1 m
C) 4.2 m
D) 4.53 m
E) 8.57 m

Question

Quizplus · Accepted Answer

The distance from the man's eyes to his feet in the mirror image is the sum of the distance from his eyes to the mirror (4.2 m) and the distance from the mirror to the image of his feet, which is also 4.2 m. However, since his eyes are 5 cm (0.05 m) below the top of his head, the total height of the man is 1.76 m, so the distance from his eyes to the ground is 1.76 - 0.05 = 1.71 m. The image of his feet in the mirror appears the same distance behind the mirror as his real feet are in front of it, so the total distance from his eyes to the image of his feet is 4.2 m (to the mirror) + 4.2 m (back to his feet's image) + 1.71 m (from his feet to his eyes) = 8.57 m.

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