What is the minimum height of a plane mirror required to see the full height of a person standing in front of it?

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One-fourth the height of the person

The full height of the person

Twice the height of the person

Half the height of the person

answer is B.

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Detailed Solution

Consider a person of height, $h$ standing in front of a plane mirror. To see the full image, light rays from the top of the head and the feet must reflect off the mirror and reach the eyes.

Since the mirror only needs to reflect the rays from the top and bottom halves of the person, the minimum height of the mirror should be half the person’s height. This is because the rays traveling from the top and bottom of the person to the eyes trace paths that only require half the mirror height to reflect the full body.

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