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March 26, 2017

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If a 2 m tall man is looking at a plane mirror from an eye which is 20 cm from the top of his head, what is the minimum length that the mirror must be so that he can just barely see his whole body in the mirror? How far up from the ground must the mirror be placed?

I'm confused about where the source/destination of each light ray should be and how to find the distance and height of the mirror after I have drawn those rays.

  • Physics - ,

    Draw the light rays going backwards, starting from his eye. For a ray diagram, represent the object and mirror as two parallel vertical lines. Use any distance X apart; it won't affect the answer. One limiting light ray should go from his eye to the mirror, bounce off and hit the top of his head. The other limiting ray should go downward from his eye and bounce off to hit his shoes. There will be a virtual source on the opposite side of the mirror, an equal distance X away.

    The only place you will actually need a mirror is between the two places where the limiting rays strike the mirror. The distance between them, using geometry, will turn out to be 1 meter. The bottom of the minimum-length mirror should be (2.0-0.2)/2 = 0.9 m above the ground.

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