A man stands in front of a mirror as shown in the figure. His eyes are 1.76 m ab

Question

A man stands in front of a mirror as shown in the figure. His eyes are 1.76 m above the floor, and the top of his head is 0.13 m higher. Find the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet. top 1.825 bottom .88 How is the distance d from the top to the bottom of the mirror related to the man's height h? Use the symbol h to represent the man's height. d= .945 How is the length of the mirror related to the distance from the floor to the top and bottom of the mirror?h

Explanation / Answer

From ray-tracing and the law of reflection, we know that the angle of incidence is equal to the angle of reflection, so the top of the mirror must extend to at least halfway between his eyes and the top of his head. The bottom must go down to halfway between his eyes and the floor. This result is independent of how far he stands from the wall. Therefore,

a=0.13/2 =0.065 m, b = 1.76/2 = 0.88 m and

L =1.76 + 0.13 -a-b =1.89- 0.065 -0.88 = 0.945 m

The bottom is b = 0.88 m from the floor and the top is b+ L = 0.88 m+0.945 m = 1.825 m from the floor.

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