Question

Suppose a man stands in front of a mirror as shown in the figure below.

a. His eyes are 1.79 m above the floor, and the top of his head is 0.13 m higher. Find the height (in m) 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 = ___m

Bottom = ___m

b. How is the distance d from the bottom of the mirror related to the man's height h?

d = ___

Answer 1

(a) The mirror must be at least half as tall as the person standing in front of the mirror. Since the eyes are 1.79 m above the floor, and the top of his head is 0.13 m higher. The lower edge of the mirror must be at a height that is half the distance between his feet and eyes i.e. 0.895 m. Similarly, as his head is 0.13 m above the eye, the upper edge of the mirror will be at a height of (1.79 m + 0.13/2 m) or 1.855 m. Therefore, the mirror height will be (1.855 m – 0.895 m) or 0.96 m which is exactly half of the man´s height (1.92 m).

Top =1.855 m

Bottom = 0.895 m

(b) The distance d from the bottom of the mirror related to the man's height h as, d = h/2.