Suppose a man stands in front of a mirror as shown in Figure 25.50. His eyes are 1.65 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. How is this distance related to the man’s height?
Figure 25.50 A full-length mirror is one in which you can see all of yourself. It need not be as big as you, and its size is independent of your distance from it.
By the law of reflection and ray tracing, 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 and the bottom must go down to halfway between his eyes and the floor. This result is independent of how far person stands from the wall.
a = b / h
a = m
a = 0.065 m
b = m
b = 0.825 m
h = 1.65 + 0.13 m
h = 1.78 m
the length of the mirror L is
L = h= (a +b)
L = 0.89 m
bottom of the smallest mirror is,
b = 0.825 m
top of the mirror from the floor is
b +L = 1.715 m
the floor the bottom of smallest mirror is 0.825 m and top is 1.715 m and height of the mirror is 0.89 m precisely one-half the height of the person.