A person is 1.7 m tall. Where should he place the top of a mirror on the wall so he can see the top of his head? Assume his eyes are 5.0 cm below the top of his head. Find a minimal vertical distance from the level of the person’s eyes to the top of the mirror.

The  minimal vertical distance from the level of the person’s eyes to the top of the mirror is 2.5 cm

Explanation:

Given;

height of the person, h = 1.7 m tall

eye level (d) is 5.0 cm below the top of his head

The minimal vertical distance from the level of the person’s eyes to the top of the mirror is will be half the distance below the top of his head.

d' = ¹/₂ d

d' = ¹/₂ x 5.0cm

d' = 2.5 cm

This can be seen if we make a diagram of him and his image formed on the mirror, such that a straight line from his eyes to top of his head on the  image formed on the mirror, passes the mirror half way to the image.

Thus, the  minimal vertical distance from the level of the person’s eyes to the top of the mirror is 2.5 cm