A person is 1.7m 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 5.3cm below the top of his head. Find a minimal vertical distance from the level of the persons eyes to the top of the mirror.

Express your answer to two significant figures and include the appropriate units.

Answer:

Light from the top of the head reflects off the mirror into the eye with the angle of reflection equaling the angle of incidence.

This means the reflection point is half way between eye-level and the top of the head

that is 5.3 / 2 = 2.65 cm

2.65cm above eye-level (2.65cm below top of head)

so this is the lowest point the top of the mirror can be for this reflection

minimal vertical distance from the level of the persons eyes to the top of the mirror = 2.65cm above eye-level