A nearsighted man cannot see objects clearly beyond 20 centimeters from his eyes. How close must he stand to a mirror in order to see what he is doing when he shaves?
Let’s call the distance the man stands from the mirror 𝑑 sub 𝑜, the object distance. And we can begin by drawing a diagram of the situation. If the man is standing in front of a plane mirror, then we know the image formed of the man will appear on the reverse side of the mirror the same distance away as the man stands from the mirror. We’re told in the problem statement that the maximum distance a man can be from an object while still seeing it clearly is 20 centimeters.
Since that is the maximum distance away from him the man can see an image and the image formed by this mirror is twice as far from the man as the mirror, that means the distance 𝑑 we’ve written at the bottom of our diagram is in fact equal to 𝑑 sub 𝑜 when the man and the image are separated by 20 centimeters. Therefore, 20 centimeters equals two times 𝑑 sub 𝑜. Or, 𝑑 sub 𝑜 equals 10 centimeters. This is how close the man must be to the mirror to see his reflection clearly.