Question

A nearsighted man cannot see objects clearly beyond 20 cm from his eyes. How close must he stand to a mirror in order to see what he is doing when he shaves?

Short answer

The nearsighted man must stand at 10 cm from the mirror.

Step-by-step solution

How do contact lenses work?

Contact lenses operate by bending light to bring it into focus on the retina, where vision receptors collect data and send it to the brain.

Given information and Formula to be used

d = 20 cm

When a person stands in front of a mirror, the distance between the item and the plane of the mirror is equal to the distance between the image and the plane of the mirror, resulting in:

$$\begin{gathered} d=2d_0 \\ {d}_0=\frac{d}{2} \end{gathered}$$ ………..(1)

The distance at which a nearsighted man must stand in front of them to see what he is doing when he shaves.

Equation (1) is obtained by substituting data values, such that

$$\begin{gathered} d_0=\frac{d}{2} \\ =\frac{20cm}{2} \\ =10cm \end{gathered}$$

Therefore, to see what he's doing when shaving, a nearsighted man should stand 10 cm away from the mirror.