Final answer:
Depth perception allows us to judge distances but becomes less effective for objects that are far away. The ability to resolve two points as distinct, like headlights that are 1.30 meters apart, diminishes with distance, hence impacting what we can see in a rear view mirror. A nearsighted person would need to stand close to a mirror, within the clear range of vision, to see his face sharply.
Step-by-step explanation:
Understanding Depth Perception and Rear View Visibility
Depth perception is a critical aspect of our vision that helps us determine how far away objects are. The ability to perceive depth deteriorates for objects positioned at a significant distance from us, typically more than a few tens of meters. For example, if you hold a pen a few inches from your face and observe it with one eye, then switch to the other eye, you'll notice a significant shift in the pen's position against the background. The phenomenon you are observing is called parallax. As you move the pen further away, this shift becomes less noticeable, and at a certain distance, your brain can no longer use this shift to accurately gauge depth.
When looking into a rear view mirror, your depth perception is limited. Objects far away in the mirror may not appear to shift much, even as you move your head slightly. The limit of perception can be illustrated with the same principle that applies to a nearsighted person who cannot see clearly beyond 20 cm. In the case of a car's headlights, which are approximately 1.30 meters apart, there is a certain distance beyond which you can no longer resolve them as separate points of light. This limit is defined by the resolving power of your eyes and helps to gauge the effective range of view in the mirror.
As for a nearsighted person, in order to see his face clearly in a mirror while shaving, he would need to stand at a distance where the image appears within his range of clear vision, which would be less than or equal to 20 cm.