The distance from your eyes to the mirror is irrelevant. It’s the distance from your eyes to a given object that counts, just as it would when you look at it without the mirror.
The light reflected from an object has to get to your eyes somehow, or else you wouldn’t see it. The light coming from things behind your back would never get to your eyes if the mirror weren’t there to turn it around. That’s all the mirror does: It takes light that would have passed you by and shoots it back at your eyes.
Suppose you’re facing the mirror and looking at an object behind you. Instead of coming straight from the object to your eyes, the light has to pass you by, go to the mirror and then come back to your eyes.
That’s a greater distance than if you had been facing the object, so it is even blurrier than if you had turned around and looked at it directly. The image of your beautiful face is also blurrier than if you were looking at it from the position of the mirror. The light has to go from your beautiful face to the mirror and back to your beautiful eyes, twice as far as if you were looking at your beautiful face from the position of the mirror.
This is all based on the fact that the farther away an object is, the fuzzier it will appear to nearsighted eyes. That’s generally true, and here’s why.
Nearsighted eyes are good at focusing light rays that are diverging, radiating out in all directions, as they are from a nearby object. But nearsighted eyes are not so good at focusing light rays that are more or less parallel, as they are from a distant object. It’s not that near and distant objects are shooting their light out differently; every object reflects light in many directions.
Remember how we drew a shining sun in kindergarten, with all those rays coming out in all directions? But when you’re far away from an object, your eyes are intercepting only a small fraction of those “all directions” rays.
It’s as if all the rays are now coming from the same, severely limited direction, like a bundle of parallel sticks, all pointing from the object straight at you. And that’s the situation, focusing parallel rays, that nearsighted eyes can’t handle well, so the object is blurred.
