How come degraded eyesight still holds with a mirror?
It's been too long since physics to have a good answer, but I know that if you look at an object in a flat mirror, the light coming off the mirror would be identical to light coming a real object in the same position. The angles of the light rays are the same. Therefore, no matter how close the mirror is to your face, your eyes treat the image as if it's coming from 10 feet away, or however far the object in the mirror is away from the mirror. Bent mirrors will change this, that's why you get the "OBJECTS IN MIRROR ARE CLOSER THAN THEY APPEAR" warning.

I made a diagram to to try and explain it better.

The eye is looking at a mirror, the light from the arrow on the left of the mirror reflects off the mirror and toward the eye. The eye sees an image that appears as if it were behind the mirror, on the right.