Can someone please explain this to me? It has been explained to me mathematically, but I can't make sense of it.

I am very nearsighted, and wear glasses. One day, I thought of a genius plan I was very excited about! If I were to stand, without glasses, with a distant object behind me, say 50 feet away, (such as a mountain, tree, etc) and hold a mirror close to my face in front, I could see the distant objects through the mirror clearly! (curing need for glasses) But when I tried the experiment it didn't work, the reflection is still blurry.

Mathematically, according to all the physics laws, the "virtual image" seen in the mirror is actually 50 feet away.????? But this seems impossible to me. Can anyone explain this in plain terms? Right now I've decided that mirrors are just magic.