Can a scope correct vision?
Yes, it can correct plain short-sightedness.
Can it correct long sightedness?
Maybe it depends on how the maker set up the eyepiece focusing.
Can it correct any astigmatism (Cylindrical correction)?
No.
Getting the reticule sharp is easy if it is done well, unfortunately a lot of shooters don't know how to do this. They adjust the reticule while looking at a target! This "leads" the eye, making it do the impossible by focusing on 2 things at once.
Here's a better way IMO.
Take a piece of plain white paper & attach it to the barrel with tape, but bend it up slightly so it totally covers the FOV of the scope. Crease it to keep it in place. If done right all you see through the scope is featureless white & a reticule.
Now adjust the rear focus till the reticule looks 100% sharp. Then close the eye, look away for 30 seconds to "reset" the eye. Close the eye again & get into position behind the scope. Now open the eye. The reticule should
immediately be razor sharp. If it isn't refocus again & repeat till it is.
If you wear glasses use them, if you don't shoot with glasses take them off for the setup so it will correspond to your eyesight at the time of firing. Make sure you are looking through the center of the eyeglass lens, the edges aren't as well corrected. If you have bifocal, or trifocal lenses check that you are looking through a single grind, not a transition between 2 grinds.
After this look at the target. If it is not also in focus the objective (front) lens system is focused somewhere other than at the distance you're shooting. With an AO scope just adjust the AO, with a fixed scope you're stuck with whatever the factory gave you, a lot more common than you might think. I've had centerfire scopes set for "100yards" set for 35, 50 & 17 yards.
