One basic optical rule of thumb is that the average human eye (which means 20/20 vision, whether the eye's "naked" or lens-corrected) can resolve about one inch at 100 yards. This doesn't mean we can see a 1" dot at that range. Instead it means we can differentiate between alternating 1/2" black-and-white lines. Beyond 100 yards they begin to appear gray.
Whether we can resolve as well at longer distances depends on atmospheric and light conditions. A lot of mirage obviously reduces resolution, but in still, clear air we should be able to differentiate between 5" black-and-white lines at 1000 yards (10 times 1/2" = 5).
With good optics, resolution increases directly with magnification. This means a 10x scope at 1000 yards, in good atmospheric conditions, should allow us to resolve those same 1/2" alternating black-and-white lines as well at 1000 yards as well as at 100 yards without optics. With a 6x scope the size of the resolvable lines would increase to about .83" (10/6 x .5).
Obviously there will be some variation not only due to atmosphere and light, but individual eyesight and the specific scope. Then there's the size of the reticle: One subtending 1/2" at 100 yards covers 5" at 1000. But a little math can provide a good indication of what's possible.
