It has been a few years since I studied this, but I am not completely senile yet so this should be close to accurate. Your eyes focus in two manners. The changing size of the pupil with changes in light, and the flexing of the lens.
The biggest problem for us old farts is the thickening or harding of the lens resulting in less flex.
The whole object of the flexing of the lens is to focus incoming light on the optic nerve. In youth clear vision occurs principally by the flexing of the lens thereby directing incoming light onto the optic nerve.
Generally speaking, near or far sightedness is caused by the light being directed off center of the optic nerve. The degree the light missing the optic nerve is the degree of impairment. If I recall correctly, the light hits above the optic nerve in far sighted people.
An older person is generally better off with a shorter barreled handgun putting both sight close to the same focal plane. With a long gun, a peep that can be looked through with out worrying about focusing on it and a front sight far enough away to be in focus is usually the best option.
I am so far sighted that I would have to have a 5 foot barrel to see the front sight clearly.