Your eye is a series of 2 lenses: the cornea, which refracts light from the air into the fluid of your eye, and a deformable lens, which varies its shape to bring an object into focus on the back of your retina.  This is fundamentally different from a camera:  in a camera, you have a lens of fixed focal length, and you vary the focus of an object by changing the distance between the lens and the film.  For your eye, you focus by having a fixed distance between the lens and the 'film' (the retina), but by changing the focal length of the lens.  In a relaxed state, your lens is relatively flat, and will focus at infinity.  As you look at objects which are close, the lens gets squeezed around the edges, so it gets fatter, and focuses on objects which are nearby.


The effective focal length of your eye's lens is close to 20 mm, giving your eye's lens an effective diopter  of +50 when it is relaxed (diopter is the inverse of focal length, in meters, hence 20 mm focal length = .020 m, and 1/.02 = 50).  Some sources indicate the eye's focal length is closer to 17.5 mm, giving it a resting diopter of + 57.  The exact distance will likely vary from person to person.

When the lens in a healthy eye tenses and changes shape, it can shift its diopter by about +4 points to focus on near objects.  For a healthy adult eye, this results in the ability to focus from infinity with a 50 diopter lens, to about 10 inches when the lens is fully compressed to a 54 diopter.

The nice thing about diopters is they are additive.  If you take a 50 diopter lens, and stack it on top of a second  50 diopter lens, you end up with an effective 100 diopter lens.  For minor vision correction we are typically talking about taking a 54 diopter eye, and adding a lens of approximately 1.0 diopter (your typical drug store reading glasses), resulting in a 55 diopter eye, which allows you to focus at a closer distance.

There are 4 things that can typically go wrong with your eye:
1.  Myopia (nearsighted).
2.  Hyperopia (farsighted).
3.  Astigmatism.
4.  Presbiopia (old eyes).

For the first two, the eye is slightly mis-shaped, so the lens works fine, the eye is just a little bigger, or smaller than it should be, so the back of the eye is not at the perfect focal point of the lens.  A simple vision lens is used to adjust where the eye focuses.

An astigmatism is when the lenses in the eye don't line up with each other.  Again, a single (albeit complex) lens can be ground to correct for this.

For presbiopia (old eyes), what happens is the crystalline lens in your eye gets stiff, so your eye can no longer adjust over the range of 4 diopter points, like it used to.  Instead of being able to focus from a 50 diopter to a 54 diopter, you can now only focus from a 50 diopter to a 53 or 52.5 diopter.  You can now no longer  focus as close as 10 inches, but are holding the newspaper at arm's length to read.  If you buy drugstore reading glasses of +1.5 diopter, these are additive to your eyes, so you can now regain effective 54 diopter eyes and focus on your reading.  However, while wearing these lenses, your relaxed vision, which was +
50 diopter, and which let you focus out to infinity, has now become a 51.5 diopter, and you can only focus out to about 10 feet while wearing reading glasses.

To see clearly while shooting, you need to take advantage of your eye's depth of field.  Depth of field (see the other technical notes) is a phenomena that while one object is in perfect focus, objects slightly closer and slightly further away will also appear to be in perfect focus.  The range of your depth of field is a function of the size of the opening in a lens, of the lenses focal length, and of the distance to the subject.

For a presbiopic shooter (including most people over 40), what you want to do is take advantage of the sight you have by:

1.  Using a small rear aperture in your sight to give you maximum depth of field.

2.  Using a corrective lens to get your eye's relaxed focus to fall at its hyperfocal distance, so the target is in focus, and your depth of field ranges as far back as possible.  If you adjust the corrective lens and the aperture size correctly, this depth of field can go all the way back to your front sight, so the sight post and the target appear in focus at the same time.