A large part of the optics of vision will concern itself with the corrections we make for imperfections in our visual system.To begin, let's look at the important parts of that system. Below is a diagram of the eye, identifying key parts needed to form a clear image onto the retina.
Myopia consists of a defect in the lens, the shape of the eyeball, or in the density of the optical components of the eye. In any case, a myopic eye can focus near objects successfully onto the retina but can't focus distant objects clearly at all. The end result is a difficult time accomodating to the various demands placed on a person with myopia or near sightedness.
Let's take a brief look at the difference between light rays which come from a close object and a distant object. We will then apply this difference in helping to find a correction for myopia.
Objects close to us present us with light rays that are diverging rapidly. To see something close to us, we have to focus these rapidly diverging rays.
Objects that are distant present light rays that have become more parallel - the angle between them has decreased to a great extent. In fact, if the distance is great compared to the size of our eyeball, the light rays for all intents are parallel to one another.
To summarize: Near objects send out diverging light rays. Distant objects send us parallel light rays. Our lens then works on those rays to focus them onto the retina where they will trigger the rods and cones which give us vision.
For diverging rays, the lens must be more curved, while for parallel rays the lens must be less curved. A set of muscles around the lens can contract to make it more rounded, while they relax to allow the lens to become less rounded. From this we see that the muscles must work in order to read while they relax to enjoy the scenery.
Normal vision - lens can curve to focus on near objects and also relax to focus on distant objects.
Myopic eye focuses near object clearly, but "over-focuses" the parallel rays from a distant object. The retinal image is thus very blurry. So the problem becomes how to make the parallel rays look more like the diverging rays the lens can handle well.
Here the correction for myopia has beendone using a concave lens. The parallel rays are diverged and the lens can focus them nicely.
LITERARY NOTE:In Lord of the Flies, Piggy's glasses are used to focus the sunlight onto a pile of wood to start the signal fire. Unfortunately, Piggy was terribly near-sighted, or myopic. His glasses, therefore, must have been concave! Thus, the sunlight must have been diverged by the lens!
We see the interesting intersection of science and literature....Lord of the Flies makes good literature, but contains a particularly bad example of physics!
Far-sighted people can focus parallel and nearly parallel light rays successfully. However, they don't do well with near object which present them with diverging light rays. Their lens could be considered too thin, or it simply won't respond to efforts to make it rounder.
To correct for hyperopia, use a converging lens. The lens will make the formerly diverging light more parallel and thus the eye's lens can focus it onto the retina in a sharp image.
So the eyeglasses for near-sighted people are concave lenses which make parallel rays more diverging. Concave lenses are reducing lenses and make the eyes look smaller than they really are.
Glasses for far-sighted people are convex lenses which make diverging light rays less divergent and more parallel. Convex lenses are magnifying lenses and make the eyes look larger than they really are.