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Here are some examples of the kind of blurred images that can result from refractive errors; we will be discussing them in more detail below. For now, note that not all kinds of blur are the same.
The intended effect of eyeglasses is focus correction. In addition, eyeglasses have small unwanted effects including magnification or reduction, distortion, color fringes, altered depth perception, etc.
The ideal way to correct focus would be to alter the shape of the lens of the eye itself. Next best would be to introduce a corrective lens placed as close as possible to the lens of the eye. Contact lenses, and new surgical techniques such as radial keratotomy which adjust the shape of the cornea of the eye, come close to this ideal.
Depending on the optical setup, lenses can act as magnifiers, lenses can introduce blur, and lenses can correct blur. Many people first encounter lenses in the form of magnifying glasses, and think of lenses as magnifiers. Eyeglasses may, in fact, have a small magnifying or reducing effect, but that is an unintentional (and undesirable) side effect. Eyeglasses do not improve vision by magnifying images; they improve vision by reducing blur.
The values given in the "sphere" and "cylinder" columns of an eyeglass prescription are lens strengths in diopters, abbreviated D. The higher the number of diopters, the stronger the lens.
A +10 diopter lens would make a good magnifying glass. Eyeglass lenses are usually much weaker, because eyeglasses do not work by magnifying; they work by correcting focus.
Stacking lenses combines their strength. A +1 diopter lens combined with a +2 diopter lens forms a +3 diopter system.
Lenses come in positive (plus) and negative (minus) strengths. You can usually tell whether a lens is positive or negative by looking through it. Positive lenses tend to enlarge things when you look through them; negative lenses tend to diminish the size of things when you look through them. Because eyeglass lenses are usually weak, they don't enlarge or diminish very much.
Positive eyeglass lenses can concentrate sunlight, like a burning glass. Usually, however, they are much too weak to set fire to anything.
This series of pictures show the shadow cast by a pair of 1 diopter drugstore "reading glasses" outdoors in sunlight as we hold it farther and farther away from a wall. As the distance from the wall increases, the shadow of the frame seems to thicken and the bright area in the center gets smaller and brighter. It slowly changes from being "eyeglass-shaped" to circular.
Negative lenses spread sunlight instead of concentrating it.
A negative lens combined with a positive lens removes some of its strength. A -2 lens combined with a +5 lens forms a +3 diopter system.
A -3 lens stacked on top of a +3 lens looks almost like clear glass, because the combined strength is 0.
In science textbooks, positive lenses are usually diagrammed as convex on both sides; negative lenses are usually diagrammed as concave on both sizes. In a real optical system, you usually get the best optical quality when most rays of light are roughly normal to the lens surface. In the case of an eyeglass lens, this means that the lens should be roughly shaped like a cup with the hollow side toward the eye. So most eyeglass lenses are meniscus in shape.