Eyeglass prescription
This article describes the optics of an ordinary eyeglass prescription, which is used to correct small refractive errors in the optical system of the eye. The effect of these errors is to create a blurred image. By correcting these errors, the eyeglass lens removes the blur.
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.
Usually:
Whatever the setup, spherical lenses act equally in all directions; it magnifies, blur or corrects blur the same amount in every direction.
An ordinary magnifying glass is a kind of spherical lens. When a spherical lens acts as a magnifier, it magnifies equally in all directions. Here, note that the magnified letters are magnified both in height and in width.
Similarly, when a spherical lens puts an optical system out of focus and introduces blur, it blurs equally in all directions:
Here is how this kind of blur looks when viewing an eye chart. This kind of blur involves no astigmatism at all; it is equally blurred in all directions.
Some kinds of magnifying glasses, made specifically for reading wide columns of print, are cylindrical lenses. When a cylindrical lens acts as a magnifier, it magnifies only in one direction. For example, the magnifier shown magnifies letters only in height, not in width.
Similarly, when a cylindrical lens puts an optical system out of focus and introduces blur, it blurs only in one direction.
This is the kind of blur that results from uncorrected astigmatism. The letters are smeared out directionally, as if an artist had rubbed his or her thumb across a charcoal drawing.A cylindrical lens of the right strength can correct this kind of blur. When viewing an eye chart, this is how this kind of blur might appear:
Compare it to the kind of blur that is equally blurred in all directions.
When an eye doctor measures your eye—a procedure known as refraction—usually he or she begins by finding the best spherical correction. If there is astigmatism, the next step is to remove it by adding the right amount of cylindrical correction.
Spherical lenses just have a strength, such as +1.0D, or -2.5D.
Astigmatism, however, causes a directional blur. Here are two examples of the kind of blur you get from astigmatism. The letters are smeared out directionally, as if an artist had rubbed his or her thumb across a charcoal drawing.
A cylindrical lens of the right strength can correct this kind of blur. The second example is a little bit more blurred, and needs a stronger cylindrical lens.
But notice that in addition to being smeared more, the second example is smeared out in a different direction.
A spherical lens is the same in all directions; you can turn it around, and it doesn't change the way it magnifies, or the way it blurs:
A cylindrical lens has both a strength and an axis. Turning it around so that the axis points in different directions changes the way it magnifies, and the way it blurs.
The total power of a cylindrical lens varies from zero along it's main axis to it's maximal value along the axis 90 degrees away. The total power of a lens with a spherical and cylindrical correction changes accordingly: along the axis specified on the prescription it is equal to the value listed under "spherical", and it reaches the sum of "spherical" and "cylindrical" along the axis perpendicular to the one listed on the prescription.Abbreviations
Blur
Eyeglasses correct focus
Lenses
Lens strength
Spherical lenses and spherical correction
Depending on the optical setup is, lenses can act as magnifiers, lenses can introduce blur, and lenses can correct blur.
Cylindrical lenses and cylindrical correction
Axis
| Spherical | Cylindrical | Axis |
| 2.00 | 1.00 | 90 |
| Spherical | Cylindrical | Axis |
| 3.00 | -1.00 | 180 |
Both of them specify a power of 2.00 diopters at the 180 degree axis and 3.00 diopters at the 90 degree axis.
The first one specifies a 2.00 spherical component, which, by itself, would give a power of 2.00 diopters along both the 180 and 90 degree axis, and adds a 1.00 cylindrical component at 90 degrees. The result is 2.00 diopters at 180 degrees and 2.00 + 1.00 = 3.00 diopters at 90 degrees.
The second specifies a 3.00 spherical component, which by itself would give a power of 3.00 diopters along both the 180 and 90 degree axis, and subtracts a 1.00 cylindrical component at 180 degrees. The result is 3.00 - 1.00 = 2.00 diopters at 180 degrees and 3.00 diopters at 90 degrees.