Eyeglass prescription

From Academic Kids

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.

Contents

Abbreviations

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  • O.D. is an abbreviation for oculus dexter, Latin for "right eye." (Some eyeglass prescriptions simply say "left" and "right" instead of "O.S." and "O.D.") Oculus means "eye." An eye doctor is sometimes called an "oculist" (although eye doctors themselves usually prefer to use either the term ophthalmogist or optometrist).
  • O.S. is an abbreviation for oculus sinister, Latin for "left eye."
  • D.V. and N.V. stand for "distant vision" and "near vision" and refer to the different corrections in the upper and lower portions of a bifocal lens. The "N.V." portion of a "single vision" lens prescription will be blank.
  • Spherical, Cylindrical, and Axis will be explained further below. Most eyeglass prescriptions will contain values here. The "spherical" and "cylindrical" columns contain lens strengths in diopters (see below); "axis" contains the direction of the cylinder axis in degrees.
  • Prism and Base are usually blank; they refer to prescription features that are used to treat muscular imbalance or other conditions that cause errors in eye orientation.

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.

Image:Specrx-letterscamblur.png
Image:Specrx-lettersastigblur.png
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Image:Specrx-lettersastigblur2.png


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Image:Specrx-letterseyeblur.png


Eyeglasses correct focus

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.

Lenses

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 they often think of lenses as magnifiers. And while eyeglasses may in fact have a small magnifying or reducing effect, that is an unintentional (and undesirable) side effect. Eyeglasses do not improve vision by magnifying images; rather, they improve vision by reducing blur. If eyeglasses worked by magnifying images, they would definitely reduce one's visual field.

Lens strength

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.

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Image:Specrx-1d2d.png

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.

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Image:Specrx-rglass1.jpg

Image:Specrx-rglass2.jpg Image:Specrx-rglass3.jpg Image:Specrx-rglass4.jpg

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.

Image:Specrx-5dm2d.png

A -3 lens stacked on top of a +3 lens looks almost like clear glass, because the combined strength is 0.

Image:Specrx-3dm3d.png

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.

Spherical lenses and spherical correction

Usually:

  • the "spherical" component is the main correction
  • the "cylindrical" component is "fine tuning."

Depending on the optical setup is, lenses can act as magnifiers, lenses can introduce blur, and lenses can correct blur.

Whatever the setup, spherical lenses act equally in all directions: they magnify, introduce blur, or correct 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.

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Specrx-sphermag1.png
Image:Specrx-sphermag1.png

Similarly, when a spherical lens puts an optical system out of focus and introduces blur, it blurs equally in all directions:

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Specrx-StarBlur.png
Image:Specrx-StarBlur.png

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.

Image:Specrx-letterscamblur.png

Amount of refractive error and degree of blur

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Image:snellen-myopia.png

The leftmost image above shows an eye chart as it might be seen by a person who needs no correction, or by a person who is wearing eyeglasses or contacts that properly correct any refractive errors he or she may have.

The images labelled 1D, 2D, and 3D give a very rough impression of the degree of blur that might be seen by someone who requires one, two, or three diopters of refractive error. For example, a nearsighted person who needs a -2.0 diopter corrective lens will see something like the 2D image when viewing an standard eye chart at the standard 20-foot distance without glasses.

A very rough rule of thumb is that there is a loss of about one line on an eye chart for each additional 0.25 to 0.5 diopters of refractive error.

The top letter on many eye charts represents 20/200 vision. Many people cannot read even this top letter without glasses. Such people sometimes wonder whether they could be legally blind. However, the definition of legal blindness is not based on vision without glasses. The U. S. Social Security administration, for example, states that "we consider you to be legally blind if your vision cannot be corrected to better than 20/200 in your better eye." In other words, what matters in evaluating legal blindness, and for many other purposes, is corrected acuity—which line of the chart can be read with proper lenses.

Cylindrical lenses and cylindrical correction

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.

Image:Specrx-cylmag1.png

Similarly, when a cylindrical lens puts an optical system out of focus and introduces blur, it blurs only in one direction.

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Specrx-StarBlurA.png
Image:Specrx-StarBlurA.png

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:

Image:Specrx-lettersastigblur.png

Compare it to the kind of blur that is equally blurred in all directions.

Image:Specrx-letterscamblur.png

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.

Axis

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.

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Specrx-lettersastigblur2.png
Image:Specrx-lettersastigblur2.png

Image:Specrx-lettersastigblur.png

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:

Image:Specrx-sphermag2.png

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Specrx-sphermag1.png
Image:Specrx-sphermag1.png

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.

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Specrx-cylmag2.png
Image:Specrx-cylmag2.png

Image:Specrx-cylmag1.png


The axis specification on a prescription gives the orientation of the axis of the cylindrical correction, and it can vary from 1 to 180 degrees:

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Axes_for_eye_glasses_cylindrical_lenses.jpg
Image:Axes for eye glasses cylindrical lenses.jpg

The total power of a cylindrical lens varies from zero along its main axis to its 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.

Distant vision and near vision


The DV portion of the prescription describes the corrections for distant vision. For most people under forty years of age, this is the only part of the prescription that is filled in. The NV or near-vision portion of the prescription is blank, because a separate correction for near vision is not needed.

The NV portion is used in prescriptions for bifocals.

In younger people, the lens of the eye is still flexible enough to accommodate over a wide range of distances. With age, the lens hardens and becomes less and less able to accommodate.

This is called "presbyopia;" the "presby-" root means "old" or "elder." (It is the same root as in the words "priest" and "presbyterian.")

The hardening of the lens is a continuous process, not something that suddenly happens in middle age. It is occurring all along. All that happens around middle age is that the process progresses to the point where it starts to interfere with reading.

When nursery school children want to examine something carefully, they just hold it very close to their eyes. They don't need magnifying glasses because they have such good near vision.

This chart (which is approximate) shows that a schoolchild has over ten diopters of accommodation, while a fifty-year-old has only two. This means that a schoolchild is able to focus on an object about 10 cm. (4") from the eye, a task for which an adult needs a magnifying glass with a rated power of about 3.5X.

Image:Specrx-accom.png

Variations in prescription writing

There is a surprising amount of variation in the way prescriptions are written; the layout and terminology used is not uniform.

When no correction is needed, the spherical power will sometimes be written as "0.00" and sometimes as "Plano" or "Pl" (because the lens, although not flat, is optically equivalent to a flat piece of glass).

When cylindrical correction is needed, the mathematics and optics of the way lenses combine mean that there are two different ways to write the same correction. One is called the plus-cylinder form and the other the minus-cylinder form. These two prescriptions are equivalent:

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.

See also

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