![optical_power_of_a_lens](https://upload.wikimedia.org/wikipedia/commons/7/7d/Optical_power_of_a_lens.svg)
A dioptre (
British spelling
Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English orthography, the two most notable variations being British and American ...
) or diopter (
American spelling
Despite the various English dialects spoken from country to country and within different regions of the same country, there are only slight regional variations in English orthography, the two most notable variations being British and American ...
) is a
unit of measurement
A unit of measurement is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can ...
with
dimension
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
of
reciprocal length Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre (symbol: m− ...
, equivalent to one
reciprocal metre Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre (symbol: m− ...
, 1 dioptre = 1 m
−1. It is normally used to express the
optical power
In optics, optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens (optics), lens, mirror, or other optical system converges or diverges light. It is equal to the Mu ...
of a
lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
or curved
mirror
A mirror or looking glass is an object that Reflection (physics), reflects an image. Light that bounces off a mirror will show an image of whatever is in front of it, when focused through the lens of the eye or a camera. Mirrors reverse the ...
, which is a
physical quantity
A physical quantity is a physical property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a ''value'', which is the algebraic multiplication of a ' Numerical value ' and a ' Unit '. For examp ...
equal to the
reciprocal
Reciprocal may refer to:
In mathematics
* Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal''
* Reciprocal polynomial, a polynomial obtained from another pol ...
of the
focal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foca ...
, expressed in
metre
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
s. For example, a 3-dioptre lens brings parallel
rays
Ray may refer to:
Fish
* Ray (fish), any cartilaginous fish of the superorder Batoidea
* Ray (fish fin anatomy), a bony or horny spine on a fin
Science and mathematics
* Ray (geometry), half of a line proceeding from an initial point
* Ray (gra ...
of light to focus at metre. A flat window has an optical power of zero dioptres, as it does not cause light to converge or diverge. Dioptres are also sometimes used for other reciprocals of distance, particularly
radii of curvature and the
vergence
A vergence is the simultaneous movement of both eyes in opposite directions to obtain or maintain single binocular vision.
When a creature with binocular vision looks at an object, the eyes must rotate around a vertical axis so that the proje ...
of optical beams.
The main benefit of using optical power rather than focal length is that the
thin lens formula
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
has the object distance, image distance, and focal length all as reciprocals. Additionally, when
relatively thin lenses are placed close together their powers approximately add. Thus, a thin 2.0-dioptre lens placed close to a thin 0.5-dioptre lens yields almost the same focal length as a single 2.5-dioptre lens.
Though the dioptre is based on the
SI-
metric system
The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...
, it has not been included in the standard, so that there is no international name or symbol for this unit of measurement—within the
international system of units
The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
, this unit for optical power would need to be specified explicitly as the
inverse metre Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre (symbol: m&min ...
(m
−1). However most languages have borrowed the original name and some national standardization bodies like
DIN
DIN or Din or din may refer to:
People and language
* Din (name), people with the name
* Dīn, an Arabic word with three general senses: judgment, custom, and religion from which the name originates
* Dinka language (ISO 639 code: din), spoken by ...
specify a unit name (dioptrie, dioptria, etc.) and unit symbol dpt. In
vision care
Ophthalmology ( ) is a surgical subspecialty within medicine that deals with the diagnosis and treatment of eye disorders.
An ophthalmologist is a physician who undergoes subspecialty training in medical and surgical eye care. Following a medic ...
the symbol D is frequently used.
The idea of numbering lenses based on the reciprocal of their focal length in metres was first suggested by Albrecht Nagel in 1866. The term ''dioptre'' was proposed by French
ophthalmologist
Ophthalmology ( ) is a surgery, surgical subspecialty within medicine that deals with the diagnosis and treatment of eye disorders.
An ophthalmologist is a physician who undergoes subspecialty training in medical and surgical eye care. Followin ...
Ferdinand Monoyer
Ferdinand Monoyer (9 May 1836 – 11 July 1912) was a French ophthalmologist, known for introducing the dioptre in 1872.
He invented the Monoyer chart, used to test visual acuity. He inserted his name in the random letters of the chart. ...
in 1872, based on earlier use of the term ''
dioptrice
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, German mathematician, mathematician, astrologer, Natural philosophy, natural philosopher and writer on music. He is a key figure in the 17th-century Scienti ...
'' by
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
.
In vision correction
The fact that optical powers are approximately
additive
Additive may refer to:
Mathematics
* Additive function, a function in number theory
* Additive map, a function that preserves the addition operation
* Additive set-functionn see Sigma additivity
* Additive category, a preadditive category with f ...
enables an
eye care professional
An eye care professional (ECP) is an individual who provides a service related to the eyes or vision. It is any healthcare worker involved in eye care, from one with a small amount of post-secondary training to practitioners with a doctoral level ...
to prescribe
corrective lens
A corrective lens is a lens (i.e. a transmissive optical device) that is typically worn in front of the eye to improve daily vision. The most common use is to treat refractive errors: myopia, hypermetropia, astigmatism, and presbyopia. Glass ...
es as a simple correction to the eye's optical power, rather than doing a detailed analysis of the entire optical system (the eye and the lens). Optical power can also be used to adjust a basic
prescription for reading. Thus an eye care professional, having determined that a
myopic
Near-sightedness, also known as myopia and short-sightedness, is an eye disease where light focuses in front of, instead of on, the retina. As a result, distant objects appear blurry while close objects appear normal. Other symptoms may include ...
(nearsighted) person requires a basic correction of, say, −2 dioptres to restore normal distance vision, might then make a further prescription of 'add 1' for reading, to make up for lack of
accommodation (ability to alter focus). This is the same as saying that −1 dioptre lenses are prescribed for reading.
In humans, the total optical power of the relaxed eye is approximately 60 dioptres.
The
cornea
The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Along with the anterior chamber and lens, the cornea refracts light, accounting for approximately two-thirds of the eye's total optical power ...
accounts for approximately two-thirds of this refractive power (about 40 dioptres) and the
crystalline lens
The lens, or crystalline lens, is a transparent biconvex structure in the eye that, along with the cornea, helps to refract light to be focused on the retina. By changing shape, it functions to change the focal length of the eye so that it can ...
contributes the remaining one-third (about 20 dioptres).
[ In focusing, the ]ciliary muscle
The ciliary muscle is an intrinsic muscle of the eye formed as a ring of smooth muscleSchachar, Ronald A. (2012). "Anatomy and Physiology." (Chapter 4) . in the eye's middle layer, uvea ( vascular layer). It controls accommodation for viewing ...
contracts to reduce the tension
Tension may refer to:
Science
* Psychological stress
* Tension (physics), a force related to the stretching of an object (the opposite of compression)
* Tension (geology), a stress which stretches rocks in two opposite directions
* Voltage or el ...
or stress
Stress may refer to:
Science and medicine
* Stress (biology), an organism's response to a stressor such as an environmental condition
* Stress (linguistics), relative emphasis or prominence given to a syllable in a word, or to a word in a phrase ...
transferred to the lens by the suspensory ligaments. This results in increased convexity of the lens which in turn increases the optical power of the eye. The amplitude of accommodation
The amplitude of accommodation is the maximum potential increase in optical power that an eye can achieve in adjusting its focus. It refers to a certain range of object distances for which the retinal image is as sharply focussed as possible.
Amp ...
is about 11 to 16 dioptres at age 15, decreasing to about 10 dioptres at age 25, and to around 1 dioptre above age 60.
Convex lens
A lens is a transmissive optics, optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a #Compound lenses, compound lens consists of several simp ...
es have positive dioptric value and are generally used to correct hyperopia
Far-sightedness, also known as long-sightedness, hypermetropia, or hyperopia, is a condition of the eye where distant objects are seen clearly but near objects appear blurred. This blurred effect is due to incoming light being focused behind, i ...
(farsightedness) or to allow people with presbyopia
Presbyopia is physiological insufficiency of accommodation associated with the aging of the eye that results in progressively worsening ability to focus clearly on close objects. Also known as age-related farsightedness (or age-related long si ...
(the limited accommodation of advancing age) to read at close range. Concave lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
es have negative dioptric value and generally correct myopia
Near-sightedness, also known as myopia and short-sightedness, is an eye disease where light focuses in front of, instead of on, the retina. As a result, distant objects appear blurry while close objects appear normal. Other symptoms may include ...
(nearsightedness). Typical glasses for mild myopia have a power of −0.50 to −3.00 dioptres, while over the counter
Over-the-counter (OTC) drugs are medicines sold directly to a consumer without a requirement for a prescription from a healthcare professional, as opposed to prescription drugs, which may be supplied only to consumers possessing a valid prescr ...
reading glasses
A corrective lens is a lens (i.e. a transmissive optical device) that is typically worn in front of the eye to improve daily vision. The most common use is to treat refractive errors: myopia, hypermetropia, astigmatism, and presbyopia. Glasse ...
are rated at +1.00 to +4.00 dioptres. Optometrist
Optometry is a specialized health care profession that involves examining the eyes and related structures for defects or abnormalities. Optometrists are health care professionals who typically provide comprehensive primary eye care.
In the Uni ...
s usually measure refractive error
Refractive error, also known as refraction error, is a problem with focus (optics), focusing light accurately on the retina due to the shape of the human eye, eye and or cornea. The most common types of refractive error are myopia, near-sightedne ...
using lenses graded in steps of 0.25 dioptres.
Curvature
The dioptre can also be used as a measurement of curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canonic ...
equal to the reciprocal of the radius
In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...
measured in metres. For example, a circle
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...
with a radius of 1/2 metre has a curvature of 2 dioptres. If the curvature of a surface of a lens is ''C'' and the index of refraction
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
is ''n'', the optical power is φ = (''n'' − 1)''C''. If both surfaces of the lens are curved, consider their curvatures as positive toward the lens and add them. This gives approximately the right result, as long as the thickness of the lens is much less than the radius of curvature
In differential geometry, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius o ...
of one of the surfaces. For a mirror the optical power is φ = 2''C''.
Relation to magnifying power
The ''magnifying power'' of a simple magnifying glass
A magnifying glass is a convex lens that is used to produce a magnified image of an object. The lens is usually mounted in a frame with a handle. A magnifying glass can be used to focus light, such as to concentrate the sun's radiation to crea ...
is related to its optical power by
:.
This is approximately the magnification observed when a person with normal vision holds the magnifying glass close to his or her eye.
See also
*Astigmatism
Astigmatism is a type of refractive error due to rotational asymmetry in the eye's refractive power. This results in distorted or blurred vision at any distance. Other symptoms can include eyestrain, headaches, and trouble driving at nig ...
* Dioptrics
Dioptrics is the branch of optics dealing with refraction, similarly the branch dealing with mirrors is known as catoptrics. Dioptrics is the study of the refraction of light, especially by lenses. Telescopes that create their image with an object ...
*Lens clock
A lens clock is a mechanical dial indicator that is used to measure the dioptric power of a lens. It is a specialized version of a spherometer. A lens clock measures the curvature of a surface, but gives the result as an optical power in diopters ...
*Lensmeter
A lensmeter or lensometer (sometimes even known as focimeter or vertometer), is an ophthalmic instrument. It is mainly used by optometrists and opticians to measure the back or front vertex power of a spectacle lens and verify the correct presc ...
*Optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
*Optometry
Optometry is a specialized health care profession that involves examining the eyes and related structures for defects or abnormalities. Optometrists are health care professionals who typically provide comprehensive primary eye care.
In the Uni ...
* Prism correction#Prism dioptres
*Vertometer
A lensmeter or lensometer (sometimes even known as focimeter or vertometer), is an ophthalmic instrument. It is mainly used by optometrists and opticians to measure the back or front vertex power of a spectacle lens and verify the correct presc ...
References
*
*
{{refend
Optics
Units of measurement
Non-SI metric units