
A dioptre (
British spelling) or diopter (
American spelling) is a
unit of measurement
A unit of measurement is a definite 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 be expressed as a mult ...
with
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coor ...
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&mi ...
, equivalent to one
reciprocal metre, 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, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of th ...
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 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 p ...
s. For example, a 3-dioptre lens brings parallel
rays 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 projec ...
of optical beams.
The main benefit of using optical power rather than focal length is that the
thin lens formula 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 decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the Intern ...
, 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, 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 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 in 1872, based on earlier use of the term ''
dioptrice'' by
Johannes Kepler.
In vision correction
The fact that optical powers are approximately
additive enables an
eye care professional 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. ...
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 ...
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 ca ...
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 ob ...
contracts to reduce the tension or stress 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 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 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 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, in ...
(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 sig ...
(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 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 Un ...
s usually measure refractive error
Refractive error, also known as refraction error, is a problem with focusing light accurately on the retina due to the shape of the eye and or cornea. The most common types of refractive error are near-sightedness, far-sightedness, astigmatism ...
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 can ...
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 radiu ...
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 creat ...
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 ni ...
* 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 obje ...
*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 diop ...
*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 pres ...
*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, ultra ...
*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 Un ...
* Prism correction#Prism dioptres
* Vertometer
References
*
*
{{refend
Optics
Units of measurement
Non-SI metric units