Dioptre
Encyclopedia
A dioptre, or diopter, is a unit of measurement of the optical power
Optical power
Optical power is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device. The dioptre is the most common unit of measurement of optical power...

of a lens
Lens (optics)
A lens is an optical device with perfect or approximate axial symmetry which transmits and refracts light, converging or diverging the beam. A simple lens consists of a single optical element...

or curved mirror
Mirror
A mirror is an object that reflects light or sound in a way that preserves much of its original quality prior to its contact with the mirror. Some mirrors also filter out some wavelengths, while preserving other wavelengths in the reflection...

, which is equal to the reciprocal
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the...

of the focal length
Focal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...

measured in metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

s (that is, 1/metres). It is thus a unit of reciprocal length
Reciprocal length
Reciprocal length or inverse length is a 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 , the reciprocal centimetre or inverse centimetre , and, in optics, the...

. For example, a 3-dioptre lens brings parallel rays
Ray (optics)
In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...

of light to focus at metre. The same unit is also sometimes used for other reciprocals of distance, particularly radii of curvature
Radius of curvature has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located in either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis...

and the vergence
Vergence (optics)
The vergence of a light bundle in optics is the reciprocal of the distance between the point of focus and a reference plane. It is measured in dioptres . Vergence can also be understood as a measure of the curvature of the optical wavefront...

of optical beams. The usage was proposed by French ophthalmologist Ferdinand Monoyer in 1872.

One benefit of quantifying a lens in terms of its optical power rather than its focal length is that when relatively thin lenses
Thin lens
[Image:Lens1.svg|thumb|A lens can be considered a thin lens if d [Image:Lens1.svg|thumb|A lens can be considered a thin lens if d [Image:Lens1.svg|thumb|A lens can be considered a thin lens if d...

are placed close together their powers approximately add. Thus a thin 2-dioptre lens placed close to a thin 0.5-dioptre lens yields almost the same focal length as a 2.5-dioptre lens would have.

Though the dioptre is based on the SI
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

-metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

it has not been included in the standard so that there is no international name or abbreviation for this unit of measurement—within the international system of units
International System of Units
The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...

this unit for optical power would need to be specified explicitly as the inverse metre (m−1). However most languages have borrowed the original name and some national standardization bodies like DIN
Deutsches Institut für Normung
is the German national organization for standardization and is that country's ISO member body. DIN is a Registered German Association headquartered in Berlin...

specify a unit name (dioptrie, dioptria, ..) and derived unit symbol "dpt".

## In optometry

The fact that optical powers are approximately additive enables an optometrist to prescribe corrective lens
Corrective lens
A corrective lens is a lens worn in front of the eye, mainly used to treat myopia, hyperopia, astigmatism, and presbyopia. Glasses or "spectacles" are worn on the face a short distance in front of the eye. Contact lenses are worn directly on the surface of the eye...

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
Eyeglass prescription
An eyeglass prescription is an order written by an eyewear prescriber, such as an optometrist or ophthalmologist, that specifies the value of all parameters the prescriber has deemed necessary to construct and/or dispense corrective lenses appropriate for a patient.If an examination indicates that...

for reading. Thus an optometrist, having determined that a myopic
Myopia
Myopia , "shortsightedness" ) is a refractive defect of the eye in which collimated light produces image focus in front of the retina under conditions of accommodation. In simpler terms, myopia is a condition of the eye where the light that comes in does not directly focus on the retina but in...

(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
Accommodation (eye)
Accommodation is the process by which the vertebrate eye changes optical power to maintain a clear image on an object as its distance changes....

(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
Cornea
The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Together with the lens, the cornea refracts light, with the cornea accounting for approximately two-thirds of the eye's total optical power. In humans, the refractive power of the cornea is...

accounts for approximately two-thirds of this refractive power and the crystalline lens
Lens (anatomy)
The 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. The lens, by changing shape, functions to change the focal distance of the eye so that it can focus on objects at various distances, thus allowing a...

(in conjunction with the aqueous and vitreous humors) contributes the remaining third. In focusing, the ciliary muscle
Ciliary muscle
The ciliary muscle is a ring of striated smooth muscle in the eye's middle layer that controls accommodation for viewing objects at varying distances and regulates the flow of aqueous humour into Schlemm's canal. It changes the shape of the lens within the eye not the size of the pupil which is...

contracts to reduce the tension
Tension (mechanics)
In physics, tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object. It is the opposite of compression. As tension is the magnitude of a force, it is measured in newtons and is always measured parallel to the string on which it applies...

or stress
Stress (physics)
In continuum mechanics, stress is a measure of the internal forces acting within a deformable body. Quantitatively, it is a measure of the average force per unit area of a surface within the body on which internal forces act. These internal forces are a reaction to external forces applied on the body...

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. As humans age, the amplitude of accommodation
Amplitude of accommodation
Amplitude of accommodation is a measurement of the eye’s ability to focus clearly on objects at near distances . This eye focusing range for a child is usually about 5–7.5 cm . For a young adult, it is 10–15 cm . The focus range for a 45-year-old adult is about 50 cm...

reduces from approximately 15 to 20 dioptres in the very young, to about 10 dioptres at age 25, to around 1 dioptre at 50 and over.

Convex lenses have positive dioptric value and are generally used to correct hyperopia
Hyperopia
Hyperopia, also known as farsightedness, longsightedness or hypermetropia, is a defect of vision caused by an imperfection in the eye , causing difficulty focusing on near objects, and in extreme cases causing a sufferer to be unable to focus on objects at any distance...

(farsightedness) or to allow people with presbyopia
Presbyopia
Presbyopia is a condition where the eye exhibits a progressively diminished ability to focus on near objects with age. Presbyopia’s exact mechanisms are not known with certainty; the research evidence most strongly supports a loss of elasticity of the crystalline lens, although changes in the...

(the limited accommodation of advancing age) to read at close range. Concave lenses have negative dioptric value and generally correct myopia
Myopia
Myopia , "shortsightedness" ) is a refractive defect of the eye in which collimated light produces image focus in front of the retina under conditions of accommodation. In simpler terms, myopia is a condition of the eye where the light that comes in does not directly focus on the retina but in...

(nearsightedness). Typical glasses for mild myopia will have a power of −1.00 to −3.00 dioptres, while over the counter
Over-the-counter drug
Over-the-counter drugs are medicines that may be sold directly to a consumer without a prescription from a healthcare professional, as compared to prescription drugs, which may be sold only to consumers possessing a valid prescription...

reading glasses will be rated at +1.00 to +3.00 dioptres. Optometrists usually measure refractive error
Refractive error
A refractive error, or refraction error, is an error in the focusing of light by the eye and a frequent reason for reduced visual acuity.-Classification:...

using lenses graded in steps of 0.25 dioptres.

## Curvature

The dioptre can also be used as a measurement of curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

equal to the reciprocal of the radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...

measured in metres. For example, a circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....

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 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 will give approximately the right result, as long as the thickness of the lens is much less than the radius of curvature
Radius of curvature has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located in either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis...

of one of the surfaces. For a mirror the optical power is φ = 2C.

## Relation to magnifying power

The magnifying power of a simple magnifier is related to its optical power. This is covered in detail in the articles on magnification
Magnification
Magnification is the process of enlarging something only in appearance, not in physical size. This enlargement is quantified by a calculated number also called "magnification"...

and magnifying glasses.

• Astigmatism
Astigmatism
An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances...

• Lens clock
Lens clock
A lens clock is a mechanical dial indicator that is used to measure 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, assuming the lens is made of a material with a...

• Lensmeter
Lensmeter
A lensmeter or lensometer, also known as a focimeter, is an ophthalmic instrument. It is mainly used by optometrists and opticians to verify the correct prescription in a pair of eyeglasses, to properly orient and mark uncut lenses, and to confirm the correct mounting of lenses in spectacle frames...

• Optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

• Optometry
Optometry
Optometry is a health care profession concerned with eyes and related structures, as well as vision, visual systems, and vision information processing in humans. Optometrists, or Doctors of Optometry, are state licensed medical professionals trained to prescribe and fit lenses to improve vision,...

• Prism correction#Prism dioptres
• Vertometer
Vertometer
Vertometer was the trade name of an instrument made by Bausch & Lomb and later by Reichert.Lensometer was the trade name of the nearly similar instrument made by American Optical.Neither the Vertometer or the Lensometer is now being made....