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
In the field of optics, transparency (also called pellucidity or diaphaneity) is the physical property of allowing light to pass through the material without appreciable light scattering by particles, scattering of light. On a macroscopic scale ...
, while a
compound 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''), ...
consists of several simple lenses (''elements''), usually arranged along a common
axis. Lenses are made from materials such as
glass or
plastic, and are
ground
Ground may refer to:
Geology
* Land, the surface of the Earth not covered by water
* Soil, a mixture of clay, sand and organic matter present on the surface of the Earth
Electricity
* Ground (electricity), the reference point in an electrical c ...
and
polished or
molded
Molding (American English) or moulding (British and Commonwealth English; see spelling differences) is the process of manufacturing by shaping liquid or pliable raw material using a rigid frame called a mold or matrix. This itself may have ...
to a desired shape. A lens can focus light to form an
image
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
, unlike a
prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called lenses, such as
microwave lenses,
electron lenses,
acoustic lenses, or
explosive lenses.
Lenses are used in various imaging devices like
telescopes,
binoculars
Binoculars or field glasses are two refracting telescopes mounted side-by-side and aligned to point in the same direction, allowing the viewer to use both eyes (binocular vision) when viewing distant objects. Most binoculars are sized to be held ...
and
cameras. They are also used as visual aids in
glasses to correct defects of vision such as
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 ...
and
hypermetropia.
History
The word ''
lens'' comes from ''
lēns'', the Latin name of the
lentil (a seed of a lentil plant), because a double-convex lens is lentil-shaped. The lentil also gives its name to a
geometric figure
A shape or figure is a graphical representation of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture, or material type.
A plane shape or plane figure is constrained to lie ...
.
Some scholars argue that the archeological evidence indicates that there was widespread use of lenses in antiquity, spanning several millennia. The so-called
Nimrud lens
The Nimrud lens, also called Layard lens, is an 8th-century BC piece of rock crystal which was unearthed in 1850 by Austen Henry Layard at the Assyrian palace of Nimrud in modern-day Iraq. It may have been used as a magnifying glass or as a burnin ...
is a rock crystal artifact dated to the 7th century BCE which may or may not have been used as a magnifying glass, or a burning glass.
Others have suggested that certain
Egyptian hieroglyphs depict "simple glass meniscal lenses".
The oldest certain reference to the use of lenses is from
Aristophanes' play ''
The Clouds'' (424 BCE) mentioning a burning-glass.
Pliny the Elder (1st century) confirms that burning-glasses were known in the Roman period.
Pliny also has the earliest known reference to the use of a
corrective lens when he mentions that
Nero was said to watch the
gladiator
A gladiator ( la, gladiator, "swordsman", from , "sword") was an armed combatant who entertained audiences in the Roman Republic and Roman Empire in violent confrontations with other gladiators, wild animals, and condemned criminals. Some gla ...
ial games using an
emerald
Emerald is a gemstone and a variety of the mineral beryl (Be3Al2(SiO3)6) colored green by trace amounts of chromium or sometimes vanadium.Hurlbut, Cornelius S. Jr. and Kammerling, Robert C. (1991) ''Gemology'', John Wiley & Sons, New York, p ...
(presumably
concave to correct for
nearsightedness, though the reference is vague). Both Pliny and
Seneca the Younger (3 BC–65 AD) described the magnifying effect of a glass globe filled with water.
Ptolemy (2nd century) wrote a book on ''
Optics'', which however survives only in the Latin translation of an incomplete and very poor Arabic translation.
The book was, however, received by medieval scholars in the Islamic world, and commented upon by
Ibn Sahl (10th century), who was in turn improved upon by
Alhazen
Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the prin ...
(''
Book of Optics
The ''Book of Optics'' ( ar, كتاب المناظر, Kitāb al-Manāẓir; la, De Aspectibus or ''Perspectiva''; it, Deli Aspecti) is a seven-volume treatise on optics and other fields of study composed by the medieval Arab scholar Ibn al- ...
'', 11th century). The Arabic translation of Ptolemy's ''Optics'' became available in Latin translation in the 12th century (
Eugenius of Palermo 1154). Between the 11th and 13th century "
reading stones" were invented. These were primitive plano-convex lenses initially made by cutting a glass sphere in half. The medieval (11th or 12th century) rock crystal
Visby lens
One of the Visby lenses in a silver setting
The Visby lenses are a collection of lens-shaped manufactured objects made of rock crystal (quartz) found in several Viking graves on the island of Gotland, Sweden, and dating from the 11th or 12th cen ...
es may or may not have been intended for use as burning glasses.
Spectacles were invented as an improvement of the "reading stones" of the high medieval period in Northern Italy in the second half of the 13th century. This was the start of the optical industry of grinding and polishing lenses for spectacles, first in Venice and Florence in the late 13th century, and later in the spectacle-making centres in both the
Netherlands and
Germany.
Spectacle makers created improved types of lenses for the correction of vision based more on empirical knowledge gained from observing the effects of the lenses (probably without the knowledge of the rudimentary optical theory of the day). The practical development and experimentation with lenses led to the invention of the compound
optical microscope around 1595, and the
refracting telescope in 1608, both of which appeared in the spectacle-making centres in the
Netherlands.
With the invention of the telescope and microscope there was a great deal of experimentation with lens shapes in the 17th and early 18th centuries by those trying to correct chromatic errors seen in lenses. Opticians tried to construct lenses of varying forms of curvature, wrongly assuming errors arose from defects in the spherical figure of their surfaces. Optical theory on
refraction and experimentation was showing no single-element lens could bring all colours to a focus. This led to the invention of the compound
achromatic lens by
Chester Moore Hall
Chester Moore Hall (9 December 1703, Leigh, Essex, England – 17 March 1771, Sutton) was a British lawyer and inventor who produced the first achromatic lenses in 1729 or 1733 (accounts differ).
He used the achromatic lens to build the first ach ...
in
England in 1733, an invention also claimed by fellow Englishman
John Dollond in a 1758 patent.
Construction of simple lenses
Most lenses are ''spherical lenses'': their two surfaces are parts of the surfaces of spheres. Each surface can be
''convex'' (bulging outwards from the lens),
''concave'' (depressed into the lens), or ''planar'' (flat). The line joining the centres of the spheres making up the lens surfaces is called the ''axis'' of the lens. Typically the lens axis passes through the physical centre of the lens, because of the way they are manufactured. Lenses may be cut or ground after manufacturing to give them a different shape or size. The lens axis may then not pass through the physical centre of the lens.
Toric or sphero-cylindrical lenses have surfaces with two different radii of curvature in two orthogonal planes. They have a different
focal power in different meridians. This forms an
astigmatic lens. An example is eyeglass lenses that are used to correct
astigmatism in someone's eye.
Types of simple lenses
Lenses are classified by the curvature of the two optical surfaces. A lens is ''biconvex'' (or ''double convex'', or just ''convex'') if both surfaces are
convex. If both surfaces have the same radius of curvature, the lens is ''equiconvex''. A lens with two
concave surfaces is ''biconcave'' (or just ''concave''). If one of the surfaces is flat, the lens is ''plano-convex'' or ''plano-concave'' depending on the curvature of the other surface. A lens with one convex and one concave side is ''convex-concave'' or ''meniscus''. It is this type of lens that is most commonly used in
corrective lenses.
If the lens is biconvex or plano-convex, a
collimated beam of light passing through the lens converges to a spot (a ''focus'') behind the lens. In this case, the lens is called a ''positive'' or ''converging'' lens. For a
thin lens in air, the distance from the lens to the spot is 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 ...
of the lens, which is commonly represented by ''f'' in diagrams and equations. An
extended hemispherical lens
The extended hemispherical lens is a commonly used lens for millimeter-wave electromagnetic radiation. Such lenses are typically fabricated from dielectric materials such as Teflon or silicon. The geometry consists of a hemisphere of radius on a ...
is a special type of plano-convex lens, in which the lens's curved surface is a full hemisphere and the lens is much thicker than the radius of curvature.
If the lens is biconcave or plano-concave, a collimated beam of light passing through the lens is diverged (spread); the lens is thus called a ''negative'' or ''diverging'' lens. The beam, after passing through the lens, appears to emanate from a particular point on the axis in front of the lens. For a thin lens in air, the distance from this point to the lens is the focal length, though it is negative with respect to the focal length of a converging lens.
Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of the two surfaces. A ''negative meniscus'' lens has a steeper concave surface and is thinner at the centre than at the periphery. Conversely, a ''positive meniscus'' lens has a steeper convex surface and is thicker at the centre than at the periphery. An ideal
thin lens with two surfaces of equal curvature would have zero
optical power, meaning that it would neither converge nor diverge light. All real lenses have nonzero thickness, however, which makes a real lens with identical curved surfaces slightly positive. To obtain exactly zero optical power, a meniscus lens must have slightly unequal curvatures to account for the effect of the lens' thickness.
Lensmaker's equation
The focal length of a lens ''in air'' can be calculated from the lensmaker's equation:
:
where
:
is the focal length of the lens,
:
is the
refractive index of the lens material,
:
is the
radius of curvature (with sign, see below) of the lens surface closer to the light source,
:
is the radius of curvature of the lens surface farther from the light source, and
:
is the thickness of the lens (the distance along the lens axis between the two
surface vertices).
The focal length ''f'' is positive for converging lenses, and negative for diverging lenses. The
reciprocal of the focal length, 1/''f'', is the
optical power of the lens. If the focal length is in metres, this gives the optical power in
dioptre
A dioptre (British spelling) or diopter (American spelling) is a unit of measurement with dimension of reciprocal length, equivalent to one reciprocal metre, 1 dioptre = 1 m−1. It is normally used to express the optical power of a lens or curv ...
s (inverse metres).
Lenses have the same focal length when light travels from the back to the front as when light goes from the front to the back. Other properties of the lens, such as the
aberrations are not the same in both directions.
Sign convention for radii of curvature ''R''1 and ''R''2
The signs of the lens' radii of curvature indicate whether the corresponding surfaces are convex or concave. The
sign convention used to represent this varies, but in this article a ''positive'' ''R'' indicates a surface's center of curvature is further along in the direction of the ray travel (right, in the accompanying diagrams), while ''negative'' ''R'' means that rays reaching the surface have already passed the center of curvature. Consequently, for external lens surfaces as diagrammed above, and indicate ''convex'' surfaces (used to converge light in a positive lens), while and indicate ''concave'' surfaces. The reciprocal of the radius of curvature is called the
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 ...
. A flat surface has zero curvature, and its radius of curvature is
infinite.
Thin lens approximation
If ''d'' is small compared to ''R''
1 and ''R''
2, then the ''
thin lens'' approximation can be made. For a lens in air, ''f'' is then given by
:
Imaging properties
As mentioned above, a positive or converging lens in air focuses a collimated beam travelling along the lens axis to a spot (known as the
focal point
Focal point may refer to:
* Focus (optics)
* Focus (geometry)
* Conjugate points, also called focal points
* Focal point (game theory)
* Unicom Focal Point, a portfolio management software tool
* Focal point review, a human resources process for ...
) at a distance ''f'' from the lens. Conversely, a
point source of light placed at the focal point is converted into a collimated beam by the lens. These two cases are examples of
image
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
formation in lenses. In the former case, an object at an infinite distance (as represented by a collimated beam of waves) is focused to an image at the focal point of the lens. In the latter, an object at the focal length distance from the lens is imaged at infinity. The plane perpendicular to the lens axis situated at a distance ''f'' from the lens is called the ''
focal plane
In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points. For ''ideal'' ...
''.
If the distances from the object to the lens and from the lens to the image are ''S''
1 and ''S''
2 respectively, for a lens of negligible thickness (
thin lens), in air, the distances are related by the thin lens formula:
:
This can also be put into the "Newtonian" form:
:
where
and
.
Therefore, if an object is placed at a distance from a positive lens of focal length ''f'', we will find an image distance ''S''
2 according to this formula. If a screen is placed at a distance ''S''
2 on the opposite side of the lens, an image is formed on it. This sort of image, which can be projected onto a screen or
image sensor, is known as a ''
real image
{{citations needed, date=June 2019
In optics, an ''image'' is defined as the collection of focus points of light rays coming from an object. A real image is the collection of focus points actually made by converging/diverging rays, while a v ...
''. This is the principle of the
camera, and also of the
human eye
The human eye is a sensory organ, part of the sensory nervous system, that reacts to visible light and allows humans to use visual information for various purposes including seeing things, keeping balance, and maintaining circadian rhythm.
...
, in which the
retina serves as the image sensor.
The focusing adjustment of a camera adjusts ''S''
2, as using an image distance different from that required by this formula produces a
defocused (fuzzy) image for an object at a distance of ''S''
1 from the camera. Put another way, modifying ''S''
2 causes objects at a different ''S''
1 to come into perfect focus.
In some cases ''S''
2 is negative, indicating that the image is formed on the opposite side of the lens from where those rays are being considered. Since the diverging light rays emanating from the lens never come into focus, and those rays are not physically present at the point where they ''appear'' to form an image, this is called a
virtual image. Unlike real images, a virtual image cannot be projected on a screen, but appears to an observer looking through the lens as if it were a real object at the location of that virtual image. Likewise, it appears to a subsequent lens as if it were an object at that location, so that second lens could again focus that light into a real image, ''S''
1 then being measured from the virtual image location behind the first lens to the second lens. This is exactly what the eye does when looking through a
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 ...
. The magnifying glass creates a (magnified) virtual image behind the magnifying glass, but those rays are then re-imaged by the
lens of the eye to create a ''real image'' on the
retina.
Using a positive lens of focal length ''f'', a virtual image results when , the lens thus being used as a magnifying glass (rather than if as for a camera). Using a negative lens () with a ''real object'' () can only produce a virtual image (), according to the above formula. It is also possible for the object distance ''S''
1 to be negative, in which case the lens sees a so-called ''virtual object''. This happens when the lens is inserted into a converging beam (being focused by a previous lens) ''before'' the location of its real image. In that case even a negative lens can project a real image, as is done by a
Barlow lens.
For a
thin lens, the distances ''S''
1 and ''S''
2 are measured from the object and image to the position of the lens, as described above. When the thickness of the lens is not much smaller than ''S''
1 and ''S''
2 or there are multiple lens elements (a
compound 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''), ...
), one must instead measure from the object and image to the
principal planes of the lens. If distances ''S''
1 or ''S''
2 pass through a
medium other than air or vacuum a more complicated analysis is required.
Magnification
The linear ''
magnification
Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in siz ...
'' of an imaging system using a single lens is given by
:
where ''M'' is the magnification factor defined as the ratio of the size of an image compared to the size of the object. The sign convention here dictates that if ''M'' is negative, as it is for real images, the image is upside-down with respect to the object. For virtual images ''M'' is positive, so the image is upright.
This magnification formula provides two easy ways to distinguish converging (''f > 0'') and diverging (''f < 0'') lenses: For an object very close to the lens (), a converging lens would form a magnified (bigger) virtual image, whereas a diverging lens would form a demagnified (smaller) image; For an object very far from the lens (), a converging lens would form an inverted image, whereas a diverging lens would form an upright image.
Linear magnification ''M'' is not always the most useful measure of magnifying power. For instance, when characterizing a visual telescope or binoculars that produce only a virtual image, one would be more concerned with the
angular magnification—which expresses how much larger a distant object appears through the telescope compared to the naked eye. In the case of a camera one would quote the
plate scale, which compares the apparent (angular) size of a distant object to the size of the real image produced at the focus. The plate scale is the reciprocal of the focal length of the camera lens; lenses are categorized as
long-focus lenses or
wide-angle lenses according to their focal lengths.
Using an inappropriate measurement of magnification can be formally correct but yield a meaningless number. For instance, using a magnifying glass of 5 cm focal length, held 20 cm from the eye and 5 cm from the object, produces a virtual image at infinity of infinite linear size: . But the ''angular magnification'' is 5, meaning that the object appears 5 times larger to the eye than without the lens. When taking a picture of the
moon using a camera with a 50 mm lens, one is not concerned with the linear magnification Rather, the plate scale of the camera is about 1°/mm, from which one can conclude that the 0.5 mm image on the film corresponds to an angular size of the moon seen from earth of about 0.5°.
In the extreme case where an object is an infinite distance away, , and , indicating that the object would be imaged to a single point in the focal plane. In fact, the diameter of the projected spot is not actually zero, since
diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
places a lower limit on the size of the
point spread function. This is called the
diffraction limit.
Aberrations
Lenses do not form perfect images, and a lens always introduces some degree of distortion or ''aberration'' that makes the image an imperfect replica of the object. Careful design of the lens system for a particular application minimizes the aberration. Several types of aberration affect image quality, including spherical aberration, coma, and chromatic aberration.
Spherical aberration
''Spherical aberration'' occurs because spherical surfaces are not the ideal shape for a lens, but are by far the simplest shape to which glass can be
ground and polished, and so are often used. Spherical aberration causes beams parallel to, but distant from, the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image. Spherical aberration can be minimised with normal lens shapes by carefully choosing the surface curvatures for a particular application. For instance, a plano-convex lens, which is used to focus a collimated beam, produces a sharper focal spot when used with the convex side towards the beam source.
Coma
''Coma'', or ''comatic aberration'', derives its name from the
comet-like appearance of the aberrated image. Coma occurs when an object off the optical axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of a lens of focal length ''f'' are focused at a point with distance from the axis. Rays passing through the outer margins of the lens are focused at different points, either further from the axis (positive coma) or closer to the axis (negative coma). In general, a bundle of parallel rays passing through the lens at a fixed distance from the centre of the lens are focused to a ring-shaped image in the focal plane, known as a ''comatic circle''. The sum of all these circles results in a V-shaped or comet-like flare. As with spherical aberration, coma can be minimised (and in some cases eliminated) by choosing the curvature of the two lens surfaces to match the application. Lenses in which both spherical aberration and coma are minimised are called ''bestform'' lenses.
Chromatic aberration
''Chromatic aberration'' is caused by the
dispersion of the lens material—the variation of its
refractive index, ''n'', with the wavelength of light. Since, from the formulae above, ''f'' is dependent upon ''n'', it follows that light of different wavelengths is focused to different positions. Chromatic aberration of a lens is seen as fringes of colour around the image. It can be minimised by using an
achromatic doublet (or ''achromat'') in which two materials with differing dispersion are bonded together to form a single lens. This reduces the amount of chromatic aberration over a certain range of wavelengths, though it does not produce perfect correction. The use of achromats was an important step in the development of the optical microscope. An
apochromat is a lens or lens system with even better chromatic aberration correction, combined with improved spherical aberration correction. Apochromats are much more expensive than achromats.
Different lens materials may also be used to minimise chromatic aberration, such as specialised coatings or lenses made from the crystal
fluorite. This naturally occurring substance has the highest known
Abbe number, indicating that the material has low dispersion.
Other types of aberration
Other kinds of aberration include ''
field curvature'', ''
barrel
A barrel or cask is a hollow cylindrical container with a bulging center, longer than it is wide. They are traditionally made of wooden staves and bound by wooden or metal hoops. The word vat is often used for large containers for liquids, ...
'' and ''
pincushion distortion'', and ''
astigmatism''.
Aperture diffraction
Even if a lens is designed to minimize or eliminate the aberrations described above, the image quality is still limited by the
diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
of light passing through the lens' finite
aperture. A
diffraction-limited lens is one in which aberrations have been reduced to the point where the image quality is primarily limited by diffraction under the design conditions.
Compound lenses
Simple lenses are subject to the
optical aberrations discussed above. In many cases these aberrations can be compensated for to a great extent by using a combination of simple lenses with complementary aberrations. A ''compound lens'' is a collection of simple lenses of different shapes and made of materials of different refractive indices, arranged one after the other with a common axis.
The simplest case is where lenses are placed in contact: if the lenses of focal lengths ''f''
1 and ''f''
2 are "
thin
Thin may refer to:
* a lean body shape. ''(See also: emaciation, underweight)''
* ''Thin'' (film), a 2006 HBO documentary about eating disorders
* Paper Thin (disambiguation), referring to multiple songs
* Thin (web server), a Ruby web-server b ...
", the combined focal length ''f'' of the lenses is given by
:
Since 1/''f'' is the power of a lens, it can be seen that the powers of thin lenses in contact are additive.
If two thin lenses are separated in air by some distance ''d'', the focal length for the combined system is given by
:
The distance from the front focal point of the combined lenses to the first lens is called the ''front focal length'' (FFL):
:
Similarly, the distance from the second lens to the rear focal point of the combined system is the ''back focal length'' (BFL):
:
As ''d'' tends to zero, the focal lengths tend to the value of ''f'' given for thin lenses in contact.
If the separation distance is equal to the sum of the focal lengths (''d'' = ''f''
1 + ''f''
2), the FFL and BFL are infinite. This corresponds to a pair of lenses that transform a parallel (collimated) beam into another collimated beam. This type of system is called an ''
afocal system'', since it produces no net convergence or divergence of the beam. Two lenses at this separation form the simplest type of
optical telescope. Although the system does not alter the divergence of a collimated beam, it does alter the width of the beam. The magnification of such a telescope is given by
:
which is the ratio of the output beam width to the input beam width. Note the sign convention: a telescope with two convex lenses (''f''
1 > 0, ''f''
2 > 0) produces a negative magnification, indicating an inverted image. A convex plus a concave lens (''f''
1 > 0 > ''f''
2) produces a positive magnification and the image is upright. For further information on simple optical telescopes, see
Refracting telescope § Refracting telescope designs.
Non spherical types
Cylindrical lenses have curvature along only one axis. They are used to focus light into a line, or to convert the elliptical light from a
laser diode into a round beam. They are also used in motion picture
anamorphic lenses.
Aspheric lenses have at least one surface that is neither spherical nor cylindrical. The more complicated shapes allow such lenses to form images with less
aberration than standard simple lenses, but they are more difficult and expensive to produce. These were formerly complex to make and often extremely expensive, but advances in technology have greatly reduced the manufacturing cost for such lenses.
A
Fresnel lens has its optical surface broken up into narrow rings, allowing the lens to be much thinner and lighter than conventional lenses. Durable Fresnel lenses can be molded from plastic and are inexpensive.
Lenticular lenses are arrays of
microlenses that are used in
lenticular printing to make images that have an illusion of depth or that change when viewed from different angles.
Bifocal lens
Bifocals are eyeglasses with two distinct optical powers. Bifocals are commonly prescribed to people with presbyopia who also require a correction for myopia, hyperopia, and/or astigmatism.
History
Benjamin Franklin is generally credited w ...
has two or more, or a graduated, focal lengths ground into the lens.
A
gradient index lens
Gradient-index (GRIN) optics is the branch of optics covering optical effects produced by a gradient of the refractive index of a material. Such gradual variation can be used to produce lenses with flat surfaces, or lenses that do not have the ab ...
has flat optical surfaces, but has a radial or axial variation in index of refraction that causes light passing through the lens to be focused.
An
axicon has a
conical
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.
A cone is formed by a set of line segments, half-lines, or lines conn ...
optical surface. It images a
point source into a line ''along'' the
optic axis, or transforms a laser beam into a ring.
Diffractive optical elements can function as lenses.
Superlenses are made from
negative index metamaterials and claim to produce images at spatial resolutions exceeding the
diffraction limit.
The first superlenses were made in 2004 using such a
metamaterial for microwaves.
Improved versions have been made by other researchers.
the superlens has not yet been demonstrated at
visible
Visibility, in meteorology, is a measure of the distance at which an object or light can be seen.
Visibility may also refer to:
* A measure of turbidity in water quality control
* Interferometric visibility, which quantifies interference contrast ...
or near-
infrared wavelengths.
A prototype flat ultrathin lens, with no curvature has been developed.
Uses
A single convex lens mounted in a frame with a handle or stand is a
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 ...
.
Lenses are used as
prosthetics for the correction of
refractive errors such as
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 ...
,
hypermetropia,
presbyopia, and
astigmatism. (See
corrective lens,
contact lens
Contact lenses, or simply contacts, are thin lenses placed directly on the surface of the eyes. Contact lenses are ocular prosthetic devices used by over 150 million people worldwide, and they can be worn to correct vision or for cosmetic ...
,
eyeglasses.) Most lenses used for other purposes have strict
axial symmetry; eyeglass lenses are only approximately symmetric. They are usually shaped to fit in a roughly oval, not circular, frame; the optical centres are placed over the
eyeballs
Eyes are organs of the visual system. They provide living organisms with vision, the ability to receive and process visual detail, as well as enabling several photo response functions that are independent of vision. Eyes detect light and conve ...
; their curvature may not be axially symmetric to correct for
astigmatism.
Sunglasses' lenses are designed to attenuate light; sunglass lenses that also correct visual impairments can be custom made.
Other uses are in imaging systems such as
monoculars,
binoculars
Binoculars or field glasses are two refracting telescopes mounted side-by-side and aligned to point in the same direction, allowing the viewer to use both eyes (binocular vision) when viewing distant objects. Most binoculars are sized to be held ...
,
telescopes,
microscopes,
cameras and
projectors
A projector or image projector is an optical device that projects an image (or moving images) onto a surface, commonly a projection screen. Most projectors create an image by shining a light through a small transparent lens, but some newer types ...
. Some of these instruments produce a
virtual image when applied to the human eye; others produce a
real image
{{citations needed, date=June 2019
In optics, an ''image'' is defined as the collection of focus points of light rays coming from an object. A real image is the collection of focus points actually made by converging/diverging rays, while a v ...
that can be captured on
photographic film
Photographic film is a strip or sheet of transparent film base coated on one side with a gelatin photographic emulsion, emulsion containing microscopically small light-sensitive silver halide crystals. The sizes and other characteristics of th ...
or an
optical sensor
A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon.
In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
, or can be viewed on a screen. In these devices lenses are sometimes paired up with
curved mirrors to make a
catadioptric system
A catadioptric optical system is one where refraction and reflection are combined in an optical system, usually via lenses (dioptrics) and curved mirrors (catoptrics). Catadioptric combinations are used in focusing systems such as searchlights, he ...
where the lens's spherical aberration corrects the opposite aberration in the mirror (such as
Schmidt
Schmidt may refer to:
* Schmidt (surname), including list of people with the surname
* Schmidt (singer) (born 1990), German pop and jazz singer
* Schmidt (lunar crater), a small lunar impact crater
* Schmidt (Martian crater), a List of craters on ...
and
meniscus
Meniscus may refer to:
*Meniscus (anatomy), crescent-shaped fibrocartilaginous structure that partly divides a joint cavity
*Meniscus (liquid)
The meniscus (plural: ''menisci'', from the Greek for "crescent") is the curve in the upper surface ...
correctors).
Convex lenses produce an image of an object at infinity at their focus; if the
sun is imaged, much of the visible and infrared light incident on the lens is concentrated into the small image. A large lens creates enough intensity to burn a flammable object at the focal point. Since ignition can be achieved even with a poorly made lens, lenses have been used as
burning-glasses for at least 2400 years.
/ref> A modern application is the use of relatively large lenses to concentrator photovoltaics, concentrate solar energy on relatively small photovoltaic cells, harvesting more energy without the need to use larger and more expensive cells.
Radio astronomy and radar systems often use dielectric lenses, commonly called a lens antenna to refract electromagnetic radiation into a collector antenna.
Lenses can become scratched and abraded. Abrasion-resistant coatings are available to help control this.
See also
* Anti-fogging treatment of optical surfaces
* Back focal plane
In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points. For ''ideal'' ...
* Bokeh
* Cardinal point (optics)
* Caustic (optics)
* Eyepiece
* F-number
* Gravitational lens
* Lens (anatomy)
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 ...
* List of lens designs
This list covers optical lens designs grouped by tasks or overall type. The field of optical lens designing has many variables including the function the lens or group of lenses have to perform, the limits of optical glass because of the index of r ...
* Numerical aperture
In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the proper ...
* Optical coating
An optical coating is one or more thin layers of material deposited on an optical component such as a lens, prism or mirror, which alters the way in which the optic reflects and transmits light. These coatings have become a key technology in th ...
s
* Optical lens design
* Photochromic lens
* Prism (optics)
An optical prism is a transparent optics, optical element with flat, polished surfaces that are designed to refraction, refract light. At least one surface must be angled — elements with two parallel surfaces are ''not'' prisms. The most fami ...
* Ray tracing
* Ray transfer matrix analysis
References
Bibliography
* Chapters 5 & 6.
*
*
External links
A chapter from an online textbook on refraction and lenses
''Thin Spherical Lenses ''
(.pdf) o
Project PHYSNET
* Article o
Ancient Egyptian lenses
*
The Use of Magnifying Lenses in the Classical World
* (with 21 diagrams)
Simulations
– Concave and Convex Lenses
OpticalRayTracer
– Open source lens simulator (downloadable java)
*
Animations demonstrating lens
by QED
{{Authority control
Optical components