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 is a lens consisting of a single optical element. A compound lens is an array of simple lenses (elements) with a common axis; the use of multiple elements allows more optical aberrations to be corrected than is possible with a single element. Manufactured lenses are typically made of glass or transparent plastic. Elements which refract electromagnetic radiation outside the visual spectrum are also called lenses: for instance, a microwave lens can be made from paraffin wax.
The variant spelling lense is sometimes seen. While it is listed as an alternative spelling in some dictionaries, most mainstream dictionaries do not list it as acceptable.
History
See also: History of opticsThe oldest lens artifact is the Nimrud lens, which is over three thousand years old, dating back to ancient Assyria. David Brewster proposed that it may have been used as a magnifying glass, or as a burning-glass to start fires by concentrating sunlight. Assyrian craftsmen made intricate engravings, and could have used such a lens in their work. Another early reference to magnification dates back to ancient Egyptian hieroglyphs in the 8th century BC, which depict "simple glass meniscal lenses".
The earliest written records of lenses date to Ancient Greece, with Aristophanes' play The Clouds (424 BC) mentioning a burning-glass (a biconvex lens used to focus the sun's rays to produce fire). The writings of Pliny the Elder (23–79) also show that burning-glasses were known to the Roman Empire, and mentions what is arguably the earliest use of a corrective lens: Nero was said to watch the gladiatorial games using an emerald (presumably concave to correct for myopia, though the reference is vague). Both Pliny and Seneca the Younger (3 BC–65) described the magnifying effect of a glass globe filled with water.
The word lens comes from the Latin name of the lentil, because a double-convex lens is lentil-shaped. The genus of the lentil plant is Lens , and the most commonly eaten species is Lens culinaris . The lentil plant also gives its name to a geometric figure.
The Iranian physicist and mathematician Ibn Sahl (c.940–c.1000) used what is now known as Snell's law to calculate the shape of lenses. Ibn al-Haytham (965–1038), known in the West as Alhazen , wrote the first major optical treatise, the Book of Optics , which contained the earliest historical proof of a magnifying device, a convex lens forming a magnified image. The book was translated into Latin in the 12th century, and became the standard textbook in the field and influenced many other writers.
Excavations at the Viking harbour town of Fröjel, Gotland, Sweden discovered in 1999 the rock crystal Visby lenses, produced by turning on pole-lathes at Fröjel in the 11th to 12th century, with an imaging quality comparable to that of 1950s aspheric lenses. The Viking lenses concentrate sunlight enough to ignite fires.
Widespread use of lenses did not occur until the use of reading stones in the 11th century and the invention of spectacles, probably in Italy in the 1280s. Scholars have noted that spectacles were invented not long after the translation of al-Haytham's book into Latin, but it is not clear what role, if any, the optical theory of the time played in the discovery. Nicholas of Cusa is believed to have been the first to discover the benefits of concave lenses for the treatment of myopia in 1451.
The Abbe sine condition, due to Ernst Abbe (1860s), is a condition that must be fulfilled by a lens or other optical system in order for it to produce sharp images of off-axis as well as on-axis objects. It revolutionized the design of optical instruments such as microscopes, and helped to establish the Carl Zeiss company as a leading supplier of optical instruments.
Construction of simple lenses
Most lenses are spherical lenses : their two surfaces are parts of the surfaces of spheres, with the lens axis ideally perpendicular to both surfaces. 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 is a form of deliberate astigmatism.
More complex are aspheric lenses. These are lenses where one or both surfaces have a shape that is neither spherical nor cylindrical. Such lenses can produce images with much less aberration than standard simple lenses.
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 or parallel beam of light travelling parallel to the lens axis and passing through the lens will be converged (or focused ) to a spot on the axis, at a certain distance behind the lens (known as the focal length ). In this case, the lens is called a positive or converging lens.
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 be emanating from a particular point on the axis in front of the lens; the distance from this point to the lens is also known as the focal length, although 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 will be thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface and will be 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 a nonzero thickness, however, which affects the optical power. 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
Sign convention of lens radii R 1 and R 2
Main article: Radius of curvature (optics)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 if R 1 is positive the first surface is convex, and if R 1 is negative the surface is concave. The signs are reversed for the back surface of the lens: if R 2 is positive the surface is concave, and if R 2 is negative the surface is convex. If either radius is infinite, the corresponding surface is flat. With this convention the signs are determined by the shapes of the lens surfaces, and are independent of the direction in which light travels through the lens.
Thin lens equation
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
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 foca
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