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Lens (optics)

Lens}} A lens is a transmissive optical device that 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), usually arranged along a common axis. Lenses are made from materials such as glass or plastic, and are ground and polished or moulded to a desired shape. A lens can focus light to form an image, 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.


]] The word comes from lēns , the Latin name of the lentil, because a double-convex lens is lentil-shaped. The lentil plant also gives its name to a geometric figure.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. Reports "lense" as listed in some dictionaries, but not generally considered acceptable. Lists "lense" as an acceptable alternate spelling. 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 is a rock crystal artifact dated to the 7th century BC 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 BC) mentioning a burning-glass. Pliny the Elder (1st century) confirms that burning-glasses were known in the Roman period. Pliny the Elder, The Natural History (trans. John Bostock) Book XXXVII, Chap. 10. Pliny also has the earliest known reference to the use of a corrective lens when he mentions that Nero was said to watch the gladiatorial games using an emerald (presumably to correct for nearsightedness, though the reference is vague).Pliny the Elder, The Natural History (trans. John Bostock) Book XXXVII, Chap. 16 Both Pliny and Seneca the Younger (3 BC–65) 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 ( Book of Optics, 11th century). The Arabic word for "lens", ʿadasa ("lentil") is a direct loan translation of Latin lens, lenticula. 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 cystal Visby lenses 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. |author2=Steven John Livesey |author3=Faith Wallis |accessdate=24 April 2011 |page=167}} 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 century,Al Van Helden. '''The Galileo Project > Science > The Telescope. Galileo.rice.edu. Retrieved on 6 June 2012. and later in the spectacle-making centres in both the Netherlands and Germany. |accessdate=6 June 2012 |date=28 September 2003 |publisher=Courier Dover Publications |isbn=978-0-486-43265-6 |page=27}} 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). |accessdate=6 June 2012 |date=12 December 2008 |publisher=Springer |isbn=978-1-4020-8865-0 |page=17}} |accessdate=6 June 2012 |year=2007 |publisher=American Philosophical Society |isbn=978-0-87169-259-7 |page=210}} 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. Microscopes: Time Line, Nobel Foundation. Retrieved 3 April 2009 |accessdate=6 June 2012 |date=1 October 2007 |publisher=Allen & Unwin |isbn=978-1-74175-383-7 |page=55}} 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 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.This paragraph is adapted from the 1888 edition of the Encyclopædia Britannica. 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 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 (bulging outwards from the lens), (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. More complex are aspheric lenses. These are lenses where one or both surfaces have a shape 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.

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 . If both surfaces have the same radius of curvature, the lens is equiconvex. A lens with two 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. The distance from the lens to the spot is the focal length of the lens, which is commonly abbreviated f in diagrams and equations. 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. The distance from this point to the lens is also known as 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: \frac{1}{f} = (n-1) \left \frac{1}{R_1} - \frac{1}{R_2} + \frac{(n-1)d}{n R_1 R_2} \right, CAUTION TO EDITORS: This equation depends on an arbitrary sign convention (explained on the page). If the signs don't match your textbook, your book is probably using a different sign convention. --> where f is the focal length of the lens, n is the refractive index of the lens material, R_1 is the radius of curvature (with sign, see below) of the lens surface closer to the light source, R_2 is the radius of curvature of the lens surface farther from the light source, and d 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 dioptres (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 R1 and R2

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. A flat surface has zero curvature, and its radius of curvature is infinity.

Thin lens approximation

If d is small compared to R1 and R2, then the thin lens approximation can be made. For a lens in air, f is then given by \frac{1}{f} \approx \left(n-1\right)\left \frac{1}{R_1} - \frac{1}{R_2} \right. CAUTION TO EDITORS: This equation depends on an arbitrary sign convention (explained on the page). If the signs don't match your textbook, your book is probably using a different sign convention. -->

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) 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 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. If the distances from the object to the lens and from the lens to the image are S1 and S2 respectively, for a lens of negligible thickness, in air, the distances are related by the thin lens formula: \frac{1}{S_1} + \frac{1}{S_2} = \frac{1}{f} . CAUTION TO EDITORS: This equation depends on an arbitrary sign convention (explained on the page). If the signs don't match your textbook, your book is probably using a different sign convention. --> This can also be put into the "Newtonian" form: x_1 x_2 = f^2,\! where x_1 = S_1-f and x_2 = S_2-f. Therefore, if an object is placed at a distance from a positive lens of focal length f, we will find an image distance S2 according to this formula. If a screen is placed at a distance S2 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. .]] This is the principle of the camera, and of the human eye. The focusing adjustment of a camera adjusts S2, as using an image distance different from that required by this formula produces a defocused (fuzzy) image for an object at a distance of S1 from the camera. Put another way, modifying S2 causes objects at a different S1 to come into perfect focus. In some cases S2 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, S1 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. 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. A prototype flat ultrathin lens, with no curvature has been developed.


A single convex lens mounted in a frame with a handle or stand is a magnifying glass. Lenses are used as prosthetics for the correction of visual impairments such as myopia, hyperopia, presbyopia, and astigmatism. (See corrective lens, contact lens, 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; 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, telescopes, microscopes, cameras and projectors. Some of these instruments produce a virtual image when applied to the human eye; others produce a real image that can be captured on photographic film or an optical sensor, or can be viewed on a screen. In these devices lenses are sometimes paired up with curved mirrors to make a catadioptric system where the lens's spherical aberration corrects the opposite aberration in the mirror (such as Schmidt and meniscus 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. linkhttp://www.gutenberg.org/files/2562/2562-h/2562-h.htm A modern application is the use of relatively large lenses to 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.{{Cite news | last = Schottner | first = G | title = Scratch and Abrasion Resistant Coatings on Plastic Lenses—State of the Art, Current Developments and Perspectives | newspaper = Journal of Sol-Gel Science and Technology | pages = 71–79 | date = May 2003 | url = http://www.springerlink.com/content/wu963135883p31r8/ | accessdate =28 December 2009 }}

See also



  • Chapters 5 & 6.

External links


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This article based upon the http://en.wikipedia.org/wiki/Lens_(optics), the free encyclopaedia Wikipedia and is licensed under the GNU Free Documentation License.
Further informations available on the list of authors and history: http://en.wikipedia.org/w/index.php?title=Lens_(optics)&action=history
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