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77-460: The term "bellows" is used by extension for a flexible bag whose volume can be changed by compression or expansion, but not used to deliver air. For example, the light-tight (but not airtight) bag allowing the distance between the lens and film of a folding photographic camera to be varied is called a bellows . "Bellows" is only used in plural. The Old English name for "bellows" was blǽstbęl(i)g , blást-bęl(i)g 'blast-bag', 'blowing-bag';

154-902: 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 , polished , or molded to the required 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 . Lenses are used in various imaging devices such as telescopes , binoculars , and cameras . They are also used as visual aids in glasses to correct defects of vision such as myopia and hypermetropia . The word lens comes from lēns ,

231-785: A Muslim majority in the Levant is presumed to have been reached by the 13th century. The majority of Levantine Muslims are Sunnis adhering to the four madhhabs ( Hanafi , Shafi'i , Hanbali and Maliki ). Islamic minorities include the Alawites and Nizari Ismailis in Syria, and Twelver Shiites in Lebanon . Levantine Christian groups include Greek Orthodox ( Antiochian Greek ), Syriac Orthodox , Eastern Catholic ( Syriac Catholic , Melkite and Maronite ), Roman Catholic ( Latin ), Nestorian , and Protestant . Armenians mostly belong to

308-405: A biconcave or plano-concave lens in a lower-index medium, 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

385-642: 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. Developments in transatlantic commerce were the impetus for the construction of modern lighthouses in the 18th century, which utilize a combination of elevated sightlines, lighting sources, and lenses to provide navigational aid overseas. With maximal distance of visibility needed in lighthouses, conventional convex lenses would need to be significantly sized which would negatively affect

462-412: 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

539-537: A lens in air, f   is then given by   1   f   ≈ ( n − 1 ) [   1   R 1   − 1   R 2     ]   . {\displaystyle \ {\frac {1}{\ f\ }}\approx \left(n-1\right)\left[\ {\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\ \right]~.} The spherical thin lens equation in paraxial approximation

616-579: 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

693-831: A spherical lens in air or vacuum for paraxial rays can be calculated from the lensmaker's equation : 1   f   = ( n − 1 ) [   1   R 1   − 1   R 2   +   ( n − 1 )   d     n   R 1   R 2     ]   , {\displaystyle {\frac {1}{\ f\ }}=\left(n-1\right)\left[\ {\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}+{\frac {\ \left(n-1\right)\ d~}{\ n\ R_{1}\ R_{2}\ }}\ \right]\ ,} where The focal length   f   {\textstyle \ f\ }

770-498: A type of bellows used by blacksmiths and smelters to increase the air flow going into the forge, with the property that air is blown out on both strokes of the handle (in contrast to simpler and more common bellows that blow air when the stroke is in one direction and refill the bellows in the other direction). These bellows blow a more constant, and thus stronger, blast than simple bellows. Such bellows existed in China at least since

847-528: A variety of Arabic descended from the pre-Islamic Arabic dialects of Syria and Hejazi Arabic , but retaining significant influence from Western Middle Aramaic . Levantine Arabic is usually classified as North Levantine Arabic in Lebanon, Syria, and parts of Turkey, and South Levantine Arabic in Palestine and Jordan. Each of these encompasses a spectrum of regional or urban/rural variations. In addition to

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924-410: A weight on it. The bottom and the middle leaves contain valves, the top one does not. Only the top lung is connected to the spout. When the bottom leaf is moved up, air is pumped from the bottom lung into the top lung. At the same time air is leaving the bellows from the top lung through the spout, but at a slower rate. This inflates the top lung. Next the bottom leaf is moved down to pull fresh air into

1001-448: Is airtight and lubricated . As the piston is pulled, air enters from the far side and the air in the near chamber is compressed and forced into a side chamber, where it flows through the nozzle. Then as it is pushed air enters from the near side and the air in the far chamber flows through the same nozzle. These have three leaves. The middle leaf is fixed in place. The bottom leaf is moved up and down. The top leaf can move freely and has

1078-403: 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

1155-407: Is convex-concave or meniscus . Convex-concave lenses are most commonly used in corrective lenses , since the shape minimizes some aberrations. For a biconvex or plano-convex lens in a lower-index medium, 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,

1232-445: Is h ), and v {\textstyle v} is the on-axis image distance from the line. Due to paraxial approximation where the line of h is close to the vertex of the spherical surface meeting the optical axis on the left, u {\textstyle u} and v {\textstyle v} are also considered distances with respect to the vertex. Moving v {\textstyle v} toward

1309-765: Is borrowed from the French levant 'rising', referring to the rising of the sun in the east, or the point where the sun rises. The phrase is ultimately from the Latin word levare , meaning 'lift, raise'. Similar etymologies are found in Greek Ἀνατολή Anatolē ( cf. Anatolia 'the direction of sunrise'), in Germanic Morgenland ( lit.   ' morning land ' ), in Italian (as in Riviera di Levante ,

1386-399: Is called the focal plane . For paraxial rays , if the distances from an object to a spherical thin lens (a lens of negligible thickness) and from the lens to the image are S 1 and S 2 respectively, the distances are related by the (Gaussian) thin lens formula : Levant The Levant ( / l ə ˈ v æ n t / lə- VANT ) is a term used to define

1463-416: Is completely round. When used in novelty photography it is often called a "lensball". A ball-shaped lens has the advantage of being omnidirectional, but for most optical glass types, its focal point lies close to the ball's surface. Because of the ball's curvature extremes compared to the lens size, optical aberration is much worse than thin lenses, with the notable exception of chromatic aberration . For

1540-794: Is derived here with respect to the right figure. The 1st spherical lens surface (which meets the optical axis at   V 1   {\textstyle \ V_{1}\ } as its vertex) images an on-axis object point O to the virtual image I , which can be described by the following equation,     n 1     u   +   n 2     v ′   =   n 2 − n 1     R 1     . {\displaystyle \ {\frac {\ n_{1}\ }{\ u\ }}+{\frac {\ n_{2}\ }{\ v'\ }}={\frac {\ n_{2}-n_{1}\ }{\ R_{1}\ }}~.} For

1617-460: 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, R 1 > 0 and R 2 < 0 indicate convex surfaces (used to converge light in a positive lens), while R 1 < 0 and R 2 > 0 indicate concave surfaces. The reciprocal of

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1694-407: Is negative with respect to the focal length of a converging lens. The behavior reverses when a lens is placed in a medium with higher refractive index than the material of the lens. In this case a biconvex or plano-convex lens diverges light, and a biconcave or plano-concave one converges it. Convex-concave (meniscus) lenses can be either positive or negative, depending on the relative curvatures of

1771-433: Is positive for converging lenses, and negative for diverging lenses. The reciprocal of the focal length,   1   f     , {\textstyle \ {\tfrac {1}{\ f\ }}\ ,} is the optical power of the lens. If the focal length is in metres, this gives the optical power in dioptres (reciprocal metres). Lenses have the same focal length when light travels from

1848-400: Is the radius of the spherical surface, n 2 is the refractive index of the material of the surface, n 1 is the refractive index of medium (the medium other than the spherical surface material), u {\textstyle u} is the on-axis (on the optical axis) object distance from the line perpendicular to the axis toward the refraction point on the surface (which height

1925-426: Is used by extension for a number of applications that do not involve air transfer. Bee smokers have bellows attached to the side to provide air to a slow burning fuel. This allows for an increased rate of combustion and a temporarily higher output of smoke on command, something desirable when calming domesticated bees . Lens (optics) A lens is a transmissive optical device that focuses or disperses

2002-1135: Is with respect to the principal planes of the lens, and the locations of the principal planes   h 1   {\textstyle \ h_{1}\ } and   h 2   {\textstyle \ h_{2}\ } with respect to the respective lens vertices are given by the following formulas, where it is a positive value if it is right to the respective vertex.   h 1 = −     ( n − 1 ) f   d     n   R 2     {\displaystyle \ h_{1}=-\ {\frac {\ \left(n-1\right)f\ d~}{\ n\ R_{2}\ }}\ }   h 2 = −     ( n − 1 ) f   d     n   R 1     {\displaystyle \ h_{2}=-\ {\frac {\ \left(n-1\right)f\ d~}{\ n\ R_{1}\ }}\ } The focal length   f   {\displaystyle \ f\ }

2079-571: The 13th and 14th centuries, the term levante was used for Italian maritime commerce in the Eastern Mediterranean, including Greece, Anatolia , Syria-Palestine , and Egypt , that is, the lands east of Venice . Eventually the term was restricted to the Muslim countries of Syria-Palestine and Egypt. The term entered English in the late 15th century from French. It derives from the Italian levante , meaning "rising", implying

2156-669: The Armenian Apostolic Church . There are also Levantines or Franco-Levantines who adhere to Roman Catholicism . There are also Assyrians belonging to the Assyrian Church of the East and the Chaldean Catholic Church . Other religious groups in the Levant include Jews , Samaritans , Yazidis and Druze . Most populations in the Levant speak Levantine Arabic ( شامي , Šāmī ),

2233-480: The Greek islands ). In 19th-century archaeology, it referred to overlapping cultures in this region during and after prehistoric times, intending to reference the place instead of any one culture. The French mandate of Syria and Lebanon (1920–1946) was called the Levant states. Today, "Levant" is the term typically used by archaeologists and historians with reference to the history of the region. Scholars have adopted

2310-807: The Latin Christians of the Levant continue to be called Levantine Christians . The Levant has been described as the "crossroads of Western Asia , the Eastern Mediterranean, and Northeast Africa ", and in geological ( tectonic ) terms as the "northwest of the Arabian Plate ". The populations of the Levant share not only geographic position, but cuisine , some customs, and history . They are often referred to as Levantines . The term Levant appears in English in 1497 , and originally meant 'the East ' or 'Mediterranean lands east of Italy'. It

2387-465: The Levant , archaeologists have found primitive pot bellows, consisting of a ceramic pot to which a loose leather hide had been attached at the top. Such pot bellows were constructed with a wide rim, so that the hide covering would transmit a maximum amount of air when pumped. The covering was fastened to the pot with a cord under an out-turned rim, or in a groove just below the rim exterior. An opening near

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2464-769: The Ottoman Sultan in 1579. The English Levant Company was founded in 1581 to trade with the Ottoman Empire , and in 1670 the French Compagnie du Levant  [ fr ] was founded for the same purpose. At this time, the Far East was known as the "Upper Levant". In early 19th-century travel writing , the term sometimes incorporated certain Mediterranean provinces of the Ottoman Empire , as well as independent Greece (and especially

2541-683: The Palestinian territories and most of Turkey southwest of the middle Euphrates . Its overwhelming characteristic is that it represents the land bridge between Africa and Eurasia . In its widest historical sense, the Levant included all of the Eastern Mediterranean with its islands; that is, it included all of the countries along the Eastern Mediterranean shores, extending from Greece in Southern Europe to Egypt and Cyrenaica (Eastern Libya) in Northern Africa . In

2618-517: The Sinai Peninsula (Asian Egypt) are sometimes included. As a name for the contemporary region, several dictionaries consider Levant to be archaic today. Both the noun Levant and the adjective Levantine are now commonly used to describe the ancient and modern culture area formerly called Syro-Palestinian or Biblical: archaeologists now speak of the Levant and of Levantine archaeology ; food scholars speak of Levantine cuisine ; and

2695-735: The Southern Levant . While the usage of the term "Levant" in academia has been restricted to the fields of archeology and literature, there is a recent attempt to reclaim the notion of the Levant as a category of analysis in political and social sciences. Two academic journals were launched in the early 2010s using the word: the Journal of Levantine Studies , published by the Van Leer Jerusalem Institute and The Levantine Review , published by Boston College . The word Levant has been used in some translations of

2772-480: 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 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

2849-512: 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

2926-412: The 5th century BC, when it was invented, and had reached Europe by the 16th century. In 240 BC, The ancient Greek inventor Ctesibius of Alexandria independently invented a double-action piston bellow used to lift water from one level to another. A piston is enclosed in a rectangular box with a handle coming out one side. The piston edges are covered with feathers, fur, or soft paper to ensure that it

3003-556: The Chinese to the bamboo-based piston bellows of Southeast Asians. The acquired piston bellows technology completely replaced the Chinese ox hide bellows that by the Song dynasty , the ox hide bellows were completely extinct. The Han dynasty Chinese mechanical engineer Du Shi (d. 38) is credited with being the first to use hydraulic power on a double-action piston pumps, through a waterwheel , to operate bellows in metallurgy. His invention

3080-979: The Gaussian thin lens equation is   1   u   + 1   v   = 1   f     . {\displaystyle \ {\frac {1}{\ u\ }}+{\frac {1}{\ v\ }}={\frac {1}{\ f\ }}~.} For the thin lens in air or vacuum where   n 1 = 1   {\textstyle \ n_{1}=1\ } can be assumed,   f   {\textstyle \ f\ } becomes   1   f   = ( n − 1 ) ( 1   R 1   − 1   R 2   )   {\displaystyle \ {\frac {1}{\ f\ }}=\left(n-1\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)\ } where

3157-432: 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 . 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 BCE which may or may not have been used as

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3234-471: 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 translation of Ptolemy's Optics became available in Latin translation in the 12th century ( Eugenius of Palermo 1154). Between

3311-732: The area that is bounded by the Taurus Mountains of Turkey in the north, the Mediterranean Sea in the west, the north Arabian Desert and Mesopotamia in the east, and Sinai in the south (which can be fully included or not). Typically, it does not include Anatolia (also known as Asia Minor), the Caucasus Mountains, or any part of the Arabian Peninsula proper. Cilicia (in Asia Minor) and

3388-405: 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. 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

3465-489: The base served to insert a pipe of perishable material whose purpose was to direct the air blast to either the furnace or crucible, and which was usually done through the mediation of a tuyère . Tuyères used in conjunction with pot bellows had the function of protecting the ends of perishable tubes leading from the pot into the fire. Places in Saharan Africa still make use of primitive pot bellows. The term "bellows"

3542-404: The bellows. While this happens the weight on the top leaf pushes it down, so air keeps leaving through the spout. This design does not increase the amount of air flow going into the forge, but provides a more constant air flow compared to a simple bellows. It also provides more even air flow than two simple bellows pumped alternately or one double-acting piston bellows. In archaeological ruins of

3619-526: The boundaries of the Levant as follows. A distinction is made between the main subregions of the Levant, the northern and the southern: The island of Cyprus is also included as a third subregion in the archaeological region of the Levant: The vast majority of Levantines are Muslims . After the Muslim conquest of the Levant in the 7th century, Islam was first introduced into the region. However,

3696-421: The development of lighthouses in terms of cost, design, and implementation. Fresnel lens were developed that considered these constraints by featuring less material through their concentric annular sectioning. They were first fully implemented into a lighthouse in 1823. Most lenses are spherical lenses : their two surfaces are parts of the surfaces of spheres. Each surface can be convex (bulging outwards from

3773-403: The distance from the lens to the spot is the focal length of the lens, which is commonly represented by f in diagrams and equations. An extended hemispherical lens 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. Another extreme case of a thick convex lens is a ball lens , whose shape

3850-426: The effect of the lens' thickness. For a single refraction for a circular boundary, the relation between object and its image in the paraxial approximation is given by n 1 u + n 2 v = n 2 − n 1 R {\displaystyle {\frac {n_{1}}{u}}+{\frac {n_{2}}{v}}={\frac {n_{2}-n_{1}}{R}}} where R

3927-567: The historical and geographical subregion that borders the Eastern Mediterranean sea to the west and core West Asia , or by the political term, Middle East to the east . In its narrowest sense, which is in use today in archaeology and other cultural contexts, it is equivalent to Cyprus and a stretch of land bordering the Mediterranean Sea in western Asia: i.e. the historical region of Syria ("Greater Syria"), which includes present-day Israel , Jordan , Lebanon , Syria ,

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4004-1499: The imaging by second lens surface, by taking the above sign convention,   u ′ = − v ′ + d   {\textstyle \ u'=-v'+d\ } and   n 2   − v ′ + d   +   n 1     v   =   n 1 − n 2     R 2     . {\displaystyle \ {\frac {n_{2}}{\ -v'+d\ }}+{\frac {\ n_{1}\ }{\ v\ }}={\frac {\ n_{1}-n_{2}\ }{\ R_{2}\ }}~.} Adding these two equations yields     n 1   u +   n 1   v = ( n 2 − n 1 ) ( 1   R 1   − 1   R 2   ) +   n 2   d     (   v ′ − d   )   v ′     . {\displaystyle \ {\frac {\ n_{1}\ }{u}}+{\frac {\ n_{1}\ }{v}}=\left(n_{2}-n_{1}\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)+{\frac {\ n_{2}\ d\ }{\ \left(\ v'-d\ \right)\ v'\ }}~.} For

4081-617: The invention, in antiquity , of the bellows. The bellows are used to deliver additional air to the fuel, raising the rate of combustion and therefore the heat output. Various kinds of bellows are used in metallurgy : Chinese bellows were originally made of ox hide with two pots as described in Mozi 's book on military technology in the Warring States period (4th century BC). By the Han dynasty , contact with Southeast Asian cultures exposed

4158-746: The island of Cyprus in Levantine studies, including the Council for British Research in the Levant , the UCLA Near Eastern Languages and Cultures department, Journal of Levantine Studies and the UCL Institute of Archaeology, the last of which has dated the connection between Cyprus and mainland Levant to the early Iron Age . Archaeologists seeking a neutral orientation that is neither biblical nor national have used terms such as Levantine archaeology and archaeology of

4235-417: 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

4312-399: 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

4389-402: 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

4466-655: The north. Two minority languages are recognized: Armenian , and Cypriot Maronite Arabic , a hybrid of mostly medieval Arabic vernaculars with strong influence from contact with Turkish and Greek, spoken by approximately 1,000 people. Western Neo-Aramaic is additionally spoken in three villages in Syria: Maaloula , Jubb'adin and Bakhah . Among diaspora communities based in the Levant, Greek , Armenian and Circassian are also spoken. According to recent ancient DNA studies, Levantines derive most of their ancestry from ancient Semitic-speaking peoples of

4543-406: 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. Lenses are classified by the curvature of the two optical surfaces. A lens

4620-694: The portion of the Liguria coast east of Genoa ), in Hungarian Kelet ('east'), in Spanish and Catalan Levante and Llevant , ('the place of rising'), and in Hebrew מִזְרָח mizraḥ ('east'). Most notably, "Orient" and its Latin source oriens meaning 'east', is literally "rising", deriving from Latin orior 'rise'. The notion of the Levant has undergone a dynamic process of historical evolution in usage, meaning, and understanding. While

4697-539: The prefix was dropped and by the eleventh century the simple bęlg , bylg , bylig ('bag') was used. The word is cognate with " belly ". There are similar words in Old Norse , Swedish, and Danish and Dutch (blaasbalg), but the derivation is not certain. 'Bellows' appears not to be cognate with the apparently similar Latin follis . Several processes, such as metallurgical iron smelting and welding , require so much heat that they could only be developed after

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4774-414: The radius of curvature is called the curvature . A flat surface has zero curvature, and its radius of curvature is infinite . This convention seems to be mainly used for this article, although there is another convention such as Cartesian sign convention requiring different lens equation forms. If d is small compared to R 1 and R 2 then the thin lens approximation can be made. For

4851-424: The reason why the term Levant has come to be used more specifically to refer to modern Syria, Lebanon, Palestine, Israel, Jordan, and the island of Cyprus . Some scholars mistakenly believed that it derives from the name of Lebanon. Today the term is often used in conjunction with prehistoric or ancient historical references. Another term for "Syria-Palestine" is Ash- Shaam ( Arabic : ٱلشَّام , /ʔaʃ.ʃaːm/ ),

4928-775: The right infinity leads to the first or object focal length f 0 {\textstyle f_{0}} for the spherical surface. Similarly, u {\textstyle u} toward the left infinity leads to the second or image focal length f i {\displaystyle f_{i}} . f 0 = n 1 n 2 − n 1 R , f i = n 2 n 2 − n 1 R {\displaystyle {\begin{aligned}f_{0}&={\frac {n_{1}}{n_{2}-n_{1}}}R,\\f_{i}&={\frac {n_{2}}{n_{2}-n_{1}}}R\end{aligned}}} Applying this equation on

5005-566: The rising of the Sun in the east, and is broadly equivalent to the term al-Mashriq ( Arabic : ٱلْمَشْرِق , [ʔal.maʃ.riq] ), meaning "the eastern place, where the Sun rises". In 1581, England set up the Levant Company to trade with the Ottoman Empire . The name Levant States was used to refer to the French mandate over Syria and Lebanon after World War I . This is probably

5082-410: The sign) would have zero optical power (as its focal length becomes infinity as shown in the lensmaker's equation ), meaning that it would neither converge nor diverge light. All real lenses have a 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

5159-408: The subscript of 2 in   n 2   {\textstyle \ n_{2}\ } is dropped. 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

5236-689: The term ash-Shām as used by the organization known as ISIL, ISIS, and other names , though there is disagreement as to whether this translation is accurate. In The Oxford Handbook of the Archaeology of the Levant: c. 8000–332 BCE (OHAL; 2013), the definition of the Levant for the specific purposes of the book is synonymous to that of the Arabic " bilad al-sham , 'the land of sham [Syria]'", translating in Western parlance to greater Syria . OHAL defines

5313-543: The term "Levantine" originally referred to the European residents of the eastern Mediterranean region, it later came to refer to regional "native" and "minority" groups. The term became current in English in the 16th century, along with the first English merchant adventurers in the region; English ships appeared in the Mediterranean in the 1570s, and the English merchant company signed its agreement (" capitulations ") with

5390-514: The term Levant to identify the region due to its being a "wider, yet relevant, cultural corpus" that does not have the "political overtones" of Syria-Palestine. The term is also used for modern events, peoples, states or parts of states in the same region, namely Cyprus , Egypt , Iraq , Israel , Jordan , Lebanon , Palestine , Syria , and Turkey are sometimes considered Levant countries (compare with Near East , Middle East , Eastern Mediterranean and West Asia ). Several researchers include

5467-862: The thin lens approximation where   d → 0   , {\displaystyle \ d\rightarrow 0\ ,} the 2nd term of the RHS (Right Hand Side) is gone, so     n 1   u +   n 1   v = ( n 2 − n 1 ) ( 1   R 1   − 1   R 2   )   . {\displaystyle \ {\frac {\ n_{1}\ }{u}}+{\frac {\ n_{1}\ }{v}}=\left(n_{2}-n_{1}\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)~.} The focal length   f   {\displaystyle \ f\ } of

5544-1110: The thin lens is found by limiting   u → − ∞   , {\displaystyle \ u\rightarrow -\infty \ ,}     n 1     f   = ( n 2 − n 1 ) ( 1   R 1   − 1   R 2   ) → 1   f   = (   n 2     n 1   − 1 ) ( 1   R 1   − 1   R 2   )   . {\displaystyle \ {\frac {\ n_{1}\ }{\ f\ }}=\left(n_{2}-n_{1}\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)\rightarrow {\frac {1}{\ f\ }}=\left({\frac {\ n_{2}\ }{\ n_{1}\ }}-1\right)\left({\frac {1}{\ R_{1}\ }}-{\frac {1}{\ R_{2}\ }}\right)~.} So,

5621-1258: The two spherical surfaces of a lens and approximating the lens thickness to zero (so a thin lens) leads to the lensmaker's formula . Applying Snell's law on the spherical surface, n 1 sin ⁡ i = n 2 sin ⁡ r . {\displaystyle n_{1}\sin i=n_{2}\sin r\,.} Also in the diagram, tan ⁡ ( i − θ ) = h u tan ⁡ ( θ − r ) = h v sin ⁡ θ = h R {\displaystyle {\begin{aligned}\tan(i-\theta )&={\frac {h}{u}}\\\tan(\theta -r)&={\frac {h}{v}}\\\sin \theta &={\frac {h}{R}}\end{aligned}}} , and using small angle approximation (paraxial approximation) and eliminating i , r , and θ , n 2 v + n 1 u = n 2 − n 1 R . {\displaystyle {\frac {n_{2}}{v}}+{\frac {n_{1}}{u}}={\frac {n_{2}-n_{1}}{R}}\,.} The (effective) focal length f {\displaystyle f} of

5698-418: The two surfaces. A negative meniscus lens has a steeper concave surface (with a shorter radius than the convex surface) and is thinner at the centre than at the periphery. Conversely, a positive meniscus lens has a steeper convex surface (with a shorter radius than the concave surface) and is thicker at the centre than at the periphery. An ideal thin lens with two surfaces of equal curvature (also equal in

5775-467: The use of a corrective lens when he mentions that Nero was said to watch the gladiatorial games using an emerald (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

5852-400: The varieties normally grouped together as "Levantine", a number of other varieties and dialects of Arabic are spoken in the Levant area, such as Levantine Bedawi Arabic (by Bedouins ) and Mesopotamian Arabic (in eastern Syria). Of the languages of Cyprus , the two official languages are Turkish and Greek. The most used languages by population are Greek in the south followed by Turkish in

5929-421: Was used to operate piston bellows of blast furnaces in order to forge cast iron . The ancient Greeks , ancient Romans , and other civilizations used bellows in bloomery furnaces producing wrought iron . Bellows are also used to send pressurized air in a controlled manner in a fired heater. In modern industry, reciprocating bellows are usually replaced with motorized blowers. Double-acting piston bellows are

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