31:
1443:. This is a paraboloidal mirror which is rotated about axes that pass through its centre of mass, but this does not coincide with the focus, which is outside the dish. If the reflector were a rigid paraboloid, the focus would move as the dish turns. To avoid this, the reflector is flexible, and is bent as it rotates so as to keep the focus stationary. Ideally, the reflector would be exactly paraboloidal at all times. In practice, this cannot be achieved exactly, so the Scheffler reflector is not suitable for purposes that require high accuracy. It is used in applications such as
1285:
1383:
1456:
1619:
46:
1670:
1515:
230:
1313:.) Because many types of energy can be reflected in this way, parabolic reflectors can be used to collect and concentrate energy entering the reflector at a particular angle. Similarly, energy radiating from the focus to the dish can be transmitted outward in a beam that is parallel to the axis of the dish.
1476:
intersects the paraboloid. However, if the reflector is used to focus incoming energy onto a receiver, the shadow of the receiver falls onto the vertex of the paraboloid, which is part of the reflector, so part of the reflector is wasted. This can be avoided by making the reflector from a segment of
1324:
that becomes stronger as the ratio of the beam diameter to the focal distance becomes larger, parabolic reflectors can be made to accommodate beams of any width. However, if the incoming beam makes a non-zero angle with the axis (or if the emitting point source is not placed in the focus), parabolic
1336:
The precision to which a parabolic dish must be made in order to focus energy well depends on the wavelength of the energy. If the dish is wrong by a quarter of a wavelength, then the reflected energy will be wrong by a half wavelength, which means that it will interfere destructively with energy
1353:
of a wavelength. The wavelength range of visible light is between about 400 and 700 nanometres (nm), so in order to focus all visible light well, a reflector must be correct to within about 20 nm. For comparison, the diameter of a human hair is usually about 50,000 nm, so the required
1477:
the paraboloid which is offset from the vertex and the axis of symmetry. The whole reflector receives energy, which is then focused onto the receiver. This is frequently done, for example, in satellite-TV receiving dishes, and also in some types of astronomical telescope (
1434:
The focus-balanced configuration (see above) requires the depth of the reflector dish to be greater than its focal length, so the focus is within the dish. This can lead to the focus being difficult to access. An alternative approach is exemplified by the
488:. This is sometimes called the "linear diameter", and equals the diameter of a flat, circular sheet of material, usually metal, which is the right size to be cut and bent to make the dish. Two intermediate results are useful in the calculation:
1704:, which is a virtually identical copy of the original that appears in the opening. The quality of the image is dependent upon the precision of the optics. Some such illusions are manufactured to tolerances of millionths of an inch.
1459:
The vertex of the paraboloid is below the bottom edge of the dish. The curvature of the dish is greatest near the vertex. The axis, which is aimed at the satellite, passes through the vertex and the receiver module, which is at the
1009:
is the aperture area of the dish, the area enclosed by the rim, which is proportional to the amount of sunlight the reflector dish can intercept. The area of the concave surface of the dish can be found using the area formula for a
1555:. This seems unlikely to be true, however, as the claim does not appear in sources before the 2nd century CE, and Diocles does not mention it in his book. Parabolic mirrors and reflectors were also studied extensively by the
1500:, in which the container of molten glass is offset from the axis of rotation. To make less accurate ones, suitable as satellite dishes, the shape is designed by a computer, then multiple dishes are stamped out of sheet metal.
1132:
1288:
Parallel rays coming into a parabolic mirror are focused at a point F. The vertex is V, and the axis of symmetry passes through V and F. For off-axis reflectors (with just the part of the paraboloid between the points
480:
is the radius of the dish from the center. All units used for the radius, focal point and depth must be the same. If two of these three quantities are known, this equation can be used to calculate the third.
699:
1402:. This allows it to be easily turned so it can be aimed at a moving source of light, such as the Sun in the sky, while its focus, where the target is located, is stationary. The dish is rotated around
1369:
Microwaves, such as are used for satellite-TV signals, have wavelengths of the order of ten millimetres, so dishes to focus these waves can be wrong by half a millimetre or so and still perform well.
1214:
1511:
somewhere above the equator stand steeper than a coaxial reflector. The effect is, that the arm to hold the dish can be shorter and snow tends less to accumulate in (the lower part of) the dish.
1414:
represents the focal length of the paraboloid, this "focus-balanced" condition occurs if the depth of the dish, measured along the axis of the paraboloid from the vertex to the plane of the
978:
891:
794:
614:
561:
1363:
315:
If a parabola is positioned in
Cartesian coordinates with its vertex at the origin and its axis of symmetry along the y-axis, so the parabola opens upward, its equation is
839:
1700:. These consist of two opposing parabolic mirrors, with an opening in the center of the top mirror. When an object is placed on the bottom mirror, the mirrors create a
1007:
416:
352:
1158:
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1259:
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372:
1776:
The closeness of this number to the value of "e", the base of natural logarithms, is just an accidental coincidence, but it does make a useful mnemonic.
1017:
296:. A parabola is the two-dimensional figure. (The distinction is like that between a sphere and a circle.) However, in informal language, the word
35:
1846:
30:
1464:
A circular paraboloid is theoretically unlimited in size. Any practical reflector uses just a segment of it. Often, the segment includes the
1333:. This is primarily of interest in telescopes because most other applications do not require sharp resolution off the axis of the parabola.
1663:
1590:"; but according to his own confession, Gregory had no practical skill and he could find no optician capable of actually constructing one.
251:
1718:
Parabolic reflectors are also a popular alternative for increasing wireless signal strength. Even with simple ones, users have reported 3
1707:
A parabolic reflector pointing upward can be formed by rotating a reflective liquid, like mercury, around a vertical axis. This makes the
185:
2113:
1602:
also commonly used parabolic mirrors to collimate a point of light from a lantern into a beam, before being replaced by more efficient
2026:
1897:
1876:
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277:
1354:
accuracy for a reflector to focus visible light is about 2500 times less than the diameter of a hair. For example, the flaw in the
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that has been reflected properly from another part of the dish. To prevent this, the dish must be made correctly to within about
1623:
255:
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1163:
2142:
2183:
1440:
1326:
1552:
136:
are reversible, parabolic reflectors can also be used to collimate radiation from an isotropic source into a parallel
1819:
240:
1486:
1918:
259:
244:
1655:
1297:), the receiver is still placed at the focus of the paraboloid, but it does not cast a shadow onto the reflector.
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165:
931:
1736:
1708:
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1532:
1508:
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is the depth of the dish (measured along the axis of symmetry from the vertex to the plane of the rim), and
753:
128:
Parabolic reflectors are used to collect energy from a distant source (for example sound waves or incoming
1355:
1301:
The parabolic reflector functions due to the geometric properties of the paraboloidal shape: any incoming
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1011:
193:
1382:
521:
1643:
1635:
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1571:
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205:
149:
1968:
pp. 465, 468, 469, A Pioneer in
Anaclastics: Ibn Sahl on Burning Mirrors and Lenses, Roshdi Rashed,
1689:, and is then transported to the venue of the Games. Parabolic mirrors are one of many shapes for a
796:
where the symbols are defined as above. This can be compared with the formulae for the volumes of a
378:".) Correspondingly, the dimensions of a symmetrical paraboloidal dish are related by the equation:
1595:
1587:
1528:
1447:, where sunlight has to be focused well enough to strike a cooking pot, but not to an exact point.
1317:
797:
133:
98:
2092:
1798:
2203:
1757:
1387:
2118:
Do-It-Yourself
Wireless Antennas Update and Wi-Fi Resource Center | WiFi Wireless Q & A
1455:
802:
2022:
1893:
1872:
1742:
1618:
1160:. The fraction of light reflected by the dish, from a light source in the focus, is given by
736:
630:
are defined as above. The diameter of the dish, measured along the surface, is then given by:
177:
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The forgotten revolution: how science was born in 300 BC and why it had to be reborn
1939:
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1603:
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knew about the properties of parabolic mirrors but chose a spherical shape for his
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that is parallel to the axis of the dish will be reflected to a central point, or "
1302:
463:
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1995:
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1514:
1610:, a German physicist, constructed the world's first parabolic reflector antenna.
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1407:
229:
161:
1426:. The angular radius of the rim as seen from the focal point is 72.68 degrees.
1701:
1599:
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1540:
292:
181:
157:
106:
94:
17:
1127:{\textstyle A={\frac {\pi R}{6D^{2}}}\left((R^{2}+4D^{2})^{3/2}-R^{3}\right)}
1659:
1556:
1469:
1406:
that pass through the focus and around which it is balanced. If the dish is
213:
209:
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169:
1823:
105:
revolving around its axis. The parabolic reflector transforms an incoming
1686:
1504:
1496:
and other non-critical applications, can be made quite simply by using a
1310:
375:
113:
converging toward the focus. Conversely, a spherical wave generated by a
102:
1358:
mirror (too flat by about 2,200 nm at its perimeter) caused severe
1719:
1630:
The most common modern applications of the parabolic reflector are in
1543:
in the third century BCE studied paraboloids as part of his study of
484:
A more complex calculation is needed to find the diameter of the dish
842:
141:
82:
78:
39:
1403:
212:, in sports reporting, and to eavesdrop on private conversations in
2067:"ALMA Doubles its Power in New Phase of More Advanced Observations"
1981:
1956:
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Strictly, the three-dimensional shape of the reflector is called a
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1617:
1513:
1454:
1415:
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90:
86:
44:
29:
1551:
that he used reflectors to set the Roman fleet alight during the
129:
694:{\textstyle {\frac {RQ}{P}}+P\ln \left({\frac {R+Q}{P}}\right)}
2018:
Electronic
Imaging in Astronomy: Detectors and Instrumentation
223:
1527:
The principle of parabolic reflectors has been known since
1410:
and made of uniform material of constant thickness, and if
196:
stations, and to locate aircraft, ships, and vehicles in
34:
One of the world's largest solar parabolic dishes at the
1539:
and proved that they focus a parallel beam to a point.
1209:{\textstyle 1-{\frac {\arctan {\frac {R}{D-F}}}{\pi }}}
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1938:
p. 72, The
Geometry of Burning-Mirrors in Antiquity,
1696:
Parabolic reflectors are popular for use in creating
1673:
Lighting the
Olympic Flame with a parabolic reflector
1267:
1244:
1222:
1865:
Apollonius of Perga's Conica: text, context, subtext
2184:
Make Big
Paraboloid Reflectors Using Plane Segments
1586:. The design he came up with bears his name: the "
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121:is reflected into a plane wave propagating as a
1574:with a mirror that was parabolic would correct
1997:A biographical dictionary of eminent Scotsmen
8:
2120:. Binarywolf.com. 2009-08-26. Archived from
1685:, using a parabolic reflector concentrating
27:Reflector that has the shape of a paraboloid
2167:Java demonstration of a parabolic reflector
258:. Unsourced material may be challenged and
208:are used to record faraway sounds such as
2143:"Slideshow: Wi-Fi Shootout in the Desert"
1492:Accurate off-axis reflectors, for use in
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376:Parabola#In a cartesian coordinate system
359:
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320:
278:Learn how and when to remove this message
2178:Animations demonstrating parabola mirror
1711:possible. The same technique is used in
1503:Off-axis-reflectors heading from medium
1381:
1283:
973:{\textstyle ({\frac {1}{3}}\pi R^{2}D).}
2114:"Parabolic Reflector Free WiFi Booster"
1789:
1769:
1422:. The radius of the rim is 2.7187
1398:of a reflector dish coincides with its
1390:of a focus-balanced parabolic reflector
886:{\textstyle ({\frac {2}{3}}\pi R^{2}D,}
36:Ben-Gurion National Solar Energy Center
789:{\textstyle {\frac {1}{2}}\pi R^{2}D,}
101:, that is, the surface generated by a
180:are used to radiate a narrow beam of
7:
1976:, #3 (September 1990), pp. 464–491,
609:{\textstyle Q={\sqrt {P^{2}+R^{2}}}}
256:adding citations to reliable sources
2091:Fitzpatrick, Richard (2007-07-14).
1917:. November 26, 1973. Archived from
1797:Fitzpatrick, Richard (2007-07-14).
1309:". (For a geometrical proof, click
750:The volume of the dish is given by
81:surface used to collect or project
1739:, paraboloids produced by rotation
556:{\textstyle P={\frac {R^{2}}{2D}}}
25:
1892:, Lucio Russo, Birkhäuser, 2004,
1598:mirror to simplify construction.
156:, and project a beam of light in
109:travelling along the axis into a
228:
132:light). Since the principles of
2049:"Prehistory of Radio Astronomy"
1624:Atacama Large Millimeter Array
1606:in the 19th century. In 1888,
1394:It is sometimes useful if the
1089:
1059:
964:
935:
909:
851:
825:
806:
743:, i.e. its logarithm to base "
722:
716:
1:
2000:. Oxford University. p.
1468:of the paraboloid, where its
1418:of the dish, is 1.8478 times
300:and its associated adjective
2172:Parabolic Reflector Antennas
2015:McLean, Ian S (2008-07-29).
1951:#1 (March 1983), pp. 53–73,
1439:, named after its inventor,
148:are used to gather light in
1570:(1663), pointed out that a
1535:described them in his book
1472:is greatest, and where the
374:is its focal length. (See "
304:are often used in place of
2220:
1715:to make solid reflectors.
1626:on the Chajnantor Plateau
1509:geostationary TV satellite
1487:James Webb Space Telescope
1325:reflectors suffer from an
834:{\textstyle (\pi R^{2}D),}
486:measured along its surface
1994:Chambers, Robert (1875).
1847:"The Scheffler-Reflector"
1531:, when the mathematician
97:. Its shape is part of a
1681:is traditionally lit at
1562:in the 13th century AD.
1378:Focus-balanced reflector
2095:. Farside.ph.utexas.edu
1867:, Michael N. Fried and
1801:. Farside.ph.utexas.edu
1737:Liquid-mirror telescope
1709:liquid-mirror telescope
1545:hydrostatic equilibrium
1518:Off-axis satellite dish
2174:www.antenna-theory.com
1851:www.solare-bruecke.org
1822:. NASA. Archived from
1674:
1627:
1519:
1461:
1391:
1356:Hubble Space Telescope
1320:, which suffer from a
1298:
1281:are defined as above.
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1255:
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1002:{\textstyle \pi R^{2}}
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411:{\textstyle 4FD=R^{2}}
368:
348:
347:{\textstyle 4fy=x^{2}}
50:
42:
1820:"Servicing Mission 1"
1672:
1644:parabolic microphones
1636:reflecting telescopes
1621:
1584:refracting telescopes
1517:
1458:
1385:
1362:until corrected with
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440:is the focal length,
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216:and law enforcement.
206:parabolic microphones
150:reflecting telescopes
48:
33:
1911:"Archimedes' Weapon"
1580:chromatic aberration
1576:spherical aberration
1572:reflecting telescope
1483:Green Bank Telescope
1360:spherical aberration
1322:spherical aberration
1318:spherical reflectors
1265:
1242:
1220:
1164:
1153:{\textstyle D\neq 0}
1138:
1018:
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897:
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517:(or the equivalent:
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252:improve this section
2145:. Wired. 2004-08-03
2093:"Spherical Mirrors"
1921:on October 12, 2007
1799:"Spherical Mirrors"
1596:Newtonian telescope
1588:Gregorian telescope
1566:, in his 1663 book
1529:classical antiquity
1451:Off-axis reflectors
1437:Scheffler reflector
1430:Scheffler reflector
728:{\textstyle \ln(x)}
99:circular paraboloid
49:Circular paraboloid
1758:Toroidal reflector
1675:
1666:and LED housings.
1628:
1547:, and it has been
1537:On Burning Mirrors
1520:
1462:
1441:Wolfgang Scheffler
1392:
1388:oblique projection
1299:
1271:
1254:{\displaystyle D,}
1251:
1232:{\displaystyle F,}
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918:{\textstyle D=R),}
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188:communications in
178:parabolic antennas
51:
43:
1826:on April 20, 2008
1743:Parabolic antenna
1713:rotating furnaces
1698:optical illusions
1553:Siege of Syracuse
1316:In contrast with
1274:{\displaystyle R}
1204:
1198:
1052:
946:
862:
765:
737:natural logarithm
685:
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510:{\textstyle P=2F}
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146:parabolic mirrors
16:(Redirected from
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1845:Administrator.
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1722:or more gains.
1683:Olympia, Greece
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1578:as well as the
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194:microwave relay
123:collimated beam
28:
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2161:External links
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2007:
1986:
1982:10.1086/355456
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1869:Sabetai Unguru
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1660:car headlights
1615:
1612:
1608:Heinrich Hertz
1604:Fresnel lenses
1568:Optica Promota
1524:
1521:
1494:solar furnaces
1452:
1449:
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1396:centre of mass
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473:{\textstyle R}
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227:
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186:point-to-point
170:car headlights
154:solar furnaces
117:placed in the
111:spherical wave
26:
24:
18:Parabolic dish
14:
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10:
9:
6:
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2124:on 2019-06-09
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1895:
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1877:90-04-11977-9
1874:
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1863:pp. 162–164,
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1753:Solar furnace
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1732:John D. Kraus
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1679:Olympic Flame
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1564:James Gregory
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268:November 2012
261:
257:
253:
247:
246:
242:
237:This section
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60:
56:
47:
41:
37:
32:
19:
2147:. Retrieved
2137:
2126:. Retrieved
2122:the original
2117:
2108:
2097:. Retrieved
2086:
2074:. Retrieved
2070:
2061:
2053:www.nrao.edu
2052:
2043:
2032:. Retrieved
2017:
2010:
1996:
1989:
1973:
1969:
1964:
1948:
1944:
1940:Wilbur Knorr
1934:
1923:. Retrieved
1919:the original
1905:
1889:
1884:
1864:
1859:
1850:
1840:
1828:. Retrieved
1824:the original
1814:
1803:. Retrieved
1792:
1772:
1717:
1706:
1695:
1676:
1629:
1614:Applications
1592:Isaac Newton
1567:
1536:
1526:
1502:
1491:
1478:
1463:
1436:
1433:
1423:
1419:
1411:
1393:
1368:
1335:
1315:
1300:
1134:. providing
1014:which gives
749:
485:
483:
314:
310:paraboloidal
309:
305:
301:
297:
291:
289:
274:
265:
250:Please help
238:
162:searchlights
127:
115:point source
74:
70:
66:
63:paraboloidal
62:
58:
54:
52:
1888:pp. 73–74,
1650:, and many
1600:Lighthouses
1560:Roger Bacon
1408:symmetrical
182:radio waves
158:flashlights
95:radio waves
2193:Categories
2149:2012-11-08
2128:2012-11-08
2099:2012-11-08
2076:11 January
2034:2012-11-08
1925:2007-08-12
1805:2012-11-08
1784:References
1702:real image
1656:spotlights
1541:Archimedes
1373:Variations
1327:aberration
843:hemisphere
735:means the
306:paraboloid
293:paraboloid
210:bird calls
200:sets. In
134:reflection
107:plane wave
79:reflective
59:paraboloid
2204:Parabolas
1830:April 26,
1764:Footnotes
1664:PAR lamps
1557:physicist
1505:latitudes
1470:curvature
1202:π
1192:−
1180:
1171:−
1145:≠
1107:−
1031:π
987:π
949:π
865:π
810:π
768:π
714:
663:
302:parabolic
239:does not
214:espionage
202:acoustics
67:reflector
55:parabolic
1726:See also
1687:sunlight
1652:lighting
1582:seen in
1216:, where
798:cylinder
354:, where
298:parabola
103:parabola
85:such as
2199:Mirrors
1549:claimed
1533:Diocles
1523:History
1351:
1339:
1329:called
260:removed
245:sources
77:) is a
2180:by QED
2025:
1896:
1875:
1485:, the
1481:, the
1466:vertex
1460:focus.
1364:COSTAR
1177:arctan
925:and a
893:where
703:where
626:, and
618:where
420:where
220:Theory
172:. In
168:, and
142:optics
140:. In
83:energy
75:mirror
40:Israel
1507:to a
1400:focus
1307:focus
1293:and P
198:radar
174:radio
119:focus
93:, or
91:sound
87:light
2078:2013
2023:ISBN
1970:Isis
1945:Isis
1894:ISBN
1873:ISBN
1832:2008
1677:The
1479:e.g.
1404:axes
1331:coma
1311:here
1261:and
927:cone
565:and
308:and
243:any
241:cite
192:and
184:for
152:and
138:beam
130:star
71:dish
69:(or
57:(or
2002:175
1978:doi
1953:doi
1489:).
1416:rim
1386:An
1303:ray
747:".
739:of
254:by
73:or
61:or
38:in
2195::
2116:.
2069:.
2051:.
2021:.
1974:81
1972:,
1949:74
1942:,
1913:.
1849:.
1720:dB
1693:.
1662:,
1658:,
1646:,
1642:,
1638:,
1634:,
1366:.
1348:20
841:a
711:ln
660:ln
622:,
312:.
204:,
176:,
164:,
160:,
144:,
89:,
65:)
53:A
2152:.
2131:.
2102:.
2080:.
2055:.
2037:.
2004:.
1984:.
1980::
1959:.
1955::
1928:.
1900:.
1879:.
1853:.
1834:.
1808:.
1424:F
1420:F
1412:F
1345:/
1342:1
1295:3
1291:1
1289:P
1269:R
1249:,
1246:D
1227:,
1224:F
1195:F
1189:D
1185:R
1168:1
1148:0
1142:D
1121:)
1115:3
1111:R
1102:2
1098:/
1094:3
1090:)
1084:2
1080:D
1076:4
1073:+
1068:2
1064:R
1060:(
1056:(
1047:2
1043:D
1039:6
1034:R
1025:=
1022:A
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991:R
968:.
965:)
962:D
957:2
953:R
944:3
941:1
936:(
913:,
910:)
907:R
904:=
901:D
881:,
878:D
873:2
869:R
860:3
857:2
852:(
829:,
826:)
823:D
818:2
814:R
807:(
784:,
781:D
776:2
772:R
763:2
760:1
745:e
741:x
723:)
720:x
717:(
701:,
688:)
683:P
679:Q
676:+
673:R
667:(
657:P
654:+
649:P
645:Q
642:R
628:R
624:D
620:F
616:,
600:2
596:R
592:+
587:2
583:P
577:=
574:Q
563:)
548:D
545:2
539:2
535:R
529:=
526:P
505:F
502:2
499:=
496:P
468:R
448:D
428:F
418:,
404:2
400:R
396:=
393:D
390:F
387:4
362:f
340:2
336:x
332:=
329:y
326:f
323:4
281:)
275:(
270:)
266:(
262:.
248:.
20:)
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