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1023:. In regions of the electromagnetic spectrum in which absorption by the material is significant, it is related to the electronic absorption spectrum through the imaginary component of the complex refractive index. The electronic absorption spectrum of an opaque material, which is difficult or impossible to measure directly, may therefore be indirectly determined from the reflection spectrum by a
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of the material. The degree of participation of each of these processes in the transmission is a function of the frequency, or wavelength, of the light, its polarization, and its angle of incidence. In general, reflection increases with increasing angle of incidence, and with increasing absorptivity
327:
paint. Matte paints exhibit essentially complete diffuse reflection, while glossy paints show a larger component of specular behavior. A surface built from a non-absorbing powder, such as plaster, can be a nearly perfect diffuser, whereas polished metallic objects can specularly reflect light very
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The reversal of images by a plane mirror is perceived differently depending on the circumstances. In many cases, the image in a mirror appears to be reversed from left to right. If a flat mirror is mounted on the ceiling it can appear to reverse
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316:. Specular reflection reflects all light which arrives from a given direction at the same angle, whereas diffuse reflection reflects light in a broad range of directions. The distinction may be illustrated with surfaces coated with
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654:{\displaystyle \mathbf {\hat {d}} _{\mathrm {s} }=\mathbf {\hat {d}} _{\mathrm {i} }-2\mathbf {\hat {d}} _{\mathrm {n} }\left(\mathbf {\hat {d}} _{\mathrm {n} }\cdot \mathbf {\hat {d}} _{\mathrm {i} }\right),}
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gave a complete statement of the law of reflection. He was first to state that the incident ray, the reflected ray, and the normal to the surface all lie in a same plane perpendicular to reflecting plane.
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is the ratio of the power of the reflected wave to that of the incident wave. It is a function of the wavelength of radiation, and is related to the refractive index of the material as expressed by
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in the rear view mirror for the driver of a car in front of it. The reversal of directions, or lack thereof, depends on how the directions are defined. More specifically a mirror changes the
1027:. The polarization of the reflected light depends on the symmetry of the arrangement of the incident probing light with respect to the absorbing transitions dipole moments in the material.
284:
When light encounters a boundary of a material, it is affected by the optical and electronic response functions of the material to electromagnetic waves. Optical processes, which comprise
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The law of reflection states that the angle of reflection of a ray equals the angle of incidence, and that the incident direction, the surface normal, and the reflected direction are
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as the incident ray, but on the opposing side of the surface normal in the plane formed by the incident and reflected rays. This behavior was first described by
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Esplanade of the
Trocadero in Paris after rain. The layer of water exhibits specular reflection, reflecting an image of the Eiffel Tower and other objects.
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Light propagates in space as a wave front of electromagnetic fields. A ray of light is characterized by the direction normal to the wave front (
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exploits specular reflectivity to study thin films and interfaces with sub-nanometer resolution, using either modern laboratory sources or
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929:{\displaystyle \mathbf {R} =\mathbf {I} -2\mathbf {\hat {d}} _{\mathrm {n} }\mathbf {\hat {d}} _{\mathrm {n} }^{\mathrm {T} };}
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64:
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uses specular reflection to study material surfaces and thin film interfaces in an analogous fashion to x-ray reflectivity.
276:
86:
1662:
Haines, Eric (2021). "Chapter 8: Reflection and
Refraction Formulas". In Marrs, Adam; Shirley, Peter; Wald, Ingo (eds.).
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368:, then the electromagnetic fields at the boundary are oscillating exactly in phase only for the specular direction.
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Measurement of specular reflection is performed with normal or varying incidence reflection spectrophotometers (
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When the light impinges perpendicularly to the surface, it is reflected straight back in the source direction.
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809:{\displaystyle \mathbf {\hat {d}} _{\mathrm {s} }=\mathbf {R} \;\mathbf {\hat {d}} _{\mathrm {i} },}
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When light strikes an interface between two materials, the reflected light is generally partially
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292:, are expressed by the difference of the refractive index on both sides of the boundary, whereas
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Waves in Focal
Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves
335:). When a ray encounters a surface, the angle that the wave normal makes with respect to the
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of the image may change. For example, the image of a right shoe will look like a left shoe.
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of the coordinate system, one axis of the coordinate system appears to be reversed, and the
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When light is propagating in a material and strikes an interface with a material of lower
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719:{\displaystyle \mathbf {\hat {d}} _{\mathrm {n} }\cdot \mathbf {\hat {d}} _{\mathrm {i} }}
324:
1034:) using a scanning variable-wavelength light source. Lower quality measurements using a
1228:{\displaystyle \theta _{\mathrm {B} }=\arctan \!\left({\frac {n_{2}}{n_{1}}}\right)\!.}
387:
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1133:{\displaystyle \theta _{\text{crit}}=\arcsin \!\left({\frac {n_{2}}{n_{1}}}\right)\!.}
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occurs: all of the light is reflected. The critical angle can be shown to be given by
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386:. The direction of a reflected ray is determined by the vector of incidence and the
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of a plane wave on a flat boundary. When the boundary size is much larger than the
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1059:, some of the light is reflected. If the angle of incidence is greater than the
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742:, the equation can be equivalently expressed as a matrix-vector multiplication:
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efficiently. The reflecting material of mirrors is usually aluminum or silver.
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1035:
365:
289:
260:, in which light is scattered away from the surface in a range of directions.
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The
Principles of Physical Optics: An Historical and Philosophical Treatment
1538:
The
Principles of Physical Optics: An Historical and Philosophical Treatment
1334:
1330:
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linearly polarized parallel to the interface. Brewster's angle is given by
730:. Different authors may define the incident and reflection directions with
1739:
1484:
A history of Greek mathematics. Volume II: From
Aristarchus to Diophantus
351:
1282:
if a person stands under it and looks up at it. Similarly a car turning
347:. Reflection of the incident ray also occurs in the plane of incidence.
17:
1439:
Specularity, Specular
Reflectance. In: Ikeuchi K. (eds) Computer Vision
218:
1706:
Mathematical and computer programming techniques for computer graphics
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Non-electromagnetic waves can also exhibit specular reflection, as in
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from the light source to the surface and the surface normal direction
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It is the same distance behind the mirror as the object is in front.
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Reflection may occur as specular, or mirror-like, reflection and
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Reflections on still water are an example of specular reflection.
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The law of reflection can also be equivalently expressed using
36:
1641:(2nd ed.). Oxford: Oxford University Press. p. 1.
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are the real and imaginary parts of the response due to the
1318:, which is specifically designed for specular reflection.
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of light emerges from the reflecting surface at the same
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signals by flying objects. The measurement technique of
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are used to enhance the specular reflection of atoms.
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Coplanar condition of specular reflection, in which
462:{\displaystyle \mathbf {\hat {d}} _{\mathrm {n} },}
67:. Unsourced material may be challenged and removed.
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999:{\displaystyle \mathbf {\hat {d}} _{\mathrm {n} }}
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500:{\displaystyle \mathbf {\hat {d}} _{\mathrm {s} }}
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421:{\displaystyle \mathbf {\hat {d}} _{\mathrm {i} }}
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1152:. However, if the light strikes the interface at
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343:and the plane defined by both directions is the
1363:. For the efficient reflection of atoms from a
1249:The image in a flat mirror has these features:
1038:quantify the glossy appearance of a surface in
1314:A classic example of specular reflection is a
309:describe the physics at the optical boundary.
1325:, specular reflection can be observed in the
360:The phenomenon of reflection arises from the
8:
1762:Practical linear algebra: a geometry toolbox
1741:Practical linear algebra: a geometry toolbox
1436:Tan, R.T. (2013), Ikeuchi, Katsushi (ed.),
272:Specular reflection from a wet metal sphere
256:Specular reflection may be contrasted with
781:
1568:. Springer Science & Business Media.
1371:are used in order to provide significant
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127:Learn how and when to remove this message
1593:sfn error: no target: CITEREFSelin2008 (
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1245:Mirror image § In three dimensions
176:{\displaystyle \theta _{i}=\theta _{r}}
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280:Diffuse reflection from a marble ball
7:
390:vector. Given an incident direction
65:adding citations to reliable sources
469:the specularly reflected direction
1256:It is the same size as the object.
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843:Householder transformation matrix
1799:(2nd ed.). Addison Wesley.
1758:from the original on 2010-03-07.
1744:. A K Peters. pp. 191–192.
1723:from the original on 2018-01-14.
1481:Sir Thomas Little Heath (1981).
1333:and the reflection of radio- or
1286:will still appear to be turning
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1367:mirror, very cold atoms and/or
1259:It is the right way up (erect).
52:needs additional citations for
726:is a scalar obtained with the
378:Snell's law § Vector form
1:
1508:Stamnes, J. J. (2017-11-13).
1666:. Apress. pp. 105–108.
1638:Optical properties of solids
1562:Iizuka, Keigo (2013-11-11).
957:{\displaystyle \mathbf {I} }
834:{\displaystyle \mathbf {R} }
1672:10.1007/978-1-4842-7185-8_8
27:Mirror-like wave reflection
1840:
1608:Mach, Ernst (2013-01-23).
1535:Mach, Ernst (2013-01-23).
1242:
375:
32:Specular Reflection (song)
29:
1709:. Springer. p. 361.
1451:10.1007/978-0-387-31439-6
1355:which reflect sound, and
1156:, the reflected light is
1065:total internal reflection
1703:Comninos, Peter (2006).
1445:, Springer, Boston, MA,
1408:Reflection (mathematics)
1359:, which reflect neutral
1025:Kramers-Kronig transform
228:states that a reflected
30:Not to be confused with
1614:. Courier Corporation.
1541:. Courier Corporation.
1793:Hecht, Eugene (1987).
1403:Reflection coefficient
1327:ionospheric reflection
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1381:Neutron reflectometry
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305:at the boundary. The
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76:"Specular reflection"
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302:electronic structure
147:
61:improve this article
1664:Ray Tracing Gems II
1057:index of refraction
1051:Internal reflection
1021:Fresnel's equations
922:
738:are represented in
195:Specular reflection
1635:Fox, Mark (2010).
1565:Engineering Optics
1413:Specular highlight
1398:Hamiltonian optics
1373:quantum reflection
1342:x-ray reflectivity
1312:
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372:Vector formulation
345:plane of incidence
341:angle of incidence
314:diffuse reflection
282:
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258:diffuse reflection
248:c. 10–70). Later,
242:Hero of Alexandria
199:regular reflection
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1824:Optical phenomena
1751:978-1-56881-234-2
1716:978-1-85233-902-9
1681:978-1-4842-7185-8
1648:978-0-19-957336-3
1621:978-0-486-17347-4
1575:978-3-662-07032-1
1548:978-0-486-17347-4
1521:978-1-351-40468-6
1494:978-0-486-24074-9
1460:978-0-387-31439-6
1369:grazing incidence
1215:
1120:
1084:
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841:is the so-called
792:
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736:Euclidean vectors
734:. Assuming these
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307:Fresnel equations
264:Law of reflection
226:law of reflection
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16:(Redirected from
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1736:Hansford, Dianne
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1393:Geometric optics
1353:acoustic mirrors
1239:Reflected images
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1734:Farin, Gerald;
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1321:In addition to
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1262:It is reversed.
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941:identity matrix
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747:
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732:different signs
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1377:ridged mirrors
1357:atomic mirrors
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1061:critical angle
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1008:
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984:
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964:and twice the
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388:surface normal
384:linear algebra
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339:is called the
337:surface normal
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78: –
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72:Find sources:
66:
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56:
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50:This article
48:
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1795:
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1767:Google Books
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1144:Polarization
1054:
1046:Consequences
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1016:Reflectivity
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1010:Reflectivity
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509:unit vectors
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117:January 2009
114:
104:
97:
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83:
71:
59:Please help
54:verification
51:
1418:Specularity
1365:solid-state
1346:synchrotron
1040:gloss units
740:column form
728:dot product
362:diffraction
333:wave normal
294:reflectance
1787:References
1778:Hecht 1987
1589:Selin 2008
1331:radiowaves
1292:handedness
1243:See also:
1158:completely
1036:glossmeter
376:See also:
366:wavelength
298:absorption
290:refraction
286:reflection
213:, such as
207:reflection
87:newspapers
1690:238899623
1335:microwave
1296:chirality
1172:θ
1150:polarized
1079:θ
983:^
903:^
882:^
869:−
790:^
760:^
703:^
693:⋅
679:^
630:^
620:⋅
606:^
580:^
567:−
553:^
529:^
484:^
443:^
405:^
217:, from a
201:, is the
165:θ
152:θ
1818:Category
1756:Archived
1738:(2005).
1721:Archived
1387:See also
1348:x-rays.
1302:Examples
352:coplanar
18:Specular
1469:5058976
1267:virtual
250:Alhazen
236:to the
219:surface
101:scholar
1803:
1796:Optics
1748:
1713:
1688:
1678:
1645:
1618:
1572:
1545:
1518:
1491:
1467:
1457:
1316:mirror
1265:It is
1186:arctan
1091:arcsin
819:where
664:where
511:) is:
318:glossy
205:-like
203:mirror
103:
96:
89:
82:
74:
1686:S2CID
1465:S2CID
1443:(PDF)
1424:Notes
1361:atoms
1338:radar
507:(all
325:matte
321:paint
234:angle
215:light
211:waves
197:, or
108:JSTOR
94:books
1801:ISBN
1746:ISBN
1711:ISBN
1676:ISBN
1643:ISBN
1616:ISBN
1595:help
1570:ISBN
1543:ISBN
1516:ISBN
1489:ISBN
1455:ISBN
1288:left
1284:left
1280:down
1278:and
1083:crit
323:and
296:and
288:and
224:The
80:news
1765:at
1668:doi
1447:doi
1329:of
968:of
230:ray
221:.
209:of
63:by
1820::
1754:.
1719:.
1684:.
1674:.
1487:.
1463:,
1453:,
1375:;
1276:up
1063:,
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246:AD
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1211:1
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1183:=
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1096:(
1088:=
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951:I
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865:I
861:=
857:R
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244:(
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156:i
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124:(
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115:(
105:·
98:·
91:·
84:·
57:.
34:.
20:)
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