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1012:. 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
648:
293:
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
316:
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
506:
923:
1262:
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
803:
713:
305:. 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
1222:
1127:
643:{\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),}
241:
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.
1008:
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
840:
456:
993:
494:
415:
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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
1016:. 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.
273:
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
339:
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
170:
1709:
951:
828:
737:
229:
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
656:
1598:
1155:
1062:
1299:
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.
1525:
320:
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 (
1333:
exploits specular reflectivity to study thin films and interfaces with sub-nanometer resolution, using either modern laboratory sources or
96:
68:
918:{\displaystyle \mathbf {R} =\mathbf {I} -2\mathbf {\hat {d}} _{\mathrm {n} }\mathbf {\hat {d}} _{\mathrm {n} }^{\mathrm {T} };}
1498:
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1635:
1608:
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1508:
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uses specular reflection to study material surfaces and thin film interfaces in an analogous fashion to x-ray reflectivity.
75:
49:
1651:
Haines, Eric (2021). "Chapter 8: Reflection and
Refraction Formulas". In Marrs, Adam; Shirley, Peter; Wald, Ingo (eds.).
420:
960:
461:
382:
257:
1793:
1744:
115:
82:
357:, then the electromagnetic fields at the boundary are oscillating exactly in phase only for the specular direction.
1019:
Measurement of specular reflection is performed with normal or varying incidence reflection spectrophotometers (
64:
346:
When the light impinges perpendicularly to the surface, it is reflected straight back in the source direction.
53:
135:
1357:
329:
1426:
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20:
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798:{\displaystyle \mathbf {\hat {d}} _{\mathrm {s} }=\mathbf {R} \;\mathbf {\hat {d}} _{\mathrm {i} },}
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1013:
1137:
When light strikes an interface between two materials, the reflected light is generally partially
934:
811:
1345:
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1049:
281:, are expressed by the difference of the refractive index on both sides of the boundary, whereas
89:
42:
1258:, meaning that the image appears to be behind the mirror, and cannot be projected onto a screen.
1391:
1315:
1233:
1009:
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1500:
Waves in Focal
Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves
1369:
324:). When a ray encounters a surface, the angle that the wave normal makes with respect to the
1287:
of the image may change. For example, the image of a right shoe will look like a left shoe.
1283:
of the coordinate system, one axis of the coordinate system appears to be reversed, and the
1783:
1138:
366:
290:
274:
195:
1044:
When light is propagating in a material and strikes an interface with a material of lower
708:{\displaystyle \mathbf {\hat {d}} _{\mathrm {n} }\cdot \mathbf {\hat {d}} _{\mathrm {i} }}
8:
1353:
1142:
1045:
286:
1023:) using a scanning variable-wavelength light source. Lower quality measurements using a
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1453:
1401:
1386:
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1330:
1217:{\displaystyle \theta _{\mathrm {B} }=\arctan \!\left({\frac {n_{2}}{n_{1}}}\right)\!.}
831:
333:
302:
246:
230:
1122:{\displaystyle \theta _{\text{crit}}=\arcsin \!\left({\frac {n_{2}}{n_{1}}}\right)\!.}
1056:
occurs: all of the light is reflected. The critical angle can be shown to be given by
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1734:
1699:
1678:
1664:
1631:
1604:
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375:. 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
1750:
1724:
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1471:
1341:
929:
720:
313:
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1295:
1048:, some of the light is reflected. If the angle of incidence is greater than the
731:, the equation can be equivalently expressed as a matrix-vector multiplication:
376:
372:
325:
317:
efficiently. The reflecting material of mirrors is usually aluminum or silver.
238:
226:
1439:
249:, in which light is scattered away from the surface in a range of directions.
1806:
1365:
1311:
954:
728:
1600:
The
Principles of Physical Optics: An Historical and Philosophical Treatment
1527:
The
Principles of Physical Optics: An Historical and Philosophical Treatment
1755:
1149:
linearly polarized parallel to the interface. Brewster's angle is given by
1004:
719:. Different authors may define the incident and reflection directions with
218:
1728:
1473:
A history of Greek mathematics. Volume II: From
Aristarchus to Diophantus
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1334:
1028:
716:
497:
350:
282:
234:
175:
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if a person stands under it and looks up at it. Similarly a car turning
336:. Reflection of the incident ray also occurs in the plane of incidence.
1428:
Specularity, Specular
Reflectance. In: Ikeuchi K. (eds) Computer Vision
1024:
354:
278:
1695:
Mathematical and computer programming techniques for computer graphics
1340:
Non-electromagnetic waves can also exhibit specular reflection, as in
417:
from the light source to the surface and the surface normal direction
1323:
1319:
1242:
It is the same distance behind the mirror as the object is in front.
128:
31:
340:
301:
Reflection may occur as specular, or mirror-like, reflection and
207:
179:
Reflections on still water are an example of specular reflection.
1304:
371:
The law of reflection can also be equivalently expressed using
306:
191:
1326:
309:
222:
203:
1630:(2nd ed.). Oxford: Oxford University Press. p. 1.
289:
are the real and imaginary parts of the response due to the
1349:
199:
1307:, which is specifically designed for specular reflection.
221:
of light emerges from the reflecting surface at the same
1329:
signals by flying objects. The measurement technique of
1469:
1368:
are used to enhance the specular reflection of atoms.
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Coplanar condition of specular reflection, in which
451:{\displaystyle \mathbf {\hat {d}} _{\mathrm {n} },}
56:. Unsourced material may be challenged and removed.
1216:
1121:
988:{\displaystyle \mathbf {\hat {d}} _{\mathrm {n} }}
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945:
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822:
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707:
642:
489:{\displaystyle \mathbf {\hat {d}} _{\mathrm {s} }}
488:
450:
410:{\displaystyle \mathbf {\hat {d}} _{\mathrm {i} }}
409:
164:
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1177:
1141:. However, if the light strikes the interface at
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332:and the plane defined by both directions is the
1352:. For the efficient reflection of atoms from a
1238:The image in a flat mirror has these features:
1027:quantify the glossy appearance of a surface in
1303:A classic example of specular reflection is a
298:describe the physics at the optical boundary.
1722:
1314:, specular reflection can be observed in the
349:The phenomenon of reflection arises from the
1751:Practical linear algebra: a geometry toolbox
1730:Practical linear algebra: a geometry toolbox
1425:Tan, R.T. (2013), Ikeuchi, Katsushi (ed.),
261:Specular reflection from a wet metal sphere
245:Specular reflection may be contrasted with
770:
1557:. Springer Science & Business Media.
1360:are used in order to provide significant
116:Learn how and when to remove this message
1691:
1582:sfn error: no target: CITEREFSelin2008 (
1294:
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1234:Mirror image § In three dimensions
165:{\displaystyle \theta _{i}=\theta _{r}}
1805:
1650:
1550:
1039:
1781:
1766:
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269:Diffuse reflection from a marble ball
1596:
1523:
379:vector. Given an incident direction
252:
54:adding citations to reliable sources
25:
1623:
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458:the specularly reflected direction
13:
1245:It is the same size as the object.
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832:Householder transformation matrix
1788:(2nd ed.). Addison Wesley.
1747:from the original on 2010-03-07.
1733:. A K Peters. pp. 191–192.
1712:from the original on 2018-01-14.
1470:Sir Thomas Little Heath (1981).
1322:and the reflection of radio- or
1275:will still appear to be turning
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1356:mirror, very cold atoms and/or
1248:It is the right way up (erect).
1132:
1034:
998:
41:needs additional citations for
1644:
1617:
1590:
1544:
1517:
1490:
1463:
1418:
715:is a scalar obtained with the
367:Snell's law § Vector form
1:
1775:
1497:Stamnes, J. J. (2017-11-13).
1655:. Apress. pp. 105–108.
1627:Optical properties of solids
1551:Iizuka, Keigo (2013-11-11).
946:{\displaystyle \mathbf {I} }
823:{\displaystyle \mathbf {R} }
7:
1661:10.1007/978-1-4842-7185-8_8
1375:
1290:
16:Mirror-like wave reflection
10:
1829:
1597:Mach, Ernst (2013-01-23).
1524:Mach, Ernst (2013-01-23).
1231:
364:
21:Specular Reflection (song)
18:
1698:. Springer. p. 361.
1440:10.1007/978-0-387-31439-6
1344:which reflect sound, and
1145:, the reflected light is
1054:total internal reflection
1692:Comninos, Peter (2006).
1434:, Springer, Boston, MA,
1412:
1397:Reflection (mathematics)
1348:, which reflect neutral
1014:Kramers-Kronig transform
217:states that a reflected
19:Not to be confused with
1603:. Courier Corporation.
1530:. Courier Corporation.
1782:Hecht, Eugene (1987).
1392:Reflection coefficient
1316:ionospheric reflection
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1370:Neutron reflectometry
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294:at the boundary. The
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65:"Specular reflection"
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291:electronic structure
136:
50:improve this article
1653:Ray Tracing Gems II
1046:index of refraction
1040:Internal reflection
1010:Fresnel's equations
911:
727:are represented in
184:Specular reflection
1624:Fox, Mark (2010).
1554:Engineering Optics
1402:Specular highlight
1387:Hamiltonian optics
1362:quantum reflection
1331:x-ray reflectivity
1301:
1214:
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361:Vector formulation
334:plane of incidence
330:angle of incidence
303:diffuse reflection
271:
263:
247:diffuse reflection
237:c. 10–70). Later,
231:Hero of Alexandria
188:regular reflection
181:
173:
162:
1813:Optical phenomena
1740:978-1-56881-234-2
1705:978-1-85233-902-9
1670:978-1-4842-7185-8
1637:978-0-19-957336-3
1610:978-0-486-17347-4
1564:978-3-662-07032-1
1537:978-0-486-17347-4
1510:978-1-351-40468-6
1483:978-0-486-24074-9
1449:978-0-387-31439-6
1358:grazing incidence
1204:
1109:
1073:
974:
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830:is the so-called
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751:
725:Euclidean vectors
723:. Assuming these
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296:Fresnel equations
253:Law of reflection
215:law of reflection
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1725:Hansford, Dianne
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1382:Geometric optics
1342:acoustic mirrors
1228:Reflected images
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1143:Brewster's angle
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928:in terms of the
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34:
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1803:
1802:
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1778:
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1723:Farin, Gerald;
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1671:
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1622:
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1595:
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1580:, p. 1817.
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1484:
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1310:In addition to
1293:
1251:It is reversed.
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978:
977:
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936:
933:
932:
930:identity matrix
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904:
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784:
773:
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739:
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721:different signs
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1769:, p. 100.
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1366:ridged mirrors
1346:atomic mirrors
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1129:
1118:
1113:
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1096:
1092:
1086:
1081:
1078:
1069:
1050:critical angle
1041:
1038:
1036:
1033:
1000:
997:
981:
973:
970:
953:and twice the
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926:
925:
914:
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893:
890:
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869:
862:
859:
855:
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834:, defined as:
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377:surface normal
373:linear algebra
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359:
328:is called the
326:surface normal
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29:
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1795:0-201-11609-X
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67: –
66:
62:
61:Find sources:
55:
51:
45:
44:
39:This article
37:
33:
28:
27:
22:
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1762:
1756:Google Books
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1133:Polarization
1043:
1035:Consequences
1020:
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1005:Reflectivity
1003:
1002:
999:Reflectivity
927:
807:
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498:unit vectors
370:
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106:January 2009
103:
93:
86:
79:
72:
60:
48:Please help
43:verification
40:
1407:Specularity
1354:solid-state
1335:synchrotron
1029:gloss units
729:column form
717:dot product
351:diffraction
322:wave normal
283:reflectance
1776:References
1767:Hecht 1987
1578:Selin 2008
1320:radiowaves
1281:handedness
1232:See also:
1147:completely
1025:glossmeter
365:See also:
355:wavelength
287:absorption
279:refraction
275:reflection
202:, such as
196:reflection
76:newspapers
1679:238899623
1324:microwave
1285:chirality
1161:θ
1139:polarized
1068:θ
972:^
892:^
871:^
858:−
779:^
749:^
692:^
682:⋅
668:^
619:^
609:⋅
595:^
569:^
556:−
542:^
518:^
473:^
432:^
394:^
206:, from a
190:, is the
154:θ
141:θ
1807:Category
1745:Archived
1727:(2005).
1710:Archived
1376:See also
1337:x-rays.
1291:Examples
341:coplanar
1458:5058976
1256:virtual
239:Alhazen
225:to the
208:surface
90:scholar
1792:
1785:Optics
1737:
1702:
1677:
1667:
1634:
1607:
1561:
1534:
1507:
1480:
1456:
1446:
1305:mirror
1254:It is
1175:arctan
1080:arcsin
808:where
653:where
500:) is:
307:glossy
194:-like
192:mirror
92:
85:
78:
71:
63:
1675:S2CID
1454:S2CID
1432:(PDF)
1413:Notes
1350:atoms
1327:radar
496:(all
314:matte
310:paint
223:angle
204:light
200:waves
186:, or
97:JSTOR
83:books
1790:ISBN
1735:ISBN
1700:ISBN
1665:ISBN
1632:ISBN
1605:ISBN
1584:help
1559:ISBN
1532:ISBN
1505:ISBN
1478:ISBN
1444:ISBN
1277:left
1273:left
1269:down
1267:and
1072:crit
312:and
285:and
277:and
213:The
69:news
1754:at
1657:doi
1436:doi
1318:of
957:of
219:ray
210:.
198:of
52:by
1809::
1743:.
1708:.
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1476:.
1452:,
1442:,
1364:;
1265:up
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235:AD
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1200:1
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1180:(
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1077:=
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969:d
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907:T
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889:d
879:n
868:d
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854:I
850:=
846:R
817:R
793:,
787:i
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767:R
763:=
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689:d
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627:i
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584:(
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233:(
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113:(
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104:(
94:·
87:·
80:·
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46:.
23:.
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