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spherical form, but rather as ellipsoids of revolution; this second extraordinary medium carries the abnormally refracted ray. By studying the symmetry of the crystal, Huygens was able to determine the direction of the axis of the ellipsoids, and from the refraction properties of the abnormal ray he established the proportion between the axes. He calculated the refraction of rays on plane sections of the crystal other than the natural crystal sides, and ultimately verified many of his results experimentally.
332:, which is independent of the propagation direction inside the crystal, having the same velocity in all directions. The extraordinary ray, on the other hand, has an ellipsoidal wavefront due to its refractive index, which varies with the propagation direction within the crystal, leading to different velocities in different directions. Thus, when light travels through the crystal, it breaks into two wave surfaces that follow distinct paths within it, resulting in two refracted rays being observed.
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The series of step-by-step investigations that follow were meant to corroborate
Huygens' explanation of strange refraction. They were prompted by early objections from Rømer and constitute one of the few examples in Huygens’s work where he provided such details regarding experiments. Huygens employed
310:
Critical to
Huygens’s analysis is that these secondary wavelets can be mathematically constructed, allowing one to work backward from the secondary wavelets to construct a primary wave which has traveled for a certain time. This is the principle on which Huygens's entire theory of light turns, and it
327:
Chapter five addresses the strange refraction of the
Iceland crystal. Huygens cuts a piece of the crystal and studies the geometry of light propagation inside it before guiding the reader through a series of step-by-step empirical investigations. His explanation of strange refraction is based on the
306:
This means that each particle in the ether is the source of a new wavefront, and although these “secondary wavelets” are characterized by
Huygens as “feeble,” points on each wavelet collectively form the primary wave that is visible as light. The new wavefront, then, is the tangential surface to all
251:
Huygens considers that the structure of matter is atomic, made up of an assembly of particles "which touch each other without composing a continuous solid." Light waves can therefore move from one particle to another without these being displaced. Another way of looking at the problem of propagation
211:
was based on three hypotheses: (1) there are inside the crystal two media in which light waves proceed, (2) one medium behaves as ordinary ether and carries the normally refracted ray, and (3) the velocity of the waves in the other medium is dependent on direction, so that the waves do not expand in
263:. He considers that the "shaking" producing light waves necessarily moves at finite speed, even if it is very high. This point is very important because its demonstrations are based on the equivalence of travel times on different paths. Huygens reports on a letter by
203:
created a puzzle regarding the physics of refraction that
Huygens wanted to solve. Huygens eventually was able to solve this problem by means of elliptical waves in 1677 and confirmed his theory by experiments mostly after critical reactions in 1679.
252:
is to consider that it is not the particles of the transparent medium which transmit light but the particles of ethereal matter which permeate the interstices of the solid or liquid matter (or even a vacuum, since light passes through the top of
319:
Chapter two briefly treats reflection while chapters three and four explore refraction. Huygens carefully explains the differences between transparent and opaque media in terms of their particulate composition, specifically exploring
416:(1818). Fresnel subsequently became aware of Huygens's work and adapted Huygens's principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in 1821. The principle is now known as the
298:, the foundation of what became known as Huygens’ Principle. His principle of propagation is a demonstration of how a wave of light (or rather a pulse) emanating from a point also results in smaller wavelets:
374:, and simple and double refraction from the rate of propagation of light waves alone. By reducing the ray to a geometrical construct devoid of physical character, Huygens was able to treat the theory of light
267:, dated from 1677, where the speed of light is said to be at least 100,000 times faster than the speed of sound, and possibly six times higher. In the latter case, the speed found by Rømer (214,000
901:
302:...each of these waves can be infinitely feeble only as compared with the , to the composition of which all the others contribute by the part of their surface which is most distant from .
248:
and which is different from that which propagates sound. This ethereal matter is composed of elastic particles of matter which collide according to laws he discovered in 1669.
385:, which occurs if the refracted ray is directed through a second crystal of which the orientation is varied. He also did not address a number of issues, such as
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these mathematical and experimental resources to achieve impressive results, some of which defied verification until the beginning of the 19th century.
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Shapiro, A. E. (1980). Huygens' kinematic theory of light. In H.J.M. Bos, M.J.S. Rudwick, H.A.M. Snelders, & R.P.W. Visser (Eds.),
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In the first chapter, Huygens describes light as a disturbance which moves in a material medium of an unknown nature which he calls
196:
147:, Huygens conceived of light as an irregular series of shock waves which proceeds with very great, but finite, velocity through the
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Another concept discussed in the first chapter is the speed of light, where
Huygens originally takes up the temporal conception of
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Although the completeness of
Huygens's analysis is impressive, he was unable to comprehend the effect that we now recognize as
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properties of the ordinary ray and the extraordinary ray. The ordinary ray has a spherical wavefront due to a constant
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Following his remarks on the propagation medium and the speed of light, Huygens gives a geometric illustration of the
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but decided to separate his theory of light from the rest of the work at the last minute, marking the transition from
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Traité de la Lumière: Où sont expliquées les causes de ce qui luy arrive dans la reflexion & dans la refraction
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were largely forgotten in the century after its publication. Many of these ideas were developed independently by
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256:). Finally, Huygens considers a third type of light propagation that would be a combination of the first two.
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393:, both of which were explained by Newton, although he had experienced them while building his telescopes.
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Shapiro, A. E. (1973). Kinematic optics: A study of the wave theory of light in the seventeenth century.
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Chapter six of the book concludes with a discussion on refraction and reflection in transparent bodies.
95:
Treatise on Light: In Which Are
Explained the Causes of That Which Occurs in Reflection & Refraction
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Lenses and Waves: Christiaan
Huygens and the Mathematical Science of Optics in the Seventeenth Century
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that was published in French in 1690. The book describes
Huygens's conception of the nature of
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is itself the origin of a secondary spherical wave, a principle known today as the
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682:"How did the wave theory of light take shape in the mind of Christiaan Huygens?"
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and others fifteen years to reconstruct Huygens's ideas of rays and wavefronts.
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is the demonstration that one could derive all the essential features of
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Pure and Applied Optics: Journal of the European Optical Society Part A
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713:"Huygens' Methods for Determining Optical Parameters in Birefringence"
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is what separates his theory from those of his predecessors.
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work. In 1672, the problem of the strange refraction of the
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Christiaan Huygens: The construction of texts and audiences
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Polarization of Light with Applications in Optical Fibers
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Theoremata de Quadratura Hyperboles, Ellipsis et Circuli
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the secondary wavelets in the direction of propagation.
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C. Huygens (translated by Silvanus P. Thompson, 1912),
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Huygens intended to publish his results as part of the
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in the early 19th century and later published in his
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794:. Translated by Thompson, S. P. Project Gutenberg.
598:"Christiaan Huygens and the foundations of optics"
995:C. Huygens (translated by Silvanus P. Thompson),
490:Notes and Records of the Royal Society of London
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117:which makes it possible to explain the laws of
163:. The book is considered a pioneering work of
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961:. University of Chicago Press. pp. 3–6.
155:. Moreover, he proposed that each point of a
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1001:archive.org/details/treatiseonlight031310mbp
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549:Complete Dictionary of Scientific Biography
460:Theories of Light, from Descartes to Newton
227:. More than a century later, it would take
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775:(pp. 200-220). Swets & Zeitlinger B.V.
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943:Archive for History of Exact Sciences, 11
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283:Huygens's illustration of a wavefront in
908:, vol. TT90, SPIE, pp. 47–75,
900:Kumar, Arun; Ghatak, Ajoy (2011-01-25),
414:Mémoire sur la Diffraction de la Lumière
171:and the first mechanistic account of an
991:archive.org/details/bub_gb_kVxsaYdZaaoC
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36:Ibn al-Haytham § Optical treatises
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362:Huygens's major accomplishment in the
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183:Huygens worked on the mathematics of
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958:The Rise of the Wave Theory of Light
902:"Double Refraction and Applications"
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570:. Archimedes. Springer Netherlands.
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989:, Leiden: Pieter van der Aa, 1690;
755:Titan - From discovery to encounter
815:(pp. 241-253). Indiana University.
130:, which Huygens aimed to replace.
25:
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638:Dijksterhuis, Fokko Jan (2004).
564:Dijksterhuis, Fokko Jan (2004).
1369:Historical physics publications
1079:De Circuli Magnitudine Inventa
1:
773:Studies on Christiaan Huygens
680:Ziggelaar, Augustine (1980).
141:, which was presented in the
106:) is a book written by Dutch
1132:Huygens' law of the pendulum
1085:De Ratiociniis in Ludo Aleae
788:Huygens, Christiaan (2005).
749:Dijksterhuis, F. J. (2004).
463:. CUP Archive. p. 186.
1384:Books by Christiaan Huygens
1014:, Project Gutenberg, 2005,
999:, London: Macmillan, 1912;
656:10.1080/0003379021000041884
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1225:Horologium (constellation)
1124:Discoveries and inventions
1016:gutenberg.org/ebooks/14725
852:10.1038/s41598-021-99049-7
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27:Book by Christiaan Huygens
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1276:Gottfried Wilhelm Leibniz
1210:Huygens-Fokker Foundation
1142:Huygens-Fresnel principle
729:10.1007/s00407-006-0115-7
711:Buchwald, Jed Z. (2007).
698:10.1080/00033798000200181
622:10.1088/0963-9659/4/6/004
418:Huygens–Fresnel Principle
404:, Huygens's ideas in the
161:Huygens–Fresnel principle
46:
1374:17th-century Dutch books
1098:Horologium Oscillatorium
955:Buchwald, J. Z. (1989).
825:Anderson, F. L. (2021).
1266:Antonie van Leeuwenhoek
1152:Huygens–Steiner theorem
484:Shapiro, A. E. (1989).
368:rectilinear propagation
275:Nature of the wavefront
1230:Prix Descartes-Huygens
543:Bos, H. J. M. (1973).
502:10.1098/rsnr.1989.0016
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322:atmospheric refraction
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254:Torricelli's barometer
187:and the properties of
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1379:French-language books
1296:Augustin-Jean Fresnel
410:Augustin-Jean Fresnel
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315:Remainder of the book
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265:Ole Christensen Rømer
175:physical phenomenon.
30:For Ibn al-Haytham's
1106:Traité de la Lumiére
987:Traité de la Lumière
914:10.1117/3.861761.ch4
596:Kubbinga, H (1995).
457:A. I. Sabra (1981).
387:chromatic aberration
169:mathematical physics
18:Traité de la Lumière
1137:Huygens' lemniscate
843:2021NatSR..1120257A
811:Howard, N. (2003).
614:1995PApOp...4..723K
545:Huygens, Christiaan
435:Luminiferous aether
207:His explanation of
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1199:Christiaan Huygens
1057:Christiaan Huygens
831:Scientific Reports
751:Huygens and optics
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240:Propagation medium
139:corpuscular theory
119:geometrical optics
111:Christiaan Huygens
60:Christiaan Huygens
42:Treatise on Light
1364:History of optics
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1091:Systema Saturnium
1012:Treatise on Light
997:Treatise on Light
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791:Treatise on Light
686:Annals of Science
644:Annals of Science
577:978-1-4020-2697-3
470:978-0-521-28436-3
406:Treatise on Light
364:Treatise on Light
355:in the manner of
285:Treatise on Light
115:light propagation
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1291:Denis Papin
1215:Huygens Gap
396:Apart from
221:geometrical
165:theoretical
153:sound waves
123:Descartes's
1354:1690 books
1348:Categories
945:, 134-266.
929:2023-12-10
441:References
372:reflection
353:refraction
189:refraction
185:light rays
127:Dioptrique
1389:Treatises
1320:Wikiquote
887:238746979
861:2045-2322
737:122012266
664:123111713
526:145336637
510:0035-9149
296:wavefront
246:ethereal,
217:Dioptrica
193:Dioptrica
157:wavefront
121:shown in
84:Published
879:34642401
424:See also
235:Contents
179:Overview
108:polymath
66:Language
1183:Huygens
870:8511121
839:Bibcode
610:Bibcode
357:Huygens
144:Opticks
133:Unlike
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135:Newton
100:French
78:Optics
69:French
56:Author
34:, see
1185:probe
1018:(and
1003:(and
883:S2CID
733:S2CID
660:S2CID
522:S2CID
514:JSTOR
391:color
351:Wave
269:km /s
149:ether
74:Genre
963:ISBN
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875:PMID
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400:and
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