|
<!-- EDIT BELOW THIS LINE -->
The term '''''plane of polarization''''' refers to the direction of [[polarization (waves)|polarization]] of [[linear polarization|linearly-polarized]] light or other [[electromagnetic radiation]]. Unfortunately the term is used with two contradictory meanings. As originally defined by [[Étienne-Louis Malus]] in 1811, the plane of polarization happened to coincide with the plane containing the direction of propagation and the ''magnetic'' vector; but this was not known at the time. In modern literature, the term ''plane of polarization'', if it is used at all, more often refers to the plane containing the direction of propagation and the ''electric'' vector, because the electric field has the greater propensity to interact with matter. That propensity, together with Malus's definition and [[Augustin-Jean Fresnel|Fresnel]]'s speculations on the [[luminiferous aether]], led early investigators to define the "plane of ''vibration''" as perpendicular to the plane of polarization and containing the direction of propagation.
This history must be taken into account when interpreting the term ''plane of polarization'' in existing literature. Sometimes the meaning can only be inferred from the context. In original writing, confusion can be avoided by specifying the orientation of a particular vector.<br style="margin-bottom: 1ex;" />
'''This page is UNDER CONSTRUCTION. Beware of loose bricks{{hsp}}!'''
== Physics of the term ==
[[File:EM-Wave.gif|thumb|Linearly-polarized (plane-polarized) electromagnetic wave, propagating in the ''x'' direction (the ''ray'' direction), with the electric field '''E''' in the ''y'' direction (vertical) and the magnetic fields '''B''' and '''H''' in the ''z'' direction (horizontal).<br style="margin-bottom: .6ex;" />In an isotropic medium, the '''D''' field is in the same direction as the '''E''' field, and the wave-normal direction is the same as the ray direction, and the ''plane of polarization'' as originally defined by Malus is the ''xz'' plane, which is normal to the '''D''' field.<br style="margin-bottom: .6ex;" />In a double-refracting crystal, the '''D''' direction and the wave-normal direction are still in the ''xy'' plane, and still perpendicular to each other; but there is generally a small angle between '''E''' and '''D''', hence the same angle between the ray and the wave-normal; and the ''plane of polarization'' as originally defined is generally no longer the ''xz'' plane, but is still the plane normal to the '''D''' field.<br style="margin-bottom: .6ex;" />In either case, the plane of ''vibration'' as defined by Fresnel is the ''xy'' plane. But ''modern'' authors tend to identify that plane as the plane of polarization!]]
{{Redirect|Fresnel}}
For [[electromagnetic radiation|electromagnetic (EM) waves]] in an ''isotropic'' medium (that is, a medium whose properties are independent of direction), the [[electric field]] [[Euclidean vector|vectors]] ('''E''' and '''D''') are in one direction, and the [[magnetic field]] vectors ('''H''' and '''B''') are in another direction, perpendicular to the first, and the direction of propagation is perpendicular to both the electric and the magnetic vectors. In this case the direction of propagation is both the ''ray'' direction and the ''wave-normal'' direction (the direction perpendicular to the [[wavefront]]). For a [[linear polarization|''linearly''-polarized]] wave (also called a ''plane''-polarized wave), the orientations of the field vectors are fixed.
{{Infobox scientist
| name = Augustin-Jean Fresnel
| image = Augustin Fresnel.jpg
| birth_date = {{Birth date|df=yes|1788|5|10}}
| birth_place = [[Broglie, Eure|Broglie]], [[Kingdom of France]] (now [[Eure]], France)
| death_date = {{death date and age|df=yes|1827|7|14|1788|5|10}}
| death_place = [[Ville-d'Avray]], [[Bourbon Restoration|Kingdom of France]] (now [[Hauts-de-Seine]], France),
| death_cause = of [[Tuberculosis]]
| resting_place = [[Père Lachaise Cemetery]]
| residence = [[France]]
| nationality = [[France|French]]
| fields = [[Physics]], [[Engineering]]
| workplaces = {{ublist
| [[Corps of Bridges, Waters and Forests|Corps des Ponts]]
| [[Athénée de Luxembourg|Athénée]] ({{smaller|1819}}){{r|brock-1909}}
| [[École Polytechnique|École Polytech.]] ({{smaller|1821–4}})}}
| education = {{ublist
| [[École Polytechnique|École Polytech.]] ({{smaller|1804–6}})
| [[École des ponts ParisTech|École des Ponts]]}}
| known_for = {{ublist
| [[Birefringence]]
| [[Diffraction]]
| [[Fresnel–Arago laws]]
| [[Fresnel equations]]
| [[Fresnel integral]]s
| [[Fresnel lens]]
| [[Fresnel number]]
| [[Fresnel rhomb]]
| [[Fresnel zone]]
| [[Huygens–Fresnel principle]]
| [[Phasor]] representation
| [[Polarization]]
| [[Physical optics|Wave optics]]}}
| influences = {{ublist
| [[Christiaan Huygens]]
| [[Thomas Young (scientist)|Thomas Young]]
| [[François Arago]]}}
| influenced = {{ublist
| [[James MacCullagh]]
| [[William Rowan Hamilton]]
| [[Humphrey Lloyd (physicist)|Humphrey Lloyd]]}}
| awards = {{ublist
| {{small|1819:}} [[French Academy of Sciences|Academy]] Grand Prix
| {{small|1824:}} ''[[Legion of Honour|Légion d'Honneur]]''
| {{small|1825:}} [[Fellow of the Royal Society|ForMemRS]]
| {{small|1827 for '24: }}[[Rumford Medal]]}}
}}
Because innumerable materials are [[dielectric]]s or [[electrical conductor|conductors]] while comparatively few are [[ferromagnetism|ferromagnets]], the [[reflection (physics)|reflection]] or [[refraction]] of EM waves (including [[light]]) is more often due to differences in the ''electric'' properties of media than to differences in their magnetic properties. That circumstance tends to draw attention to the ''electric'' vectors, so that we tend to think of the direction of polarization as the direction of the electric vectors, and the "plane of polarization" as the plane containing the electric vectors and the direction of propagation.
'''Augustin-Jean Fresnel''' ({{IPAc-en|f|r|eɪ|ˈ|n|ɛ|l}}, {{respell|fray|NEL|'}}; {{IPA-fr|ɔ.ɡy.stɛ̃ ʒɑ̃ fʁɛ.nɛl|lang}}; 10 May 1788 – 14 July 1827) was a [[France|French]] civil [[engineer]] and [[physicist]] whose research in [[optics]] led to the almost universal acceptance of the wave theory of light, and the rejection of any remnant of [[Isaac Newton|Newton]]'s [[corpuscular theory of light|corpuscular theory]], from the 1830s<ref>Darrigol, 2012, pp.{{nnbsp}}220–23.</ref> until the end of the 19th century.
[[File:Screen dish antenna.jpg|thumb|left|Vertically-polarized parabolic-grid [[microwave]] antenna. In this case the stated polarization refers to the alignment of the electric ('''E''') field, hence the alignment of the closely spaced metal ribs in the reflector.]]
But he is perhaps better known for inventing the ''catadioptric'' (reflective/refractive) [[Fresnel lens]] and for pioneering the use of "stepped" lenses to extend the visibility of [[lighthouse]]s, saving unknown numbers of lives at sea. The simpler ''dioptric'' (purely refractive) stepped lens, first proposed by [[Georges-Louis Leclerc, Comte de Buffon|Count Buffon]]{{r|chisholm-1911-lighthouse}} and independently reinvented by Fresnel, is used in screen [[magnifying glass|magnifiers]] and in condenser lenses for [[overhead projector|overhead projectors]].
Indeed, that is the convention used in the online ''Encyclopædia Britannica'',{{r|luntz}} and in [[Richard Feynman|Feynman]]'s lecture on polarization.{{r|feynman-1963}} In the latter case one must infer the convention from the context: Feynman keeps emphasizing the direction of the ''electric'' ('''E''') vector and leaves the reader to presume that the "plane of polarization" contains that vector — and this interpretation indeed fits the examples he gives. The same vector is used to describe the polarization of radio signals and [[antenna (radio)#Polarization|antennas]].
By expressing [[Christiaan Huygens|Huygens]]' principle of secondary waves and [[Thomas Young (scientist)|Young]]'s principle of [[interference (wave propagation)|interference]] in quantitative terms, and supposing that simple colors consist of ''[[sine wave|sinusoidal]]'' waves, Fresnel gave the first satisfactory explanation of [[diffraction]] by straight edges, including the first explanation of rectilinear propagation that would satisfy a modern physicist.<ref>Darrigol, 2012, p.{{hsp}}205.</ref> By further supposing that light waves are purely ''[[transverse wave|transverse]]'', he explained the nature of [[polarization]] and lack thereof, the mechanism of ''chromatic polarization'' (the colors produced when polarized light is passed through a slice of doubly-refractive crystal followed by a second polarizer), and the [[transmission coefficient|transmission]] and [[reflection coefficient]]s at a boundary between transparent [[isotropy|isotropic]] media (including [[Brewster's angle]]). Then, by generalizing the relationship between wave speed and polarization for [[calcite]], he accounted for the directions and polarizations of the refracted rays in [[birefringence|doubly-refractive]] crystals of the ''biaxial'' class (those for which Huygens' secondary wavefronts are not axisymmetric). The period between the first publication of his pure-transverse-wave hypothesis and the presentation of his solution to the biaxial problem was less than a year. Later, by allowing the reflection coefficient to be ''[[complex number|complex]]'', he accounted for the change in polarization due to [[total internal reflection]], as exploited in the [[Fresnel rhomb]]. Defenders of the established corpuscular theory could not match his quantitative explanations of so many phenomena on so few assumptions.
If the medium is magnetically isotropic but electrically ''non''-isotopic (like a [[birefringence|double-refracting]] crystal), the magnetic vectors '''H''' and '''B''' are still parallel, and the electric vectors '''E''' and '''D''' are still perpendicular to both, and the ray direction is still perpendicular to '''E''' and the magnetic vectors, and the wave-normal direction is still perpendicular to '''D''' and the magnetic vectors; but there is generally a small angle between the electric vectors '''E''' and '''D''', hence the same angle between the ray direction and the wave-normal direction.{{r|lunney-weaire-2006|p=26–7}} Hence '''D''', '''E''', the wave-normal direction, and the ray direction are all in the same plane, and it is all the more natural to define that plane as the "plane of polarization".
Fresnel's legacy is the more remarkable in view of his lifelong battle with [[tuberculosis]], to which he succumbed at the age of 39. Although he did not become a public celebrity in his short lifetime, he lived just long enough to receive due recognition from his peers, including (on his deathbed) the [[Rumford Medal]] of the [[Royal Society of London]], and his name recurs frequently in the modern terminology of optics and waves.
This "natural" definition of the plane of polarization depends on the theory of EM waves developed by [[James Clerk Maxwell|Maxwell]] in the 1860s. But the word ''polarization'' was coined about 50 years earlier, and the associated mystery dates back even further.
Inevitably, after the wave theory of light was subsumed by [[James Clerk Maxwell|Maxwell]]'s [[electromagnetism|electromagnetic]] theory in the 1860s and '70s, the magnitude of Fresnel's contribution was somewhat obscured. In the period between Fresnel's unification of physical optics and Maxwell's wider unification, a contemporary authority, Professor [[Humphrey Lloyd (physicist)|Humphrey Lloyd]], described Fresnel's transverse-wave theory as "the noblest fabric which has ever adorned the ___domain of physical science, Newton's system of the universe alone excepted."{{r|lloyd-1841}}<br style="margin-bottom: 1ex;" />
== EarlyHistory lifeof the term ==
Polarization was discovered — but not named or understood — by [[Christiaan Huygens|Huygens]], as he investigated the [[birefringence|double refraction]] of "Iceland crystal" (transparent [[calcite]], now called [[Iceland spar]]). The essence of his discovery, published in his ''Treatise on Light'' (1690), was as follows. When a ray (meaning a narrow beam of light) passes through two similarly oriented calcite crystals at normal (perpendicular) incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second. But when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa. At intermediate positions of the second crystal, each ray emerging from the first is doubly refracted by the second, giving four rays in total; and as the crystal is rotated from the initial orientation to the perpendicular one, the brightnesses of the rays vary, giving a smooth transition between the extreme cases in which there are only two final rays.{{r|huygens-1690|p=92–4}}
[[File:Augustin Fresnel buste Broglie.jpg|thumb|Monument to Augustin Fresnel on the facade of his birthplace at 2 Rue Augustin Fresnel, [[Broglie, Eure|Broglie]] (facing Rue Jean François Mérimée),{{r|martan-2014}} inaugurated on 14 September 1884.{{r|bibmed|academie}} The inscription, when translated, says:<br style="margin-bottom: 0.6ex;" />"Augustin Fresnel, engineer of Bridges and Roads, member of the Academy of Sciences, creator of lenticular lighthouses, was born in this house on 10 May 1788. The theory of light owes to this emulator of Newton the highest concepts and the most useful applications."{{r|martan-2014|perchet-2011}}]]
Huygens defined a ''principal section'' of a calcite crystal as a plane normal to a natural surface and parallel to the axis of the obtuse solid angle.{{r|huygens-1690|p=55–6}} This axis was parallel to the axes of the [[spheroid]]al [[Huygens–Fresnel principle|secondary waves]] by which he (correctly) explained the directions of the extraordinary refraction.
=== Family ===
Augustin-Jean Fresnel (also called Augustin Jean or simply Augustin), born in [[Broglie, Eure|Broglie]], [[Normandy]], on 10 May 1788, was the second of four sons of the architect Jacques Fresnel (1755–1805){{r|favre}} and his wife Augustine, ''née'' Mérimée (1755?–1833).{{r|jeanelie}} In 1790, following the [[French Revolution|Revolution]], Broglie became part of the [[Departments of France|département]] of [[Eure]]. The family moved twice — in 1790 to [[Cherbourg-Octeville|Cherbourg]],<ref>Levitt, 2013, p.{{hsp}}23.</ref> and in 1794{{r|silliman-2008|p=166}} to Jacques' home town of [[Mathieu, Calvados|Mathieu]], where Madame Fresnel remained as a widow,{{r|boutry-1948|p=590}} outliving two of her sons.
The first son, Louis (1786–1809), was admitted to the [[École Polytechnique]], became a lieutenant in the artillery, and was killed at [[Jaca]], [[Spain]], the day before his 23rd birthday.{{r|jeanelie}} The third, Léonor (1790–1869),{{r|favre}} followed Augustin into civil [[engineer]]ing, succeeded him as Secretary of the Lighthouse Commission,<ref>Levitt, 2013, p.{{hsp}}99.</ref> and helped to edit his collected works.<ref>Fresnel, 1866–70.</ref> The fourth, [[Fulgence Fresnel]] (1795–1855), became a noted linguist, diplomat, and orientalist, and occasionally assisted Augustin with negotiations.<ref>Levitt, 2013, p.{{hsp}}72.</ref>
Their mother's brother Jean François "Léonor" Mérimée (1757–1836),{{r|jeanelie}} father of the writer [[Prosper Mérimée]] (1803–1870), was a [[painting|paint artist]] who turned his attention to the [[chemistry]] of painting. He became the permanent secretary of the [[École des Beaux-Arts]] (School of Fine Arts) and a professor at the École polytechnique, and was the initial point of contact between Augustin and the leading optical physicists of the day (see below).
=== Education ===
Augustin and his brothers were initially home-schooled by their mother. Augustin, a sickly child, was considered the slow one, hardly beginning to read until the age of eight. At ten he was undistinguished except for his ability to turn tree-branches into toy bows and cannon that worked far too well, earning himself the title ''l'homme de génie'' (the man of genius) from his accomplices, and a united crackdown from their elders.<ref>Levitt, 2013, pp.{{nnbsp}}24–5.</ref>{{r|boutry-1948|p=590–91}}
In 1801, Augustin was sent to the ''École centrale'' at [[Caen]], as company for Louis. But Augustin lifted his performance: in 1804 he was accepted into the École Polytechnique, being placed 17th in the entrance examination, in which his solutions to geometry problems impressed the examiner, [[Adrien-Marie Legendre]]. As the surviving records of the École Polytechnique begin in 1808, we know little of Augustin Fresnel's time there, except that he apparently excelled in geometry and drawing — in spite of continuing poor health — and made few if any friends. Graduating in 1806, he then enrolled at the [[École des ponts ParisTech|École Nationale des Ponts et Chaussées]] (National School of Bridges and Roads, also known as "ENPC" or "École des Ponts"), from which he graduated in 1809, entering the service of the [[Corps of Bridges, Waters and Forests|Corps des Ponts et Chaussées]] as an ''ingénieur ordinair aspirant'' (ordinary engineer in training). Directly or indirectly, the "Corps des Ponts" would be his sole or main employer for the rest of his life.{{r|chisholm-1911-fresnel}}<ref>Levitt, 2013, pp.{{nnbsp}}25–7.</ref>{{r|boutry-1948|p=591–2,601}}
=== Religious formation ===
Fresnel's parents were [[Catholic Church|Roman Catholics]] of the [[Jansenism|Jansenist]] sect, characterized by an extreme [[Augustine of Hippo|Augustinian]] view of [[original sin]]. In the home-schooling that the boys received from their mother, religion took first place. In 1802, Mme Fresnel wrote to Louis concerning Augustin:
{{quote|I pray God to give my son the grace to employ the great talents, which he has received, for his own benefit, and for the God of all. Much will be asked from him to whom much has been given, and most will be required of him who has received most.{{r|kneller-1911|p=147}} }}
Augustin Fresnel remained a Jansenist.<ref>Levitt, 2013, p.{{hsp}}24.</ref> He indeed regarded his intellectual talents as a gift from God, and considered it his duty to use them for the benefit of others.{{r|kneller-1911|p=148}} Plagued by poor health, and determined to do his duty before death thwarted him, he shunned pleasures and worked to the point of exhaustion.{{r|silliman-2008|p=166}} According to his fellow engineer Alphonse Duleau, who helped to nurse him through his final illness, Fresnel saw the study of nature as part of the study of the power and goodness of God. He placed virtue above science and genius. Yet in his last days he needed "strength of soul," not against death alone, but against "the interruption of discoveries… of which he hoped to derive useful applications."{{r|kneller-1911|p=148–9n}} Although Jansenism is considered [[heresy|heretical]] by the Roman Catholic Church, the brief article on Fresnel in the ''[[Catholic Encyclopedia]]'' (1909) does not mention his Jansenism, but describes him as "a deeply religious man and remarkable for his keen sense of duty."{{r|brock-1909}}
== Engineering assignments ==
Fresnel was initially posted to the western département of [[Vendée]]. His letters from that period reveal his distaste for commanding and reprimanding.<ref>Levitt, 2013, pp.{{nnbsp}}27-8.</ref>
In 1811, Fresnel anticipated what became known as the [[Solvay process]] for producing [[sodium carbonate|soda ash]], except that recovery of the [[ammonia]] was not considered.{{r|reilly-1951|p=291}} That may explain why leading chemists, who learned of Fresnel's idea through his uncle Léonor, eventually thought it uneconomic.<ref>Levitt, 2013, p.{{hsp}}29.</ref><ref>The surviving correspondence on soda ash extends from August 1811 to April 1812; see Fresnel, 1866–70, [https://archive.org/details/oeuvrescompltes00fresgoog v.{{hsp}}2 (1868)], pp.{{nnbsp}}810–17.</ref>
About 1812, Fresnel was sent to [[Nyons]], in the southern département of [[Drôme]], to assist with the imperial highway that was to connect Spain and Italy.{{r|silliman-2008|p=166}} It is from Nyons that we have the first evidence of Fresnel's interest in optics. On 15 May 1814, while work was slack due to [[Napoleon]]'s defeat,{{r|boutry-1948|p=590–91}} Fresnel wrote a "P.S." to his ''brother'' Léonor, saying in part:
{{quote|I would also like to have papers that might tell me about the discoveries of French physicists on the polarization of light. I saw in the ''Moniteur'' of a few months ago that [[Jean-Baptiste Biot|Biot]] had read to the Institut a very interesting mémoire on the ''polarization of light''. Though I break my head, I cannot guess what that is.<ref>Fresnel, 1866–70, [https://archive.org/details/oeuvrescompltes00fresgoog v.{{hsp}}2 (1868)], p.{{hsp}}819.</ref>}}
(Concerning the name ''Institut'', note that the French [[French Academy of Sciences|Académie des Sciences]] was merged with other ''académies'' to form the [[Institut de France]] in 1795. In 1816 the Académie des Sciences regained its original name, but remained part of the Institut.)
In March 1815, describing Napoleon's return from [[Elba]] as "an attack on civilization",{{r|silliman-2008|p=166}} Fresnel departed without leave, hastened to [[Toulouse]], and offered his services to the royalist resistance. But he was manifestly in no condition to fight. Returning to Nyons in defeat, he was threatened and had his windows broken. During the [[Hundred Days]] he was placed on suspension, which he was eventually allowed to spend at his mother's house in Mathieu. There he used his enforced leisure to begin his optical experiments.<ref>Levitt, 2013, pp.{{nnbsp}}38-9.</ref>{{r|boutry-1948|p=594}}
== Contributions to physical optics ==
=== Historical context ===
[[File:Refraction - Huygens-Fresnel principle.svg|thumb|Ordinary refraction from a medium of higher wave velocity to a medium of lower wave velocity, as explained by Huygens. Successive positions of the wavefront are shown in blue before refraction, and in green after refraction. For ''ordinary'' refraction, the secondary wavefronts (gray curves) are spherical, so that the rays (straight gray lines) are perpendicular to the wavefronts.]]
The [[corpuscular theory of light]], favored by [[Isaac Newton]] and accepted by nearly all of Fresnel's seniors, easily explained [[rectilinear propagation]]: the corpuscles obviously moved very fast, so that their paths were very nearly straight. The wave theory, as developed by [[Christiaan Huygens]] in his ''[[Treatise on Light]]'' (1690),{{r|huygens-1690}} explained rectilinear propagation on the assumption that each point crossed by a traveling wavefront becomes the source of a ''secondary wavefront''. Given the initial position of a traveling wavefront, any later position (according to Huygens) was the common [[tangent]] surface ([[envelope (mathematics)|envelope]]) of the secondary wavefronts emitted from the earlier position. As the extent of the common tangent was limited by the extent of the initial wavefront, the repeated application of Huygens' construction to a plane wavefront of limited extent (in a uniform medium) gave a straight, parallel beam. While this construction indeed predicted rectilinear propagation, it was difficult to reconcile with the common observation that wavefronts on the surface of water can bend around obstructions, and with the similar behavior of sound waves — causing Newton to maintain, to the end of his life, that if light consisted of waves it would "bend and spread every way" into the shadows.{{r|newton-1730|p=362}}
Huygens' theory neatly explained the ordinary law of [[specular reflection|reflection]] and the ordinary law of refraction ([[Snell's law]]), provided that the secondary waves traveled slower in ''denser'' media (those of higher [[refractive index]]). The corpuscular theory, with the hypothesis that the corpuscles were subject to forces acting perpendicular to surfaces, explained the same laws equally well,<ref>Darrigol, 2012, pp.{{nnbsp}}93–4,{{hsp}}103.</ref> albeit with the implication that light traveled ''faster'' in denser media; that implication was wrong, but could not be directly disproven with the technology of Newton's time or even Fresnel's time (see ''[[Fizeau–Foucault apparatus]]'').
The outstanding strength of Huygens' theory was his explanation of the [[birefringence|double refraction]] of "[[Iceland spar|Iceland crystal]]" ([[calcite]]) on the assumption that the secondary waves are spherical for the ordinary refraction (which satisfies Snell's law) and [[spheroid]]al for the ''extraordinary'' refraction (which does not).{{r|huygens-1690|p=52–105}} In general, Huygens' common-tangent construction implies that rays are ''paths of least time'' between successive positions of the wavefront, in accordance with [[Fermat's principle]].{{r|deWitte-1959}}{{r|young-mw|p=225–6}} In the special case of ''spherical'' secondary wavefronts, Huygens' construction implies that the rays are ''perpendicular to the wavefront''; indeed, the law of ''ordinary'' refraction can be separately derived from that premise.
[[File:Ggb in soap bubble 3.JPG|thumb|left|Altered colors of skylight reflected in a soap bubble, due to thin-film interference (formerly called "thin-plate" interference).]]
Although Newton rejected the wave theory, he noticed its potential to explain colors, including the colors of "[[thin-film interference|thin plates]]" (e.g., "[[Newton's rings]]", and the colors of skylight reflected in soap bubbles), on the assumption that light consists of ''periodic'' waves, with the lowest frequencies (longest wavelenths) at the red end of the spectrum, and the highest frequencies (shortest wavelenths) at the violet end. In 1672 he published a heavy hint to that effect,<ref>Darrigol, 2012, p.{{hsp}}87.</ref>{{r|newton-1672e|p=5088–9}} but contemporary supporters of the wave theory failed to act on it: [[Robert Hooke]] treated light as a periodic sequence of pulses but did not use frequency as the criterion of color,<ref>Darrigol, 2012, pp.{{nnbsp}}53–6.</ref> while Huygens treated the waves as individual pulses without any periodicity.{{r|huygens-1690|p=17}} Newton himself tried to explain colors of thin plates using the corpuscular theory, by supposing that his corpuscles had the wavelike property of alternating between "fits of easy transmission" and "fits of easy reflection",<ref>Darrigol, 2012, pp.{{nnbsp}}98–100.</ref> the distance between "fits" depending on color.{{r|newton-1730|p=345–8}} It was not until 1801 that [[Thomas Young (scientist)|Thomas Young]], in the [[Bakerian Lecture]] for that year, cited Newton's hint,{{r|young-1801|p=18–19}} and accounted for the colors of a thin plate as the combined effect of the front and back reflections, which reinforce or cancel each other according to the ''wavelength'' and the thickness.{{r|young-1801|p=37–9}} He similarly explained the colors of "striated surfaces" (e.g., [[diffraction grating|gratings]]) as the wavelength-dependent reinforcement or cancelation of reflections from adjacent lines.{{r|young-1801|p=35–7}} Young described this reinforcement or cancelation as ''[[interference (wave propagation)|interference]]''.
Neither Newton nor Huygens satisfactorily explained ''[[diffraction]]'' — the blurring and fringing of shadows where, according to rectlinear propagation, they ought to be sharp. Newton, who called diffraction "inflexion", supposed that rays of light passing close to obstacles were bent ("inflected"), but his explanation was only qualitative.<ref>Darrigol, 2012, pp.{{nnbsp}}101–2.</ref> Huygens' common-tangent construction, without modifications, could not accommodate diffraction at all. Two such modifications were proposed by Young in the same 1801 Bakerian Lecture: first, that the secondary waves near the edge of an obstacle could diverge into the shadow, but only weakly, due to limited reinforcement from other secondary waves;{{r|young-1801|p=25–7}} and second, that diffraction by an edge was caused by interference between two rays: one inflected while passing near the edge, and the other reflected off the edge.{{r|young-1801|p=42–4}} These were the earliest suggestions that the degree of diffraction depends on wavelength.<ref>Darrigol, 2012, pp.{{nnbsp}}177–9.</ref> Later, in the 1803 Bakerian lecture, Young ceased to regard inflection as a separate phenomenon,{{r|young-mw|p=188}} and produced evidence that diffraction fringes ''inside'' shadow of a narrow obstacle were due to interference: when the light from one side was blocked, the internal fringes disappeared.{{r|young-mw|p=179–81}} But Young was alone in such efforts until Fresnel entered the field.<ref>Darrigol, 2012, p.{{hsp}}187.</ref>
Huygens, in his celebrated study of double refraction, noticed something that he could not explain: when a ray passes through two similarly oriented calcite crystals at normal incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second; but when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa.{{r|huygens-1690|p=92–4}} This discovery gave Newton another reason to reject the wave theory: rays of light evidently had "sides".{{r|newton-1730|p=358–61}} Corpuscles could have sides{{r|newton-1730|p=373–4}} (or ''poles'', as they would later be called); but waves of light could not,{{r|newton-1730|p=363}} because (so it seemed) any such waves would need to be [[longitudinal wave|longitudinal]] (with vibrations in the direction of propagation). Newton offered an alternative "Rule" for the extraordinary refraction,{{r|newton-1730|p=356}} which rode on his authority through the 18th century, although he made "no known attempt to deduce it from any principles of optics, corpuscular or otherwise."{{r|buchwald-1980|p=327}}
[[File:Calcite and polarizing filter.gif|thumb|300px|Printed label seen through a doubly-refracting calcite crystal and a modern polarizer, rotated to show the different polarizations of the two images.]]
In 1808 the double refraction of calcite was investigated experimentally, with unprecedented accuracy, by [[Étienne-Louis Malus]], and found to be consistent with Huygens' spheroid construction, not Newton's "Rule".{{r|buchwald-1980}} But, during the same investigation, Malus also noticed that when a ray of light is reflected off water at the appropriate angle, it behaves like ''one'' of the two rays emerging from a calcite crystal.<ref>Darrigol, 2012, pp.{{nnbsp}}191–2.</ref> It was Malus who coined the term ''polarization'' to describe this behavior, although the polarizing angle became known as [[Brewster's angle]] after its dependence on the refractive index was determined in 1815 by [[David Brewster]].{{r|brewster-1815}} In 1809, Malus further discovered that the intensity of light passing through ''two'' polarizers is proportional to the squared cosine of the angle between them,<ref>Darrigol, 2012, p.{{hsp}}192.</ref> whether the polarizers work by reflection or double refraction, and that ''all'' doubly-refracting crystals produce both extraordinary refraction and polarization.{{r|young-mw|p=249–50}} As the corpuscularists started trying to explain these things in terms of polar "molecules" of light, the wave theorists had ''no working hypothesis'' on the nature of polarization, prompting Young to remark that Malus's experiments "present greater difficulties to the advocates of the undulatory theory than any other facts with which we are acquainted."{{r|young-mw|p=233}}
=== Interference ===
In connexion with his study of the theory and phenomena of diffraction and interference he devised his double mirrors and biprism in order to obtain two sources of light independent of apertures or the edges of opaque obstacles.{{r|brock-1909}}
=== Diffraction ===
In 1818 he read a memoir on diffraction for which in the ensuing year he received the prize of the Académie des Sciences at Paris.{{r|fresnel-1819b}}
The [[Fresnel diffraction]] equation is an approximation of [[Kirchhoff's diffraction formula|Kirchhoff-Fresnel diffraction]] that can be applied to the propagation of waves in the [[near and far field|near field]].<ref>[[Max Born|M. Born]] & E. Wolf, Principles of Optics, 1999, Cambridge University Press, Cambridge</ref> It is used to calculate the [[diffraction pattern]] created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the [[near and far field|far field]] region is given by the [[Fraunhofer diffraction]] equation.
=== Polarization ===
=== Partial reflection ===
[[reflectance|reflectivity]], [[reflection coefficient]], [[Fresnel equations]], [[computer graphics]], rendering of water.
Circularly polarized light he obtained by means of a rhomb of glass, known as "Fresnel’s rhomb", having obtuse angles of 126°, and acute angles of 54°.{{r|chisholm-1911-fresnel}}
=== Double refraction ===
and by modeling the medium as an array of particles subject to
[[restoring force|restoring forces]], with simplifying assumptions
inspired by sound waves,
=== Ether drag ===
His first memoir (1814) was a
demonstration of the phenomenon of the stellar
aberration.{{r|ripley-dana-1879}}
[[aberration of light]], not published; [[aether drag hypothesis]]
=== Reception ===
== Lighthouses and the Fresnel lens ==
=== Prior art ===
Fresnel was not the first person to focus a lighthouse beam using a lens. That distinction apparently belongs to the London glasscutter Thomas Rogers, who proposed the idea to [[Trinity House]] in 1788.{{r|tag-prior}} The first Rogers lenses, 53cm in diameter and 14cm thick at the center, were installed at the [[Old Lower Lighthouse]] at [[Portland Bill]] in 1789.<ref>Levitt, 2013, p.{{hsp}}57.</ref> Further samples followed at [[Baily Lighthouse|Howth Baily]], [[North Foreland]], and at least four other locations.{{r|tag-prior}} But much of the light was wasted by absorption in the glass.
[[File:Fresnel lens.svg|thumb|upright|1: Cross-section of Buffon/Fresnel lens. 2: Cross-section of conventional [[Lens (optics)#Types of simple lenses|plano-convex lens]] of equivalent power. (Buffon's version was [[Lens (optics)#Types of simple lenses|biconvex]].<ref>Levitt, 2013, p.{{hsp}}59.</ref>)]]
Nor was Fresnel the first to suggest replacing a convex lens with a series of concentric annular prisms, to reduce weight and absorption. In 1748, [[Georges-Louis Leclerc, Comte de Buffon|Count Buffon]] proposed grinding such prisms as steps in a single piece of glass.{{r|chisholm-1911-lighthouse}} In 1790{{r|condorcet-1790}} (although secondary sources give the date as 1773{{r|appleton-1861|p=609}} or 1788{{r|tag-2017}}), the [[Marquis de Condorcet]] suggested that it would be easier to make the annular sections separately and assemble them on a frame; but even that was impractical at the time.{{r|tag-fres}}<ref>Levitt, 2013, p.{{hsp}}71.</ref> These designs were intended not for lighthouses,{{r|chisholm-1911-lighthouse}} but for [[burning glass|burning glasses]].{{r|appleton-1861|p=609}} Brewster, however, proposed a system similar to Condorcet's in 1811,{{r|chisholm-1911-lighthouse|ripley-dana-1879|tag-2017}} and by 1820 was advocating its use in British lighthouses.{{r|chisholm-1911-brewster}}
=== Prototypes ===
Meanwhile, in June 1819, Fresnel was engaged by the ''Commission des phares'' (Commission of Lighthouses) on the recommendation of Arago (a member of the Commission since 1813), to review possible improvements in lighthouse illumination.{{r|tag-fres}} The Commission had been established by Napoleon in 1811, and placed under the Corps des Ponts — Fresnel's employer.<ref>Levitt, 2013, pp.{{nnbsp}}49–50.</ref>
On 29 August 1819, unaware of the Buffon-Condorcet-Brewster proposal,{{r|ripley-dana-1879|tag-fres}} Fresnel presented his first report, in which he recommended what he called ''lentilles à échelons'' (lenses by steps) to replace the reflectors then in use, which reflected only about half of the incident light.<ref>Levitt, 2013, pp.{{nnbsp}}56,{hsp}58.</ref> One of the assembled commissioners, [[Jacques Charles]], recalled Buffon's suggestion. Fresnel was disappointed to discover that he had again "broken through an open door".<ref>Levitt, 2013, p.{{hsp}}59.</ref> But, whereas Buffon's version was [[Lens (optics)#Types of simple lenses|biconvex]] and in one piece, Fresnel's was [[Lens (optics)#Types of simple lenses|plano-convex]] and made of multiple prisms for easier construction. With an official budget of 500 francs, Fresnel approached three manufacturers. The third, François Soleil, found a way to remove defects by reheating and remolding the glass. Arago assisted Fresnel with the design of a modified [[Argand lamp]] with concentric wicks (a concept that Fresnel attributed to [[Benjamin Thompson|Count Rumford]]{{r|fresnel-1822-phares|p=11}}), and accidentally discovered that fish glue was heat-resistant, making it suitable for use in the lens. The prototype, with a lens panel 55cm square, containing 97 polygonal (not annular) prisms, was finished in March 1820 — and so impressed the Commission that Fresnel was asked for a full eight-panel version. Completed a year later, largely at Fresnel's personal expense, this model had panels 72cm square. In a public spectacle on the evening of 13 April 1821, it was demonstrated by comparison with the most recent reflectors, which it suddenly rendered obsolete.<ref>Levitt, 2013, pp.{{nnbsp}}59–66.</ref>
(Fresnel acknowledged the British lenses and Buffon's invention in a memoir published in 1822.{{r|fresnel-1822-phares|p=2–4}}. The date of that memoir may be the source of the claim that Fresnel's lighthouse advocacy began two years later than Brewster's;{{r|chisholm-1911-brewster}} but the text makes it clear that Fresnel's involvement began no later than 1819.{{r|fresnel-1822-phares|p=1}})
{{clear}}
[[File:Calcite and polarizing filter.gif|thumb|300px|Printed label seen through a double-refracting calcite crystal and a modern polarizing filter rotated to show the different polarizations of the two images.]]
=== Fresnel's innovations ===
The term ''polarization'' was coined by [[Étienne-Louis Malus]] (pronounced {{respell|ma|LOOSE|'}}) in 1811.{{r|buchwald-1989|p=54}} In 1808, in the midst of confirming Huygens' geometric description of double refraction (while disputing his physical explanation), Malus had discovered that when a ray of light is reflected off a non-metallic surface at the appropriate angle, it behaves like ''one'' of the two rays emerging from a calcite crystal.{{r|buchwald-1989|p=31–43}} As this behavior had previously been known exclusively in connection with double refraction, Malus described it in that context. In particular, he defined the ''plane of polarization'' of a polarized ray as the plane, containing the ray, in which a principal section of a calcite crystal must lie in order to cause only ''ordinary'' refraction.{{r|buchwald-1989|p=45}} His definition was all the more reasonable because it meant that when a ray was polarized by reflection (off an isotopic medium), the plane of polarization was the plane of incidence and reflection — that is, the plane containing the incident ray, the normal to the reflective surface, and the polarized reflected ray. But, as we now know, this plane happens to contain the ''magnetic'' vectors of the polarized ray, not the electric vectors; the component of the electric vector normal to that plane (i.e., parallel to the surface) is reflected to some extent for ''any'' angle of incidence, due to the change in [[permittivity]] at the surface.
[[File:Fresnel lighthouse lens diagram.png|thumb|246px|Cross-section of a first-generation Fresnel lighthouse lens, with sloping mirrors ''m,n'' above and below the refractive panel ''RC'' (with central segment ''A''). If the cross-section in every vertical plane through the lamp ''L'' is the same, the light is spread evenly around the horizon.]]
The modern implication of Malus's definition — that the plane of polarization contains the ''magnetic'' vectors — survives in the online Merriam-Webster dictionary.{{r|merriamW}}
Fresnel's next lens was a rotating apparatus with eight "bull's-eye" panels, made in annular arcs by [[Saint-Gobain]],<ref>Levitt, 2013, p.{{hsp}}71.</ref> giving eight rotating beams — to be seen by mariners as a periodic flash. Above and behind each main panel was a smaller, sloping bull's-eye panel of trapezoidal outline with trapezoidal elements.{{r|gombert-2017}} This refracted the light to a sloping plane mirror, which then reflected it horizontally, 7 degrees ahead of the main beam, increasing the duration of the flash.{{r|fresnel-1822-phares|p=13,25}} Below the main panels were 128 small mirrors arranged in four rings, stacked like the slats of a [[louver]] or [[Venetian blind]]. Each ring, shaped like a [[frustum]] of a [[cone]], reflected the light to the horizon, giving a fainter steady light between the flashes. The official test, conducted on the ''[[Arc de Triomphe]]'' on 20 August 1822, was witnessed by the Commission — and by [[Louis XVIII of France|Louis XVIII]] and his entourage — from 32km away. The apparatus was stored at [[Bordeaux]] for the winter, and then reassembled at [[Cordouan Lighthouse]] under Fresnel's supervision. On 25 July 1823, the world's first lighthouse Fresnel lens was lit.<ref>Levitt, 2013, pp.{{nnbsp}}72–3.</ref> It was about this time that Fresnel started coughing up blood.<ref>Levitt, 2013, p.{{hsp}}97.</ref>{{r|watson-2016|p=146}}
In 1821, [[Augustin-Jean Fresnel]], having already explained [[diffraction]] in terms of the [[wave theory of light]], announced his hypothesis that light waves are exclusively ''[[transverse wave|transverse]]'' and therefore ''always'' polarized, and that what we call "unpolarized" light is in fact light whose polarization is rapidly and randomly changing.{{r|buchwald-1989|p=227–9}} On that hypothesis, he proceeded to explain nearly all the remaining optical phenomena known at that time.{{r|frankel-1976|p=169}}
In May 1824,{{r|ripley-dana-1879}} Fresnel was promoted to Secretary of the ''Commission des phares'', becoming the first member of that body to draw a salary.<ref>Levitt, 2013, p.{{hsp}}82.</ref> He was also an examiner at the École Polytechnique (since 1821),{{r|brock-1909}} but poor health soon induced him to resign that post and save his energy for his lighthouse work.<ref>Levitt, 2013, p.{{hsp}}97.</ref>
In deriving his [[Fresnel equations|eponymous equations]] for the reflection and transmission coefficients at the interface between two transparent media, Fresnel thought in terms of [[s-wave|shear waves]] in [[elasticity (physics)|elastic solids]], and supposed that a higher [[refractive index]] corresponded to a higher [[density]] of the [[luminiferous aether]]. But, as [[James MacCullagh]] later pointed out, that supposition does not work for double-refracting crystals (in which at least one refractive index varies with direction), because density is not directional; under Fresnel's analogy, a complete explanation of refraction would require a directional variation in [[stiffness]] of the aether ''within'' one medium, plus a variation in density ''between'' media. To avoid this complication, MacCullagh supposed that a higher refractive index corresponded to the same density but a greater elastic ''compliance'' (lower stiffness). Fresnel's supposition led to results that agreed with observation (on partial reflection and transmission) if he further supposed that the vibrations were ''normal'' to the plane of polarization. So began the distinction between the "plane of vibration" and the "plane of polarization". MacCullagh, in contrast, had to suppose that the two planes were the same — i.e., that the vibrations were ''within'' the plane of polarization. (This story was recounted in 1856 by [[Baden Powell (mathematician)|Baden Powell]].{{r|powell-1856}})
In the same year he designed the first ''fixed'' lens — for spreading light evenly around the horizon{{r|tag-fres}} while minimizing waste above or below. This had the familiar reflecting (''catoptric'') rings above and below the refracting (''dioptric'') panels. But the curved refracting surfaces were segments of toroids about a common vertical axis, so that the dioptric panel looked like a cylindrical drum and the entire apparatus looked like a beehive.
Thus attention was focused on whether the plane of vibration could be determined experimentally with the technology of the time. Consider a fine [[diffraction grating]] illuminated at normal incidence. At large angles of diffraction, the grating will appear somewhat edge-on, so that the directions of vibration will be crowded towards the direction parallel to the plane of the grating. If the planes of polarization coincide with the planes of vibration (''à la'' MacCullagh), they will be crowded in the same direction; and if the planes of polarization are ''normal'' to the planes of vibration (''à la'' Fresnel), the planes of polarization will be crowded in the normal direction. To measure the crowding, one could vary the polarization of the incident light in equal steps, and determine the planes of polarization of the diffracted light in the usual manner. Such an experiment was devised, and performed in 1849, by [[Sir George Stokes, 1st Baronet|George Gabriel Stokes]], and it found in favor of Fresnel.{{r|powell-1856|p=19–20;{{hsp}}}}{{r|stokes-1849|p=4–5}}
In 1825 he unveiled the ''Carte des phares'' (Lighthouse Map), calling for a system of 51 lighthouses plus smaller harbor lights, in a hierarchy of lens sizes (called ''orders'', the first order being the largest), with different characteristics to facilitate recognition: a constant light (from a fixed lens), one flash per minute (from a rotating lens with eight panels), and two per minute (sixteen panels). On 1 February 1825, the second lighthouse Fresnel lens entered service: a third-order fixed lens at Dunkirk.<ref>Levitt, 2013, pp.{{nnbsp}}83–4.</ref>
This is surprising in view of MacCullagh's point that density is not directional. If we attempt an analogy between shear waves in a non-isotropic elastic solid and EM waves in a magnetically isotropic but electrically non-isotropic crystal, the density must correspond to the magnetic [[permeability (electromagnetism)|permeability]] (both being non-directional), and the compliance must correspond to the electric [[permittivity]] (both being directional). The result is that the velocity of the solid corresponds to the '''H''' field,{{r|carcione-cavallini-1995}} so that the mechanical vibrations of the shear wave are in the direction of the ''magnetic'' vibrations of the EM wave. But Stokes's experiment was bound to detect the ''electric'' vibrations, because those were the vibrations that interacted with the grating (and with most other objects). In short, MacCullagh's "vibrations" were the ones that had a mechanical analog, but Fresnel's were the ones that were going to be detected in optical experiments. But that clarification raises another difficulty: the analogy between permeability and aether density allows very little variation in aether density among non-magnetic media and is therefore incompatible with Fresnel's hypothesis that aether density is the main criterion of refractive index.{{r|analogies}}
Also in 1825, Fresnel extended his fixed design by adding a rotating array outside the fixed array.{{r|tag-fres}} Each panel of the rotating array refracted part of the fixed light from a horizontal fan into a narrow beam.
== History meets physics ==
[[File:MuseeMarine-phareFresnel-p1000466.jpg|thumb|left|First-order rotating catadioptric Fresnel lens, dated 1870, displayed at the ''[[Musée national de la Marine]]'', Paris. In this case the dioptric prisms (inside the bronze circles) and catadioptric prisms (outside) are arranged to give a purely flashing light with four flashes per rotation. The assembly stands 2.54 metres tall and weighs about 1.5 tonnes.]]
The "vibrations" identified by Fresnel were taken as tangential to the wavefronts.{{r|aldis-1879|p=8,9}} In electromagnetic terms, that identifies the direction of vibration as the '''D''' direction. In a double-refracting crystal, it was conventional to take the ''wave-normal'' direction as the propagation direction to be included in the plane of polarization.{{r|aldis-1879|p=20}} So the plane of polarization was normal to the wavefront. As the vibration was in both the plane of vibration and the plane tangential to the wavefront, both planes being normal to the plane of polarization, it followed that the plane of polarization was simply the plane normal to the vibration.{{r|aldis-1879|p=9}} In electromagnetic terms, that identifies the plane of polarization as simply the plane normal to '''D'''.
To reduce the loss of light in the reflecting elements, Fresnel proposed to replace each mirror with a ''catadioptric'' prism, through which the light would travel by refraction through the first surface, then [[total internal reflection]] off the second surface, then refraction through the third surface.<ref>Levitt, 2013, pp.{{nnbsp}}79–80.</ref> The result was the lighthouse lens as we now know it. In 1826 he assembled a small model for use on the [[Canal Saint-Martin]],{{r|musee}} but he did not live to see a full-sized version.
Hence the old and new definitions of the plane of polarization may be stated succinctly and precisely as follows:
The first large catadioptric lenses were made in 1842 for the lighthouses at Gravelines and [[Île Vierge]]; these were fixed third-order lenses whose catadoptric rings (made in segments) were one metre in diameter. The first-order [[Skerryvore]] lens, installed in 1844, was only partly catadoptric; it was similar to the Cordouan lens except that the lower slats were replaced by French-made catadioptric prisms, while mirrors were retained at the top. The first ''fully'' catadioptric first-order lens, installed at Ailly in 1852, also gave eight rotating beams plus a fixed light at the bottom; but its top section had eight catadioptric panels focusing the light about 4 degrees ahead of the main beams, in order to lengthen the flashes. The first fully catadioptric lens with ''purely revolving'' beams — also of first order — was installed at [[Saint-Clément-des-Baleines]] in 1854, and marked the completion of Fresnel's original ''Carte des phares''.<ref>Levitt, 2013, pp.{{nnbsp}}108–10, 113–16.</ref>
* Under the old definition, the plane of polarization is the plane normal to the '''D''' field.
* Under the new definition, the plane of polarization is the plane normal to the '''B''' field.
The former definition implies that the plane of polarization contains the magnetic vectors; the latter implies that it contains the electric vectors.
As the new electromagnetic theory further emphasized the ''electric'' vibrations (because of their interactions with matter), whereas the old "plane of polarization" contained the ''magnetic'' vectors, the new theory would have tended to reinforce the convention that the plane of vibration was normal to the plane of polarization — but only if one was familiar with the historical definition of the plane of polarization. If one was influenced by physical considerations ''alone'', then, as Feynman{{r|feynman-1963}} and the ''Britannica''{{r|luntz}} illustrate, one would pay attention to the electric vectors, assume that the "plane" of polarization (if one needed such a concept) contained those vectors, and not bother to define a separate "plane of vibration". Moreover, it is not clear that a "plane of polarization" is needed at all: knowing what field vectors are involved, we can specify the polarization by specifying the orientation of a particular vector.
[[File:Flat flexible plastic sheet lens.JPG|thumb|Close-up view of a thin plastic Fresnel lens.]]
=== LaterRemaining developmentsuses ===
There is at least one context in which the ambiguity of the "plane of polarization" does no harm. In an optically ''[[optical rotation|chiral]]'' medium — that is, one in which the "plane of polarization" gradually rotates as the wave propagates — the choice of definition does not affect the existence or direction ("handedness") of the rotation.
Production of one-piece stepped lenses (roughly as envisaged by Buffon) eventually became profitable. By the 1870s, in the [[United States]], such lenses were made of pressed glass and used with small lights on ships and piers.{{r|ripley-dana-1879}} Similar lenses, with finer steps, serve as condensers in [[overhead projector|overhead projectors]]. Still finer steps can be found in low-cost plastic "sheet" [[magnifying glass|magnifiers]].
There is also a context in which the original definition might still suggest itself. In a non-magnetic non-chiral crystal of the ''[[optic axis of a crystal|biaxial]]'' class (in which there is no ordinary refraction, but both refractions violate [[Snell's law]]), there are three mutually perpendicular planes for which the speed of light is isotropic within the plane provided that the electric vectors are normal to the plane.{{r|jenkins-white-1976}} That context naturally draws attention to a plane normal to the vibrations as envisaged by Fresnel, and that plane is indeed the plane of polarization as defined by Malus.
{{clear}}
In most contexts, however, the concept of a "plane of polarization" distinct from a plane containing the electric "vibrations" has arguably become redundant, and has certainly become a source of confusion.
== Honors ==
[[File:Bust of Augustin Fresnel by David d'Angers-MnM 41 OA 256 D-IMG 8741.jpg|thumb|Bust of Augustin Fresnel by [[David d'Angers]] (1854), formerly in the lighthouse of [[Hourtin]], [[Gironde]], and now exhibited at the {{nowrap|''[[Musée national de la Marine]]''}}.]]
In 1823, Fresnel was unanimously elected a member of the [[French Academy of Sciences|Académie des Sciences]].{{r|brock-1909}}{{r|chisholm-1911-fresnel}} In 1824<ref>Levitt, 2013, p.{{hsp}}77.</ref> he was made a ''chevalier de la Légion d'honneur'' (Knight of the [[Legion of Honour]]).{{r|academie}} Meanwhile in Britain, the wave theory was yet to take hold; late in 1824, Fresnel wrote to Thomas Young, saying in part:
{{quote|I am far from denying the value that I attach to the praise of English scholars, or pretending that they would not have flattered me agreeably. But for a long time this sensibility, or vanity, which is called the love of glory, has been much blunted in me: I work far less to capture the public's votes than to obtain an inner approbation which has always been the sweetest reward of my efforts. Doubtless I have often needed the sting of vanity to excite me to pursue my researches in moments of disgust or discouragement; but all the compliments I received from MM. Arago, Laplace, and Biot never gave me as much pleasure as the discovery of a theoretical truth and the confirmation of my calculations by experiment.{{r|young-mw|p=402–3}} }}
But "the praise of English scholars" soon followed. On 9 June 1825, Fresnel was made a Foreign Member of the [[Royal Society|Royal Society of London]].{{r|royalS-2007}} In 1827{{r|chisholm-1911-fresnel|rines-1919}} he was awarded the Society's [[Rumford Medal]] for the year 1824, "For his Development of the Undulatory Theory as applied to the Phenomena of Polarized Light, and for his various important discoveries in Physical Optics."{{r|royalS-rumford}}
The monument to Fresnel at his birthplace (see [[#Early life|above]]) was dedicated on 14 September 1884 with a speech by {{nowrap|[[Jules Jamin]]}}, permanent secretary of the Académie des Sciences.{{r|academie|jamin-1884}} "{{smaller|FRESNEL}}" is among the [[List of the 72 names on the Eiffel Tower|72 names embossed on the Eiffel Tower]] (on the south-east side, fourth from the left). In the 19th century, as every lighthouse in France acquired a Fresnel lens, every one acquired a bust of Fresnel, seemingly watching over the coastline that he had made safer.<ref>Levitt, 2013, p.{{hsp}}233</ref>
{{clear}}
== Decline and death ==
[[File:Tombe d'Augustin Fresnel - Père Lachaise.JPG|thumb|Fresnel's grave at [[Père Lachaise Cemetery]], Paris, photographed in 2014.]]
Fresnel's health, which had always been poor, deteriorated in the winter of 1822-3, increasing the urgency of his original research, and causing him to turn down an invitation from Thomas Young to write an article on double refraction for the ''[[Encyclopædia Britannica]]''. In the spring he recovered enough, in his own view, to supervise the installation at Cordouan. Soon afterwards, it became clear that his condition was [[tuberculosis]].<ref>Levitt, 2013, pp.{{nnbsp}}75–6,{{nnbsp}}97</ref>
In 1824 he was told that if he wanted to live longer, he needed to scale back his activities. Perceiving his lighthouse work to be his most important duty, he resigned from the École Polytechnique. His last note to the Académie, read on 13 June 1825, described the first [[radiometer]] and attributed the observed repulsive force to a temperature difference.{{r|boutry-1948|p=601–2}} In 1826 he found time to answer some queries from the British astronomer [[John Herschel]] for an article on light, which was eventually published in the ''[[Encyclopædia Metropolitana]]''.<ref>Darrigol, 2012, pp.{{nnbsp}}220–21.</ref> It was Herschel who recommended Fresnel for the Royal Society's Rumford Medal.{{r|boutry-1948|p=603}}
Fresnel's cough worsened in the winter of 1826-7. In the spring, being too ill to return to Mathieu, he was carried to [[Ville-d'Avray]], 12km west of Paris, where he was joined by his mother. On 6 July, Arago arrived to deliver the Rumford Medal. Sensing Arago's distress, Fresnel whispered that "the most beautiful crown means little, when it is laid on the grave of a friend." Fresnel did not have the strength to reply to the Royal Society. He died eight days later, on [[Bastille Day]].<ref>Levitt, 2013, p.{{hsp}}98.</ref>{{r|boutry-1948|p=602}}
Fresnel is buried at [[Père Lachaise Cemetery]], Paris. The [[commons:category:Grave of Augustin Fresnel (Père-Lachaise, division 14)|inscription on his headstone]] is partly eroded away; the legible part says, when translated, "To the memory of Augustin Jean FRESNEL, member of the [[Institut de France|Institute of France]]."
{{clear}}
== Posthumous publications ==
== Unfinished business ==
=== Ether models ===
=== Conical refraction ===
Although Fresnel identified what we now call the biradial and binormal
axes, he did not explore the shapes of the surfaces near these axes. A
few years later, that issue came to the attention of Hamilton.
== Legacy ==
[[File:Cordouan6.jpg|thumb|The lantern room of the [[Cordouan Lighthouse]], in which the first Fresnel lens entered service in 1823. The current fixed catadioptric "beehive" lens replaced Fresnel's original rotating lens in 1854.{{r|pharedeC}}]]
With a century after Fresnel's initial proposal, more than 10,000 lights with Fresnel lenses marked coastlines around the world.<ref>Levitt, 2013, p.{{hsp}}19.</ref> The numbers of lives saved can only be guessed at. Concerning the other benefits, the science historian Theresa H. Levitt has remarked:
{{quote|Everywhere I looked, the story repeated itself. The moment a Fresnel lens appeared at a ___location was the moment that region becamed linked into the world economy.<ref>Levitt, 2013, p.{{hsp}}8.</ref>}}
In the history of physical optics, Fresnel's successful revival of the wave theory nominates him as the pivotal figure between Newton, who held that light consisted of corpuscles, and [[James Clerk Maxwell|Maxwell]], who established that light waves are electromagnetic. Whereas [[Albert Einstein|Einstein]] described Maxwell's work as "the most profound and the most fruitful that physics has experienced since the time of Newton,"{{r|jamesCMF}} commentators of the era between Fresnel and Maxwell made similarly strong statements about Fresnel:
* MacCullagh, as early as 1830, wrote that Fresnel's mechanical theory of double refraction "would do honour to the sagacity of Newton".{{r|macCullagh-1830|p=78}}.
* Lloyd, after his experimental confirmation of conical refraction, lived for another 48 years. In 1834, in his ''Report on the progress and present state of physical optics'' for the [[British Association for the Advancement of Science|British Science Association]], he wrote:<blockquote>The theory of Fresnel… will, I am persuaded, be regarded as the finest generalization in physical science which has been made since the discovery of universal gravitation.{{r|lloyd-1834|p=382}}</blockquote>In 1841 Lloyd published his ''Lectures on the Wave-theory of Light'', in which he described Fresnel's transverse-wave theory as "the noblest fabric which has ever adorned the ___domain of physical science, Newton's system of the universe alone excepted."{{r|lloyd-1841}} The same description was retained in the "second edition", published under the title ''Elementary Treatise on the Wave-theory of Light'' (1857), and in the "third edition",{{r|lloyd-1873}} which appeared in the same year as Maxwell's ''Treatise on Electricity and Magnetism'' (1873).<br style="margin-bottom: 1ex;" />
* [[William Whewell]], in all three editions of his ''History of the Inductive Sciences'' (1837, 1847, and 1857), at the end of Book IX, compared the histories of physical astronomy and physical optics and concluded:
{{quote|It would, perhaps, be too fanciful to attempt to establish a parallelism between the prominent persons who figure in these two histories. If we were to do this, we must consider Huyghens and Hooke as standing in the place of Copernicus, since, like him, they announced the true theory, but left it to a future age to give it development and mechanical confirmation; Malus and Brewster, grouping them together, correspond to [[Tycho Brahe]] and [[Johannes Kepler|Kepler]], laborious in accumulating observations, inventive and happy in discovering laws of phenomena; and Young and Fresnel combined, make up the Newton of optical science.{{r|whewell-1857|p=370-71}} }}
What Whewell called the "true theory" has since undergone two major revisions. The first, by Maxwell, specified the physical fields whose variations constitute the waves of light. The second, initiated by Einstein's explanation of the [[photoelectric effect]], supposed that the energy of light waves was divided into [[quantum|quanta]], which were eventually identified with particles called [[photon|photons]]. But photons did not exactly correspond to Newton's corpuscles; for example, Newton's explanation of ordinary refraction required the corpuscles to travel faster in media of higher refractive index, which photons do not. Nor did photons displace waves; rather, they led to the paradox of [[wave–particle duality]].
Although Fresnel did not know that light waves are electromagnetic, he managed to construct the world's first coherent theory of light. In retrospect, this shows that his methods are applicable to multiple types of waves. And although light is now known to have both wavelike and particle-like aspects, it is the wavelike aspect that more easily explains the phenomena studied by Fresnel. In these respects, Fresnel's theory has stood the test of time, and Whewell's premature triumphalism contains an abiding truth.
== References ==
{{Reflist|20em|refs=
<ref name=aldis-1879>W.S. Aldis, [https://archive.org/details/chapteronfresnel00aldirich ''A Chapter on Fresnel's Theory of Double Refraction''], 2nd Ed., Cambridge: Deighton, Bell, & Co., 1879.</ref>
<ref name=academie>Académie des Sciences, ''Membres…'' [http://www.academie-sciences.fr/pdf/dossiers/Fresnel/Fresnel_oeuvre.htm "Augustin Fresnel"], accessed 21 August 2017; [https://web.archive.org/web/20170215201835/http://www.academie-sciences.fr/pdf/dossiers/Fresnel/Fresnel_oeuvre.htm archived] 15 February 2017.</ref>
<ref name=analogies>Concerning the limitations of elastic-electromagnetic analogies, see (e.g.) O. Darrigol, ''A History of Optics: From Greek Antiquity to the Nineteenth Century'', Oxford, 2012, pp.{{nnbsp}}227–32.</ref>
<ref name=appleton-1861>D. Appleton & Co., "Sea-lights", ''Dictionary of Machines, Mechanics, Engine-work, and Engineering'', 1861, [https://archive.org/details/appletonsdiction02appl v.{{hsp}}2].</ref>
<ref name=buchwald-1989>J.Z. Buchwald, ''The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century'', University of Chicago Press, 1989.</ref>
<ref name=bibmed>Bibliothèques et Médiathèque, [http://www.culture-evreux.fr/EXPLOITATION/Default/doc/ALOES/1587928/inauguration-a-broglie-le-14-septembre-1884-du-buste-d-augustin-fresnel "Inauguration à Broglie, le 14 septembre 1884 du buste d'Augustin Fresnel"], accessed 4 September 2017.</ref>
<ref name=carcione-cavallini-1995>J.M. Carcione and F. Cavallini, [http://www.lucabaradello.it/carcione/CC95b.pdf "On the acoustic-electromagnetic analogy"], ''Wave Motion'', Vol.{{nnbsp}}21 (1995), pp.{{nnbsp}}149–62. (Note that the authors' analogy is only two-dimensional.)</ref>
<ref name=boutry-1948>G.-A. Boutry, "Augustin Fresnel: His time, life and work, 1788–1827", ''Science Progress'', v.{{hsp}}36, no.{{hsp}}144 (October 1948), pp. 587–604; [http://www.jstor.org/stable/43413515 jstor.org/stable/43413515].</ref>
<ref name=feynman-1963>R.P. Feynman, R.B. Leighton, and M. Sands, ''The Feynman Lectures on Physics'', California Institute of Technology, 1963–2013, Volume {{serif|I}}, [http://feynmanlectures.caltech.edu/I_33.html Lecture 33].</ref>
<ref name=brewster-1815>D. Brewster, [http://rstl.royalsocietypublishing.org/content/105/125.full.pdf "On the laws which regulate the polarisation of light by reflexion from transparent bodies"], ''Philosophical Transactions of the Royal Society'', v.{{hsp}}105, pp.{{nnbsp}}125–59, read 16 March 1815.</ref>
<ref name=frankel-1976>E. Frankel, "Corpuscular optics and the wave theory of light: The science and politics of a revolution in physics", ''Social Studies of Science'', Vol.{{nnbsp}}6, No.{{hsp}}2 (May 1976), pp.{{nnbsp}}141–84.</ref>
<ref name=brock-1909>H.M. Brock, [[s:Catholic Encyclopedia (1913)/Augustin-Jean Fresnel|"Fresnel, Augustin-Jean"]], ''Catholic Encyclopedia'', 1907–12, v.{{hsp}}6 (1909).</ref>
<ref name=chisholmhuygens-1911-brewster1690>HC. Chisholm (ed.)Huygens, "Brewster,''Traité Sirde David",la Lumière''Encyclopedia Britannica'',(Leiden: 11th Ed.Van der Aa, 19111690), translated by S.P. Thompson as ''[http://www.gutenberg.org/filesebooks/19699/19699-h/19699-h.htm14725 v.{{hsp}}4, pt.3Treatise on Light]'', University of Chicago Press, 1912.</ref>
<ref name=jenkins-white-1976>Cf. F.A. Jenkins and H.E. White, ''Fundamentals of Optics'', 4th Ed., New York: McGraw-Hill, 1976, Fig.{{nnbsp}}26{{serif|I}} (p.{{hsp}}554).</ref>
<ref name=buchwald-1980>J.Z. Buchwald, "Experimental investigations of double refraction from Huygens to Malus", ''Archive for History of Exact Sciences'', v.{{hsp}}21, no.{{hsp}}4 (December 1980), pp.{{nnbsp}}311–373.</ref>
<ref name=lunney-weaire-2006> J.G. Lunney and D. Weaire, "The ins and outs of conical refraction", ''Europhysics News'', Vol.{{nnbsp}}37, No.{{hsp}}3 (May–June 2006), pp.{{nnbsp}}26–9; [http://dx.doi.org/10.1051/epn:2006305 doi.org/10.1051/epn:2006305].</ref>
<ref name=chisholm-1911-fresnel>H. Chisholm (ed.), [http://www.gutenberg.org/files/37736/37736-h/37736-h.htm#ar19 "Fresnel, Augustin Jean"], ''Encyclopedia Britannica'', 11th Ed., 1911.</ref>
<ref name=chisholm-1911-lighthouseluntz>HM. ChisholmLuntz (ed.?) et al., [httphttps://www.gutenbergbritannica.orgcom/filesscience/41472radiation/41472The-h/41472structure-h.htmand-properties-of-matter#ar2ref398787 "LighthouseDouble refraction"], ''EncyclopediaEncyclopædia Britannica'', 11thaccessed 15 Ed.,September 19112017.</ref>
<ref name=condorcetmerriamW>Merriam-1790>NWebster, Inc. de Condorcet, [https://bookswww.googlemerriam-webster.com.au/books?id=o99ZAAAAcAAJdictionary/plane%20of%20polarization ''Éloge"Plane deof M. le Comte de Buffon''polarization"], Paris:accessed Chez15 Buisson,September 1790, pp. 11–122017.</ref>
<ref name=powell-1856>B. Powell, [https://archive.org/stream/s4philosophicalmag12londuoft#page/n13/mode/2up "On the demonstration of Fresnel's formulas for reflected and refracted light; and their applications"], ''Philosophical Magazine and Journal of Science'', Series 4, Vol.{{nnbsp}}12, No.{{hsp}}76 (July 1856), pp.{{nnbsp}}1–20.</ref>
<ref name=deWitte-1959>A.J. de Witte, "Equivalence of Huygens' principle and Fermat's principle in ray geometry", ''American Journal of Physics'', v.{{hsp}}27, no.{{hsp}}5 (May 1959), pp.{{nnbsp}}293–301. ''Erratum'': In Fig.{{nnbsp}}7(b), each instance of "ray" should be "normal" (noted in v.{{hsp}}27, no.{{hsp}}6, p.{{hsp}}387).</ref>
<ref name=stokes-1849>G.G. Stokes, [https://archive.org/stream/transactionsofca09camb#page/n15/mode/2up "On the dynamical theory of diffraction"] (read 26 November 1849), ''Transactions of the Cambridge Philosophical Society'', Vol.{{nnbsp}}9, Part 1 (1851), pp.{{nnbsp}}1–62.</ref>
<ref name=favre>J.H. Favre, "Augustin Fresnel", gw.geneanet.org, accessed 30 August 2017.</ref>
<ref name=fresnel-1819b>A. Fresnel, "Mémoire sur la diffraction de la lumière" (deposited 1818, "crowned" 1819), in ''Oeuvres complètes'', [https://books.google.com/books?id=1l0_AAAAcAAJ v.{{hsp}}1], pp. 247–364, partly translated as "Fresnel's prize memoir on the diffraction of light", in [https://archive.org/details/wavetheoryofligh00crewrich Crew, 1900], pp. 81–144. (Not to be confused with the earlier memoir of the same title in ''Annales de Chimie et de Physique'', 1:239–81, 1816.)</ref>
<ref name=fresnel-1822-phares>A. Fresnel, "Mémoire sur un nouveau système d'éclairage des phares", read at the Académie des Sciences on 29 July 1822, translated by T. Tag as [http://uslhs.org/sites/default/files/attached-files/Fresnel%27s%20Memoire%20-%20Translation.pdf "Memoir Upon A New System Of Lighthouse Illumination"], U.S. Lighthouse Society, accessed 26 August 2017; [https://web.archive.org/web/20160819111647/http://uslhs.org/sites/default/files/attached-files/Fresnel's%20Memoire%20-%20Translation.pdf archived] 19 August 2016.</ref>
<ref name=gombert-2017>D. Gombert, photograph of the [https://www.flickr.com/photos/gebete29/32970312394/in/photostream/ ''Optique de Cordouan''] in the [http://www.pnr-armorique.fr/Visiter/Musees-maisons-a-themes/Musee-des-Phares-et-Balises/collection-du-musee collection of the ''Musée des Phares et Balises''], [[Ushant|Ouessant]], France, 23 March 2017.</ref>
<ref name=jamesCMF>James Clerk Maxwell Foundation, [http://www.clerkmaxwellfoundation.org/html/about_maxwell.html "Who was James Clerk Maxwell?"], accessed 6 August 2017; [https://web.archive.org/web/20170630003106/http://www.clerkmaxwellfoundation.org/html/about_maxwell.html archived] 30 June 2017.</ref>
<ref name=jamin-1884>J. Jamin, [http://www.academie-sciences.fr/pdf/dossiers/Fresnel/Fresnel_pdf/Fresnel_eloge_1884.pdf ''Discours prononcé au nom de l'Académie des Sciences à l'inauguration du monument de Fresnel''], Broglie, 14 September 1884; accessed 6 September 2017.</ref>
<ref name=jeanelie>'jeanelie' (author), "Augustine Charlotte Marie Louise Merimee" and "Louis Jacques Fresnel", gw.geneanet.org, accessed 30 August 2017.</ref>
<ref name=kneller-1911>K.A. Kneller (tr. T.M. Kettle), [https://archive.org/details/christianitylead00knelrich ''Christianity and the Leaders of Modern Science: A contribution to the history of culture in the nineteenth century''], Freiburg im Breisgau: B. Herder, 1911, pp. 147–9.</ref>
<ref name=lloyd-1834>H. Lloyd, "Report on the progress and present state of physical optics", [https://books.google.com/books?id=mtU4AAAAMAAJ ''Report of the Fourth Meeting of the British Association for the Advancement of Science''] (held at Edinburgh in 1834), London: J. Murray, 1835, pp. 295–413.</ref>
<ref name=lloyd-1841>H. Lloyd, [https://archive.org/details/lecturesonwavet00lloygoog ''Lectures on the Wave-theory of Light''], Dublin: Milliken, 1841, Part II, Lecture III, p.26.</ref>
<ref name=lloyd-1873>H. Lloyd, ''Elementary Treatise on the Wave-theory of Light'', [https://archive.org/details/elementarytreati00lloyrich 3rd Ed.], London: Longmans, Green, & Co., 1873, p.167. (Cf. [https://archive.org/details/wavetheorylight00lloyrich 2nd Ed.], 1857, p.136.)</ref>
<ref name=macCullagh-1830>J. MacCullagh, "On the Double Refraction of Light in a Crystallized Medium, according to the Principles of Fresnel", ''Trans. Royal Irish Academy'', v.{{hsp}}16 (1830), pp. 65–78; [http://www.jstor.org/stable/30079025 jstor.org/stable/30079025].</ref>
<ref name=martan-2014>'martan' (author), [http://maisons.natales.over-blog.com/2014/05/eure-27.html "Eure (27)"], ''Guide National des Maisons Natales'', 30 May 2014.</ref>
<ref name=musee>Musée national de la Marine, [http://mnm.webmuseo.com/ws/musee-national-marine/app/collection/record/9067 "Appareil catadioptrique, Appareil du canal Saint-Martin"], accessed 26 August 2017; [https://web.archive.org/web/20170826030358/http://mnm.webmuseo.com/ws/musee-national-marine/app/collection/record/9067 archived] 26 August 2017.</ref>
<ref name=newton-1672e>I. Newton, [http://rstl.royalsocietypublishing.org/content/7/81-91/5084.full.pdf "Mr. Isaac Newtons !(sic)! answer to some considerations upon his doctrine of light and colors"] (in reply to Hooke), ''Philosophical Transactions of the Royal Society'', v.{{hsp}}7 (1672), pp.{{nnbsp}}5084–5103.</ref>
<ref name=newton-1730>I. Newton, ''Opticks'' (4th Ed., London, 1730), with Foreword by A. Einstein and Introduction by E.T. Whittaker (London: George Bell & Sons, 1931), with Preface by I.B. Cohen and Analytical Table of Contents by D.H.D. Roller, Mineola, NY: Dover, 1952.</ref>
<ref name=perchet-2011>D. Perchet, [https://e-monumen.net/patrimoine-monumental/monument-a-augustin-fresnel-broglie/ "Monument à Augustin Fresnel – Broglie"], e-monumen.net, 5 July 2011.</ref>
<ref name=pharedeC>Phare de Cordouan, [http://www.phare-de-cordouan.fr/lighting-systems.html "The lighting systems of the Cordouan Lighthouse"], accessed 26 August 2017; [https://web.archive.org/web/20160922153001/http://www.phare-de-cordouan.fr/lighting-systems.html archived] 22 September 2016.</ref>
<ref name=reilly-1951>D. Reilly, "Salts, acids & alkalis in the 19th century: A comparison between advances in France, England & Germany", ''Isis'', v.{{hsp}}42, no.{{hsp}}4 (December 1951), pp.{{nnbsp}}287–96; [http://www.jstor.org/stable/226807 jstor.org/stable/226807].</ref>
<ref name=rines-1919>G.E. Rines (ed.), "Fresnel, Augustin Jean", ''Encyclopedia Americana'', 1918–20, v.{{hsp}}12 (1919), [https://babel.hathitrust.org/cgi/pt?id=wu.89094370657;view=1up;seq=111 p.93]. (This entry inaccurately describes Fresnel as the "discoverer" of polarization of light and as a "Fellow" of the Royal Society, whereas in fact he ''explained'' polarization and was a "Foreign Member" of the Society; see text.)</ref>
<ref name=ripley-dana-1879>G. Ripley & C.A. Dana (ed.), "Fresnel, Augustin Jean", ''American Cyclopedia'', [https://archive.org/details/americancyclopae07ripluoft v.{{hsp}}7], pp.486–9.</ref> (Contrary to this entry [p.486], calcite and quartz were ''not'' the only doubly refractive crystals known before Fresnel; see text.)</ref>
<ref name=royalS-2007>Royal Society, ''List of Fellows of the Royal Society 1660–2007'', A–J, July 2001, p.{{hsp}}130.</ref>
<ref name=royalS-rumford>Royal Society, [https://royalsociety.org/grants-schemes-awards/awards/rumford-medal/ "Rumford Medal"] (with link to full list of past winners), accessed 2 September 2017.</ref>
<ref name=silliman-2008>R.H. Silliman, "Fresnel, Augustin Jean", ''Complete Dictionary of Scientific Biography'', Detroit: Charles Scribner's Sons, 2008, v.{{hsp}}5, pp. 165–71. (The [http://www.encyclopedia.com/people/science-and-technology/physics-biographies/augustin-jean-fresnel version at ''encyclopedia.com''] lacks the diagram and equations.)</ref>
<ref name=tag-2017>T. Tag, [http://uslhs.org/chronology-lighthouse-events "Chronology of Lighthouse Events"], U.S. Lighthouse Society, accessed 22 August 2017; [https://web.archive.org/web/20170408105558/http://uslhs.org/chronology-lighthouse-events archived] 8 April 2017.</ref>
<ref name=tag-prior>T. Tag, [http://uslhs.org/lens-use-prior-fresnel "Lens use prior to Fresnel"], U.S. Lighthouse Society, accessed 12 August 2017; [https://web.archive.org/web/20170520114102/http://uslhs.org/lens-use-prior-fresnel archived] 20 May 2017.</ref>
<ref name=tag-fres>T. Tag, [http://uslhs.org/fresnel-lens "The Fresnel lens"], U.S. Lighthouse Society, accessed 12 August 2017; [https://web.archive.org/web/20160722002916/http://uslhs.org/fresnel-lens archived] 22 July 2017.</ref>
<ref name=watson-2016>B. Watson, ''Light: A Radiant History from Creation to the Quantum Age'', New York: Bloomsbury, 2016.</ref>
<ref name=whewell-1857>W. Whewell, ''History of the Inductive Sciences: From the Earliest to the Present Time'', 3rd Ed., London: J.W. Parker & Son, 1857, [https://archive.org/details/bub_gb_cBSrVEkaR8EC v.{{hsp}}2].</ref>
<ref name=whittaker-1910>E.T. Whittaker, [https://archive.org/details/historyoftheorie00whitrich ''A History of the Theories of Aether and Electricity: From the age of Descartes to the close of the nineteenth century''], Longmans, Green, & Co., 1910.</ref>
<ref name=young-1801>T. Young, [http://rstl.royalsocietypublishing.org/content/92/12.full.pdf "On the Theory of Light and Colours"] (Bakerian Lecture), ''Philosophical Transactions of the Royal Society'', v.{{hsp}}92, (1802), pp.{{nnbsp}}12–48, read 12 November 1801.</ref>
<ref name=young-mw>T. Young (ed. G. Peacock), ''Miscellaneous Works of the late Thomas Young'', London: J. Murray, 1855, [https://books.google.com/books?id=GyzPAAAAMAAJ v.{{hsp}}I].</ref>
}}
{{Portal bar|History of science|Physics}}
== Bibliography ==
* H. Crew (ed.), 1900, [https://archive.org/details/wavetheoryofligh00crewrich ''The Wave Theory of Light: Memoirs by Huygens, Young and Fresnel''], American Book Co.
* O. Darrigol, 2012, ''A History of Optics: From Greek Antiquity to the Nineteenth Century'', Oxford.
* A. Fresnel (ed. H. de Senarmont, E. Verdet, L. Frenel), 1866–70, ''Oeuvres complètes d'Augustin Fresnel'' (3 vols.), Paris: Imprimerie Impériale; [https://books.google.com/books?id=1l0_AAAAcAAJ v.{{hsp}}1 (1866)], [https://archive.org/details/oeuvrescompltes00fresgoog v.{{hsp}}2 (1868)], [https://archive.org/details/oeuvrescompltes01fresgoog v.{{hsp}}3 (1870)].
* T.H. Levitt, 2013, ''A Short Bright Flash: Augustin Fresnel and the Birth of the Modern Lighthouse'', New York: W.W. Norton.
* {{OL author|2296238A}}
== External links ==
* {{Wikiquote-inline}}
<nowiki>
{{Portal bar|Biography|History of science|Physics}}
{{Authority control}}
{{DEFAULTSORT:Fresnel, Augustin-Jean}}
[[Category:Light]]
[[Category:Optics]]
[[Category:Physical optics]]
[[Category:Polarization (waves)]]
[[Category:Electromagnetic radiation]]
[[Category:Antennas (radio)]]
[[Category:History of physics]]
[[Category:Optical physicists]]
[[Category:19th-century physicists]]
[[Category:French physicists]]
[[Category:French civil engineers]]
[[Category:École Polytechnique alumni]]
[[Category:École des Ponts ParisTech alumni]]
[[Category:Corps des ponts]]
[[Category:Members of the French Academy of Sciences]]
[[Category:Foreign Members of the Royal Society]]
[[Category:People from Eure]]
[[Category:1788 births]]
[[Category:1827 deaths]]
[[Category:Burials at Père Lachaise Cemetery]]
[[Category:19th-century deaths from tuberculosis]]
[[Category:Infectious disease deaths in France]]
</nowiki>
|
