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=== 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 ==
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=== 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 ===
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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}})
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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.
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
[[File:Flat flexible plastic sheet lens.JPG|thumb|Close-up view of a thin plastic Fresnel lens.]]
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[[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 But "the 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>
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=== 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 ==
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[[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
* 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}}.
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* 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]].
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== References ==
{{Reflist|
<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=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=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=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=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=brock-1909>H.M. Brock, [[s:Catholic Encyclopedia (1913)/Augustin-Jean Fresnel|"Fresnel, Augustin-Jean"]], ''Catholic Encyclopedia'', 1907–12, v.6 (1909).</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=chisholm-1911-brewster>H. Chisholm (ed.), "Brewster, Sir David", ''Encyclopedia Britannica'', 11th Ed., 1911, [http://www.gutenberg.org/files/19699/19699-h/19699-h.htm v.4, pt.3].</ref>▼
▲<ref name=chisholm-1911-brewster>H. Chisholm (ed.), "Brewster, Sir David", ''Encyclopedia Britannica'', 11th Ed., 1911, [http://www.gutenberg.org/files/19699/19699-h/19699-h.htm v.{{hsp}}4, pt.3].</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=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>
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<ref name=chisholm-1911-lighthouse>H. Chisholm (ed.), [http://www.gutenberg.org/files/41472/41472-h/41472-h.htm#ar2 "Lighthouse"], ''Encyclopedia Britannica'', 11th Ed., 1911.</ref>
<ref name=condorcet-1790>
<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=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>
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<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>
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<ref name=watson-2016>B. Watson, ''Light: A Radiant History from Creation to the Quantum Age'', New York: Bloomsbury, 2016.</ref>
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<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>
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<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.I].</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>
}}
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* 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.
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