Augustin-Jean Fresnel[note 1] (10 May 1788 – 14 July 1827) was a French civil engineer andphysicist whose research inoptics led to the almost unanimous acceptance of thewave theory of light, fully supplantingNewton'scorpuscular theory, from the late 1830s [3] until the end of the 19th century. He is perhaps better known for inventing thecatadioptric (reflective/refractive)Fresnel lens and for pioneering the use of "stepped" lenses to extend the visibility oflighthouses, saving countless lives at sea. The simplerdioptric (purely refractive) stepped lens, first proposed byCount Buffon[4] and independently reinvented by Fresnel, is used in screenmagnifiers and in condenser lenses foroverhead projectors.
Fresnel gave the first satisfactory explanation ofdiffraction by straight edges, including the first satisfactory wave-based explanation of rectilinear propagation.[5] By further supposing that light waves are purelytransverse, Fresnel explained the nature ofpolarization. He then worked ondouble refraction.
Fresnel had a lifelong battle withtuberculosis, to which he succumbed at the age of 39. He lived just long enough to receive recognition from his peers, including (on his deathbed) theRumford Medal of theRoyal Society, and his name is ubiquitous in the modern terminology of optics and waves. After the wave theory of light was subsumed byMaxwell'selectromagnetic theory in the 1860s, some attention was diverted from the magnitude of Fresnel's contribution. In the period between Fresnel's unification of physical optics and Maxwell's wider unification, a contemporary authority,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". [6]
Monument to Augustin Fresnel on the facade of his birthplace at 2 Rue Augustin Fresnel,Broglie (facing Rue Jean François Mérimée),[7] inaugurated on 14 September 1884.[8][9] The inscription, when translated, says: "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." [7][10]
Augustin-Jean Fresnel (also called Augustin Jean or simply Augustin), born in Broglie,Normandy, on 10 May 1788, was the second of four sons of the architect Jacques Fresnel[11] and his wife Augustine,née Mérimée.[12] The family moved twice—in 1789/90 toCherbourg,[13] and in 1794 [14] to Jacques's home town ofMathieu, where Augustine would spend 25 years as a widow.[15]
The first son, Louis, was admitted to theÉcole Polytechnique, became a lieutenant in the artillery, and was killed in action atJaca, Spain.[12] The third, Léonor,[11] followed Augustin into civilengineering, succeeded him as secretary of the Lighthouse Commission,[16] and helped to edit his collected works.[17] The fourth,Fulgence Fresnel, became a linguist, diplomat, and orientalist, and occasionally assisted Augustin with negotiations.[18][19] Fulgence died in Baghdad in 1855 having led a mission to explore Babylon.[19]
The Fresnel brothers were initially home-schooled by their mother. The sickly Augustin was considered the slow one, not inclined to memorization;[21][22] but the popular story that he hardly began to read until the age of eight is disputed.[23] At the age of nine or ten he was undistinguished except for his ability to turn tree-branches into toy bows and guns that worked far too well, earning himself the titlel'homme de génie (the man of genius) from his accomplices, and a united crackdown from their elders.[24][25][26]
In 1801, Augustin was sent to theÉcole Centrale atCaen, as company for Louis. But Augustin lifted his performance: in late 1804 he was accepted into the École Polytechnique, being placed 17th in the entrance examination.[27][28][29] As the detailed records of the École Polytechnique begin in 1808, we know little of Augustin's time there, except that he made few if any friends and—in spite of continuing poor health—excelled in drawing and geometry:[30] in his first year he took a prize for his solution to a geometry problem posed byAdrien-Marie Legendre.[31][32] Graduating in 1806, he then enrolled at theÉcole 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 theCorps des Ponts et Chaussées as aningénieur ordinaire aspirant (ordinary engineer in training). Directly or indirectly, he was to remain in the employment of the "Corps des Ponts" for the rest of his life.[33][14][34]
Fresnel's parents wereRoman Catholics of theJansenist sect, characterized by an extremeAugustinian view oforiginal sin. Religion took first place in the boys' home-schooling. In 1802, his mother said:
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.[35]
Augustin remained a Jansenist.[36] He regarded his intellectual talents as gifts from God, and considered it his duty to use them for the benefit of others.[37] 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. In his last days he prayed for "strength of soul", not against death alone, but against "the interruption of discoveries ... of which he hoped to derive useful applications". [38]
Jansenism is consideredheretical by the Roman Catholic Church, and Grattan-Guinness suggests this is why Fresnel never gained a permanent academic teaching post;[39] his only teaching appointment was at theAthénée in the winter of 1819–20.[40][41] The article on Fresnel in theCatholic Encyclopedia does not mention his Jansenism, but describes him as "a deeply religious man and remarkable for his keen sense of duty". [40]
Fresnel was initially posted to the westerndépartement ofVendée. There, in 1811, he anticipated what became known as theSolvay process for producingsoda ash, except that recycling of theammonia was not considered.[42] That difference may explain why leading chemists, who learned of his discovery through his uncle Léonor, eventually thought it uneconomic.[43]
Nyons, France, 19th century, drawn by Alexandre Debelle (1805–1897)
About 1812, Fresnel was sent toNyons, in the southerndépartement ofDrôme, to assist with the imperial highway that was to connect Spain and Italy.[14] It is from Nyons that we have the first evidence of his interest in optics. On 15 May 1814, while work was slack due toNapoleon's defeat,[44] Fresnel wrote apostscript to his brother Léonor, saying in part:
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 theMoniteur of a few months ago thatBiot had read to the Institute a very interesting memoir on thepolarization of light. Though I break my head, I cannot guess what that is.[45]
As late as 28 December he was still waiting for information, but by 10 February 1815 he had received Biot's memoir.[46][47] (TheInstitut de France had taken over the functions of the FrenchAcadémie des Sciences and otheracadémies in 1795. In 1816 theAcadémie des Sciences regained its name and autonomy, but remained part of the institute.[48])
In March 1815, perceiving Napoleon's return fromElba as "an attack on civilization",[49] Fresnel departed without leave, hastened toToulouse and offered his services to the royalist resistance, but soon found himself on the sick list. Returning to Nyons in defeat, he was threatened and had his windows broken. During theHundred 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.[50][51][52]
Fresnel made major contributions to several areas ofphysical optics. These included studies ofdiffraction (1815–1818), where he explained the colored fringes seen in shadows of objects illuminated by narrow beams, and conducted double-mirror experiments. He studiedpolarization (1816–1823), discovering that the two images produced by abirefringent crystal could not be combined to create a diffraction pattern. A third area that he studied wasdouble refraction (1821–1826), where he found that neither of the tworefractions in atopaz crystal could have been produced by ordinary spherical secondary waves.[3]
1: Cross-section of Buffon/Fresnel lens. 2: Cross-section of conventionalplano-convex lens of equivalent power. (Buffon's version wasbiconvex.[53])
On 21 June 1819, Fresnel was "temporarily" seconded by theCommission des Phares (Commission of Lighthouses) to review possible improvements in lighthouse illumination.[54][55][56]
By the end of August 1819, Fresnel recommendedlentilles à échelons (lenses by steps) to replace the reflectors then in use, which reflected only about half of the incident light.[57][58] Where Buffon's version wasbiconvex and in one piece, Fresnel's wasplano-convex and made of multiple prisms for easier construction. In a public spectacle on the evening of 13 April 1821, his design was demonstrated by comparison with the most recent reflectors, which it suddenly rendered obsolete.[59][60]
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.
Fresnel's next lens was a rotating apparatus with eight "bull's-eye" panels, made in annular arcs bySaint-Gobain,[61] 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.[62][63] The official test, conducted on the unfinishedArc de Triomphe on 20 August 1822, was witnessed by the commission—and byLouis XVIII and his entourage—from 32km away. The apparatus was reassembled atCordouan Lighthouse under Fresnel's supervision. On 25 July 1823, the world's first lighthouse Fresnel lens was lit.[64][65]
In May 1824,[66] Fresnel was promoted to secretary of theCommission des Phares, becoming the first member of that body to draw a salary,[67] albeit in the concurrent role of Engineer-in-Chief.[68]
In the same year he designed the firstfixed lens—for spreading light evenly around the horizon while minimizing waste above or below,[56] in a beehive-shaped design.[69] The second Fresnel lens to enter service was a fixed lens, of third order, installed at Dunkirk by 1 February 1825.[70] It had a 16-sided polygonal plan.[71]
In 1825, Fresnel extended his fixed-lens design by adding a rotating array outside the fixed array. Each panel of the rotating array was to refract part of the fixed light from a horizontal fan into a narrow beam.[56][72]
Also in 1825, Fresnel unveiled theCarte des Phares (Lighthouse Map), calling for a system of 51 lighthouses plus smaller harbor lights, in a hierarchy of lens sizes (calledorders, 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).[73]
First-order rotating catadioptric Fresnel lens, dated 1870, displayed at theMusée national de la Marine, Paris. In this case the dioptric prisms (inside the bronze rings) 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.
In late 1825,[74] 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.[75] The result was the lighthouse lens as we now know it. In 1826 he assembled a small model for use on theCanal Saint-Martin.[76]
Fresnel was elected to theSociété Philomathique de Paris in April 1819,[77] and in 1822 became one of the editors of the Société's Bulletin des Sciences.[78] As early as May 1817, at Arago's suggestion, Fresnel applied for membership of the Académie des Sciences, but received only one vote.[77] The successful candidate on that occasion was Joseph Fourier. In November 1822, Fourier's elevation to Permanent Secretary of the Académie created a vacancy in the physics section, which was filled in February 1823 byPierre Louis Dulong, with 36 votes to Fresnel's 20. But in May 1823, after another vacancy was left by the death ofJacques Charles, Fresnel's election was unanimous.[79][80][81] In 1824,[82] Fresnel was made achevalier de la Légion d'honneur (Knight of theLegion of Honour).[9]
Meanwhile, in Britain, the wave theory was yet to take hold; Fresnel wrote to Thomas Young in November 1824, saying in part:
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 fromMM. 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.[83]
But "the praise of English scholars" soon followed. On 9 June 1825, Fresnel was made a Foreign Member of theRoyal Society of London.[84] In 1827[29][85] he was awarded the society'sRumford 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". [86]
A monument to Fresnel at his birthplace[7][10] (seeabove) was dedicated on 14 September 1884[8] with a speech byJules Jamin, Permanent Secretary of the Académie des Sciences.[9][87] "FRESNEL" is among the72 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.[88] The lunar featuresPromontorium Fresnel andRimae Fresnel were later named after him,[89] and so was asteroid10111 Fresnel.[90]
Fresnel's grave at Père Lachaise Cemetery, Paris, photographed in 2018
Fresnel's health, which had always been poor, deteriorated in the winter of 1822–1823, increasing the urgency of his original research, and (in part) preventing him from contributing an article on polarization and double refraction for theEncyclopædia Britannica.[91][92] The memoirs on circular and elliptical polarization and optical rotation,[93] and on the detailed derivation of the Fresnel equations and their application to total internal reflection,[94] date from this period. In the spring he recovered enough, in his own view, to supervise the lens installation at Cordouan. Soon afterwards, it became clear that his condition wastuberculosis.[95]
In 1824, he was advised 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 as an examiner at the École Polytechnique, and closed his scientific notebooks. His last note to the Académie, read on 13 June 1825, described the firstradiometer and attributed the observed repulsive force to a temperature difference.[96][97][98] Although his fundamental research ceased, his advocacy did not; as late as August or September 1826, he found the time to answerHerschel's queries on the wave theory.[99] It was Herschel who recommended Fresnel for the Royal Society's Rumford Medal.[100]
Fresnel's cough worsened in the winter of 1826–1827, leaving him too ill to return to Mathieu in the spring. The Académie meeting of 30 April 1827 was the last that he attended. In early June he was carried toVille-d'Avray, 12 kilometres (7.5 mi) west of Paris. There his mother joined him. 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, onBastille Day.[101][102][103][104]
Fresnel's "second memoir" on double refraction[105] was not printed until late 1827, a few months after his death.[106] Until then, the best published source on his work on double refraction was an extract of that memoir, printed in 1822.[107] His final treatment of partial reflection and total internal reflection,[94] read to the Académie in January 1823, was thought to be lost until it was rediscovered among the papers of the deceasedJoseph Fourier (1768–1830), and was printed in 1831. Until then, it was known chiefly through an extract printed in 1823 and 1825. The memoir introducing the parallelepiped form of the Fresnel rhomb,[108] read in March 1818, was mislaid until 1846,[109][110][111] and then attracted such interest that it was soon republished in English.[112] Most of Fresnel's writings on polarized light before 1821—including his first theory of chromatic polarization (submitted 7 October 1816) and the crucial "supplement" of January 1818 [113]—were not published in full until hisOeuvres complètes ("complete works") began to appear in 1866.[114] The "supplement" of July 1816, proposing the "efficacious ray" and reporting the famous double-mirror experiment, met the same fate,[115] as did the "first memoir" on double refraction.[116]
Publication of Fresnel's collected works was itself delayed by the deaths of successive editors. The task was initially entrusted toFélix Savary, who died in 1841. It was restarted twenty years later by the Ministry of Public Instruction. Of the three editors eventually named in theOeuvres,Sénarmont died in 1862,Verdet in 1866, and Léonor Fresnel in 1869, by which time only two of the three volumes had appeared.[117][118] At the beginning of vol. 3 (1870), the completion of the project is described in a long footnote by "J. Lissajous".[119]
Not included in theOeuvres[120] are two short notes by Fresnel on magnetism, which were discovered among Ampère's manuscripts.[121]: 104 In response toØrsted's discovery ofelectromagnetism in 1820, Ampère initially supposed that the field of a permanentmagnet was due to a macroscopic circulatingcurrent. Fresnel suggested instead that there was amicroscopic current circulating around each particle of the magnet. In his first note, he argued that microscopic currents, unlike macroscopic currents, would explain why a hollow cylindrical magnet does not lose its magnetism when cut longitudinally. In his second note, dated 5 July 1821, he further argued that a macroscopic current had the counterfactual implication that a permanent magnet should be hot, whereas microscopic currents circulating around the molecules might avoid the heating mechanism.[121]: 101–104 He was not to know that the fundamental units of permanent magnetism are even smaller than molecules (seeElectron magnetic moment). The two notes, together with Ampère's acknowledgment, were eventually published in 1885.[122]
Fresnel's essayRêveries of 1814 has not survived.[123] The article "Sur les Différents Systèmes relatifs à la Théorie de la Lumière" ("On the Different Systems relating to the Theory of Light"), which Fresnel wrote for the newly launched English journalEuropean Review,[124] was received by the publisher's agent in Paris in September 1824. The journal failed before Fresnel's contribution could be published. Fresnel tried unsuccessfully to recover the manuscript. The editors of his collected works were unable to find it, and concluded that it was probably lost.[125]
In 1810, Arago found experimentally that the degree of refraction of starlight does not depend on the direction of the earth's motion relative to the line of sight. In 1818, Fresnel showed that this result could be explained by the wave theory,[126] on the hypothesis that if an object with refractive index moved at velocity relative to the external aether (taken as stationary), then the velocity of light inside the object gained the additional component. He supported that hypothesis by supposing that if the density of the external aether was taken as unity, the density of the internal aether was, of which the excess, namely, was dragged along at velocity, whence theaverage velocity of the internal aether was. The factor in parentheses, which Fresnel originally expressed in terms of wavelengths,[127] became known as theFresnel drag coefficient.[128]
In his analysis of double refraction, Fresnel supposed that the different refractive indices in different directions within thesame medium were due to a directional variation in elasticity, not density (because the concept of mass per unit volume is not directional). But in his treatment of partial reflection, he supposed that the different refractive indices ofdifferent media were due to different aether densities, not different elasticities.[129][130]
The analogy between light waves and transverse waves in elastic solids does not predictdispersion—that is, the frequency-dependence of the speed of propagation, which enablesprisms to produce spectra and causes lenses to suffer fromchromatic aberration. Fresnel, inDe la Lumière and in the second supplement to his first memoir on double refraction, suggested that dispersion could be accounted for if the particles of the medium exerted forces on each other over distances that were significant fractions of a wavelength.[131][132][133][134][135] Later, more than once, Fresnel referred to the demonstration of this result as being contained in a note appended to his "second memoir" on double refraction.[136][137] No such note appeared in print, and the relevant manuscripts found after his death showed only that, around 1824, he was comparing refractive indices (measured by Fraunhofer) with a theoretical formula, the meaning of which was not fully explained.[138]
In the 1830s, Fresnel's suggestion was taken up by Cauchy,Baden Powell, andPhilip Kelland, and it was found to be tolerably consistent with the variation of refractive indices with wavelength over thevisible spectrum for a variety of transparent media (seeCauchy's equation).[139][140][141] These investigations were enough to show that the wave theory was at least compatible with dispersion; if the model of dispersion was to be accurate over a wider range of frequencies, it needed to be modified so as to take account of resonances within the medium (seeSellmeier equation).[142]
The analytical complexity of Fresnel's derivation of the ray-velocity surface was an implicit challenge to find a shorter path to the result. This was answered by MacCullagh in 1830, and byWilliam Rowan Hamilton in 1832.[143][144][145]
The lantern room of theCordouan 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.[146]
Within a century of Fresnel's initial stepped-lens proposal, more than 10,000 lights with Fresnel lenses were protecting lives and property around the world.[147] Concerning the other benefits, the science historian Theresa H. Levitt has remarked:
Everywhere I looked, the story repeated itself. The moment a Fresnel lens appeared at a location was the moment that region became linked into the world economy.[148]
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, andJames Clerk Maxwell, who established that light waves are electromagnetic. WhereasAlbert Einstein described Maxwell's work as "the most profound and the most fruitful that physics has experienced since the time of Newton", [149] 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".[144]: 78
Lloyd, in hisReport on the progress and present state of physical optics (1834) for theBritish Association for the Advancement of Science, surveyed previous knowledge of double refraction and declared:
The theory of Fresnel to which I now proceed,—and which not only embraces all the known phenomena, but has even outstripped observation, and predicted consequences which were afterwards fully verified,—will, I am persuaded, be regarded as the finest generalization in physical science which has been made since the discovery of universal gravitation.[150]
In 1841, Lloyd published hisLectures 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". [6]
William Whewell, in all three editions of hisHistory 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:
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 andHooke as standing in the place ofCopernicus, 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 toTycho Brahe andKepler, laborious in accumulating observations, inventive and happy in discovering laws of phenomena; and Young and Fresnel combined, make up the Newton of optical science.[151]
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. Without the benefit of this knowledge, Fresnel managed to construct the world's first coherent theory of light, showing in retrospect that his methods are applicable to multiple types of waves. The second revision, initiated by Einstein's explanation of thephotoelectric effect, supposed that the energy of light waves was divided intoquanta, which were eventually identified with particles calledphotons. 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. Neither did photons displace waves; rather, they led to the paradox ofwave–particle duality. Moreover, the phenomena studied by Fresnel, which included nearly all the optical phenomena known at his time, are still most easily explained in terms of thewave nature of light. So it was that, as late as 1927, the astronomerEugène Michel Antoniadi declared Fresnel to be "the dominant figure in optics". [152]
^abH. Lloyd,Lectures on the Wave-theory of Light, Dublin: Milliken, 1841, Part II, Lecture III, p. 26. The same description was retained in the "second edition", published under the titleElementary Treatise on the Wave-theory of Light (London: Longman, Brown, Green, Longmans, & Roberts, 1857; p. 136), and in the"third edition" (London: Longmans, Green, & Co., 1873; p. 167), which appeared in the same year as Maxwell'sTreatise on Electricity and Magnetism.
^abc'martan' (author),"Eure (27)",Guide National des Maisons Natales, 30 May 2014.
^abBibliothèques et Médiathèque, "Inauguration à Broglie, le 14 Septembre 1884 du buste d'Augustin Fresnel",archived 28 July 2018.
^That age was given by Arago in his elegy (Arago, 1857, p. 402) and widely propagated (Encyclopædia Britannica, 1911;Buchwald 1989, p. 111;Levitt 2013, p. 24; etc.). But the reprint of the elegy at the end of Fresnel's collected works bears a footnote, presumably by Léonor Fresnel, saying that "eight" should be "five or six", and regretting "the haste with which we had to collect the notes that were belatedly requested for the biographical part of this speech" (Fresnel, 1866–70, vol. 3, p. 477n). Silliman (1967, p. 9n) accepts the correction.
^Arago, 1857, p. 403. Fresnel's solution was printed in theCorrespondance sur l'École polytechnique, No. 4 (June–July 1805),pp. 78–80, and reprinted in Fresnel, 1866–70, vol. 2, pp. 681–684.Boutry (1948, p. 591) takes this story as referring to the entrance examination.
^Kneller 1911, p. 147. Kneller interprets the quote as referring to Augustin; but Verdet (in Fresnel, 1866–70, vol. 1, pp. xcviii–xcix), cited by Silliman (1967, p. 8), gives it a different context, referring to Louis's academic success.
^Reilly, D. (December 1951). "Salts, acids & alkalis in the 19th century; a comparison between advances in France, England & Germany".Isis; an International Review Devoted to the History of Science and Its Cultural Influences.42 (130):287–296.doi:10.1086/349348.ISSN0021-1753.PMID14888349.
^Cf.Silliman 1967, pp. 28–33;Levitt 2013, p. 29;Buchwald 1989, pp. 113–114. The surviving correspondence on soda ash extends from August 1811 to April 1812; see Fresnel, 1866–70, vol. 2, pp. 810–817.
^G. Ripley and C.A. Dana (eds.),"Fresnel, Augustin Jean",American Cyclopædia, 1879, vol. 7, pp. 486–489. Contrary to this entry (p. 486), calcite and quartz werenot the only doubly refractive crystals known before Fresnel; see (e.g.)Young 1855, pp. 250 (written 1810) and pp. 262,266,277 (written 1814), andLloyd 1834, pp. 376–377.
^Royal Society,List of Fellows of the Royal Society 1660–2007,A–J, July 2007, p. 130.
^G.E. Rines (ed.), "Fresnel, Augustin Jean",Encyclopedia Americana, 1918–20, vol. 12 (1919),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 heexplained polarization and was a "Foreign Member" of the Society; see text.)
^Royal Society,"Rumford Medal" (with link to full list of past winners), accessed 2 September 2017.
^A. Fresnel, "Mémoire sur la double réfraction que les rayons lumineux éprouvent en traversant les aiguilles de cristal de roche suivant les directions parallèles à l'axe" ("Memoir on the double refraction that light rays undergo in traversing the needles of rock crystal [quartz] in directions parallel to the axis"), read 9 December 1822; printed in Fresnel, 1866–70, vol. 1, pp. 731–751 (full text), pp. 719–29 (extract, first published inBulletin de la Société philomathique for 1822, pp. 191–198).
^abA. Fresnel, "Mémoire sur la loi des modifications que la réflexion imprime à la lumière polarisée" ("Memoir on the law of the modifications that reflection impresses on polarized light"), read 7 January 1823; reprinted in Fresnel, 1866–70, vol. 1, pp. 767–799 (full text, published 1831), pp. 753–762 (extract, published 1823). See especially pp. 773 (sine law), 757 (tangent law), 760–761 and 792–796 (angles of total internal reflection for given phase differences).
^A. Fresnel, "Supplément au Mémoire sur les modifications que la réflexion imprime à la lumière polarisée" ("Supplement to the Memoir on the modifications that reflection impresses on polarized light"), signed 15 January 1818, submitted for witnessing 19 January 1818; printed in Fresnel, 1866–70, vol. 1, pp. 487–508.
^abA.K.T. Assis and J.P.M.C. Chaib,Ampère's Electrodynamics ("Analysis of the meaning and evolution of Ampère’s force between current elements, together with a complete translation of his masterpiece:Theory of Electrodynamic Phenomena, Uniquely Deduced from Experience"), Montreal: Apeiron, 2015.
^J. Joubert (ed.),Collection de Mémoires relatifs à la Physique, vol. 2 (being Part 1 ofMémoires sur l'électrodynamique), Paris: Gauthier-Villars, 1885, pp. 140 (Ampère's acknowledgment), 141–147 (Fresnel's notes).
^Fresnel, 1866–70, vol. 2, p. 803n. Grattan-Guinness (1990, p. 884n) gives the year of composition as 1825, but this does not match the primary sources.
^W.R. Hamilton, "Third supplement to an essay on the theory of systems of rays",Transactions of the Royal Irish Academy, vol. 17, pp. v–x,1–144, read 23 Jan.& 22 Oct.1832;jstor.org/stable/30078785 (author's introduction dated June 1833; volume started 1831(?), completed 1837).
^Opening sentence in E.M. Antoniadi, "Le centenaire d'Augustin Fresnel",L'Astronomie (Paris), vol. 41,pp. 241–246 (June 1927), translated as "The centenary of Augustin Fresnel" inAnnual Report of the Board of Regents of the Smithsonian Institution, Washington, 1927,pp. 217–220.
D.F.J. Arago (tr. B. Powell), 1857, "Fresnel" (elegy read at the Public Meeting of the Academy of Sciences, 26 July 1830), in D.F.J. Arago (tr. W.H. Smyth, B. Powell, and R. Grant),Biographies of Distinguished Scientific Men (single-volume edition), London: Longman, Brown, Green, Longmans, & Roberts, 1857,pp. 399–471. (On the translator's identity, see pp. 425n,452n.) Erratum: In the translator's note on p. 413, a plane tangent to the outer sphere at pointt should intersect the refractive surface (assumed flat); then,through that intersection, tangent planes should be drawn to the inner sphere and spheroid (cf. Mach, 1926, p. 263).
D.F.J. Arago and A. Fresnel, 1819, "Mémoire sur l'action que les rayons de lumière polarisée exercent les uns sur les autres",Annales de Chimie et de Physique, Ser. 2, vol. 10, pp. 288–305, March 1819; reprinted in Fresnel, 1866–70, vol. 1,pp. 509–522; translated as"On the action of rays of polarized light upon each other", inCrew 1900, pp. 145–155
Boutry, G.-A. (October 1948), "Augustin Fresnel: His time, life and work, 1788–1827",Science Progress,36 (144):587–604,JSTOR43413515
Buchwald, J.Z.; Fox, R., eds. (2013), "Optics in the Nineteenth Century",The Oxford Handbook of the History of Physics, Oxford, pp. 445–472,ISBN978-0-19-969625-3{{citation}}: CS1 maint: work parameter with ISBN (link)
Darrigol, O. (2012),A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford,ISBN978-0-19-964437-7
Elton, J. (July 2009), "A Light to Lighten our Darkness: Lighthouse Optics and the Later Development of Fresnel's Revolutionary Refracting Lens 1780–1900",International Journal for the History of Engineering & Technology,79 (2):183–244,doi:10.1179/175812109X449612
Frankel, E. (September 1974),The search for a corpuscular theory of double refraction: Malus, Laplace and the price [sic] competition of 1808, vol. 18, Centaurus, pp. 223–245
Frankel, E. (May 1976), "Corpuscular optics and the wave theory of light: The science and politics of a revolution in physics",Social Studies of Science,6 (2):141–184,doi:10.1177/030631277600600201,JSTOR284930
A. Fresnel, 1815a, Letter to Jean François "Léonor" Mérimée, 10 February 1815 (Smithsonian Dibner Library, MSS 546A), printed in G. Magalhães, "Remarks on a new autograph letter from Augustin Fresnel: Light aberration and wave theory",Science in Context, vol. 19, no. 2 (June 2006), pp. 295–307,doi:10.1017/S0269889706000895, at p. 306 (original French) and p. 307 (English translation)
A. Fresnel, 1816, "Mémoire sur la diffraction de la lumière" ("Memoir on the diffraction of light"),Annales de Chimie et de Physique, Ser. 2, vol. 1, pp. 239–281 (March 1816); reprinted as "Deuxième Mémoire ..." ("Second Memoir ...") in Fresnel, 1866–70, vol. 1, pp. 89–122. Not to be confused with the later "prize memoir" (Fresnel, 1818b)
A. Fresnel, 1818a, "Mémoire sur les couleurs développées dans les fluides homogènes par la lumière polarisée", read 30 March 1818 (according to Kipnis, 1991, p. 217), published 1846; reprinted in Fresnel, 1866–70, vol. 1,pp. 655–683; translated by E. Ronalds & H. Lloyd as"Memoir upon the colours produced in homogeneous fluids by polarized light", in Taylor, 1852, pp. 44–65 (Cited page numbers refer to the translation.)
A. Fresnel, 1818b, "Mémoire sur la diffraction de la lumière" ("Memoir on the diffraction of light"), deposited 29 July 1818, "crowned" 15 March 1819, published (with appended notes) inMémoires de l'Académie Royale des Sciences de l'Institut de France, vol. V (for 1821 & 1822, printed 1826),pp. 339–475; reprinted (with notes) in Fresnel, 1866–70, vol. 1,pp. 247–383; partly translated as"Fresnel's prize memoir on the diffraction of light", inCrew 1900, pp. 81–144.Not to be confused with the earlier memoir with the same French title (Fresnel, 1816)
A. Fresnel, 1818c, "Lettre de M. Fresnel à M. Arago sur l'influence du mouvement terrestre dans quelques phénomènes d'optique",Annales de Chimie et de Physique, Ser. 2, vol. 9, pp. 57–66 & plate after p. 111 (Sep. 1818), & pp. 286–287 (Nov. 1818); reprinted in Fresnel, 1866–70, vol. 2,pp. 627–636; translated as"Letter from Augustin Fresnel to François Arago, on the influence of the movement of the earth on some phenomena of optics" in K.F. Schaffner,Nineteenth-Century Aether Theories, Pergamon, 1972 (doi:10.1016/C2013-0-02335-3), pp. 125–135; also translated (with several errors) by R.R. Traill as "Letter from Augustin Fresnel to François Arago concerning the influence of terrestrial movement on several optical phenomena",General Science Journal, 23 January 2006 (PDF, 8 pp.)
A. Fresnel, 1821a, "Note sur le calcul des teintes que la polarisation développe dans les lames cristallisées" et seq.,Annales de Chimie et de Physique, Ser. 2, vol. 17, pp. 102–111 (May 1821), 167–196 (June 1821), 312–315 ("Postscript", July 1821); reprinted (with added section nos.) in Fresnel, 1866–70, vol. 1, pp. 609–648; translated as "On the calculation of the tints that polarization develops in crystalline plates, & postscript",Zenodo: 4058004 /doi:10.5281/zenodo.4058004, 2021
A. Fresnel, 1821b, "Note sur les remarques de M. Biot ...",Annales de Chimie et de Physique, Ser. 2, vol. 17, pp. 393–403 (August 1821); reprinted (with added section nos.) in Fresnel, 1866–70, vol. 1, pp. 601–608; translated as "Note on the remarks of Mr. Biot relating to colors of thin plates",Zenodo: 4541332 /doi:10.5281/zenodo.4541332, 2021
A. Fresnel, 1821c, Letter to D.F.J.Arago, 21 September 1821, in Fresnel, 1866–70, vol. 2, pp. 257–259; translated as"Letter to Arago on biaxial birefringence",Wikisource, April 2021
A. Fresnel, 1822a,De la Lumière (On Light), in J. Riffault (ed.),Supplément à la traduction française de la cinquième édition du "Système de Chimie" par Th.Thomson, Paris: Chez Méquignon-Marvis, 1822, pp. 1–137,535–539; reprinted in Fresnel, 1866–70, vol. 2, pp. 3–146; translated by T. Young as "Elementary view of the undulatory theory of light",Quarterly Journal of Science, Literature, and Art, vol. 22 (Jan.– Jun.1827), pp. 127–141,441–454; vol. 23 (Jul.– Dec.1827), pp. 113–35,431–448; vol. 24 (Jan.– Jun.1828), pp. 198–215; vol. 25 (Jul.– Dec.1828), pp. 168–191,389–407; vol. 26 (Jan.– Jun.1829), pp. 159–165.
A. Fresnel, 1822b, "Mémoire sur un nouveau système d'éclairage des phares", read 29 July 1822; reprinted in Fresnel, 1866–70, vol. 3,pp. 97–126; translated by T. Tag as"Memoir upon a new system of lighthouse illumination", U.S. Lighthouse Society, accessed 26 August 2017; 19 August 2016 (Cited page numbers refer to the translation.)
A. Fresnel, 1827, "Mémoire sur la double réfraction",Mémoires de l'Académie Royale des Sciences de l'Institut de France, vol. VII (for 1824, printed 1827),pp. 45–176; reprinted as "Second mémoire ..." in Fresnel, 1866–70, vol. 2,pp. 479–596; translated by A.W. Hobson as"Memoir on double refraction", in Taylor, 1852, pp. 238–333. (Cited page numbers refer to the translation. For notable errata in the original edition, and consequently in the translation, see Fresnel, 1866–70, vol. 2, p. 596n.)
A. Fresnel (ed. H. de Sénarmont, E. Verdet, and L. Fresnel), 1866–70,Oeuvres complètes d'Augustin Fresnel (3 volumes), Paris: Imprimerie Impériale;vol. 1 (1866),vol. 2 (1868),vol. 3 (1870)
Grattan-Guinness, I. (1990),Convolutions in French Mathematics, 1800–1840, vol. 2, Basel: Birkhäuser, chapter 13 (pp. 852–915, "The entry of Fresnel: Physical optics, 1815–1824") and chapter 15 (pp. 968–1045, "The entry of Navier and the triumph of Cauchy: Elasticity theory, 1819–1830"),ISBN3-7643-2238-1
C. Huygens, 1690,Traité de la Lumière (Leiden: Van der Aa), translated by S.P. Thompson asTreatise on Light, University of Chicago Press, 1912; Project Gutenberg, 2005. (Cited page numbers match the 1912 edition and the Gutenberg HTML edition.)
Jenkins, F.A.; White, H.E. (1976),Fundamentals of Optics (4th ed.), New York: McGraw-Hill,ISBN0-07-032330-5
Kipnis, N. (1991),History of the Principle of Interference of Light, Basel: Birkhäuser, chapters VII, VIII,ISBN978-3-0348-9717-4
Kneller, K.A. (1911),Christianity and the Leaders of Modern Science: A contribution to the history of culture in the nineteenth century, translated by Kettle, T.M., Freiburg im Breisgau: B. Herder, pp. 146–149
Levitt, T.H. (2009),The Shadow of Enlightenment: Optical and Political Transparency in France, 1789–1848, Oxford,ISBN978-0-19-954470-7
Levitt, T.H. (2013),A Short Bright Flash: Augustin Fresnel and the Birth of the Modern Lighthouse, New York: W.W. Norton,ISBN978-0-393-35089-0
Lloyd, H. (1834), "Report on the progress and present state of physical optics",Report of the Fourth Meeting of the British Association for the Advancement of Science, no. 4, London: J. Murray, pp. 295–413
Mach, E. (1926),The Principles of Physical Optics: An Historical and Philosophical Treatment, translated by Anderson, J.S.; Young, A.F.A., London: Methuen & Co.
I. Newton, 1730,Opticks: or, a Treatise of the Reflections, Refractions, Inflections, and Colours of Light, 4th Ed. (London: William Innys, 1730; Project Gutenberg, 2010); republished with foreword by A. Einstein and Introduction by E.T. Whittaker (London: George Bell & Sons, 1931); reprinted with additional Preface by I.B. Cohen and Analytical Table of Contents by D.H.D. Roller, Mineola, NY: Dover, 1952, 1979 (with revised preface), 2012 (Cited page numbers match the Gutenberg HTML edition and the Dover editions.)
Silliman, R.H. (1967),Augustin Fresnel (1788–1827) and the Establishment of the Wave Theory of Light (PhD dissertation; submitted 1967, accepted 1968), Princeton University; available from ProQuest (missing the first page of the preface)
Silliman, R.H. (2008), "Fresnel, Augustin Jean",Complete Dictionary of Scientific Biography, vol. 5, Detroit: Charles Scribner's Sons, pp. 165–171 (Theversion atencyclopedia.com lacks the diagram and equations.)
