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"Fresnel" redirects here. For other uses, see Fresnel (disambiguation).
Augustin-Jean Fresnel
Born(1788-05-10)10 May 1788
Broglie, Kingdom of France (now Eure, France)
Died14 July 1827(1827-07-14) (aged 39)
Ville-d'Avray, Kingdom of France (now Hauts-de-Seine, France),
Cause of deathof Tuberculosis
Resting placePère Lachaise Cemetery
NationalityFrench
Alma mater
Known for
Awards
Scientific career
FieldsPhysics, Engineering
Institutions

Augustin-Jean Fresnel (/freɪˈnɛl/ fray-NEL; Template:IPA-fr; 10 May 1788 – 14 July 1827) was a 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 Newton's corpuscular theory, from the 1830s[2] until the end of the 19th century.

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 lighthouses, saving unknown numbers of lives at sea. The simpler dioptric (purely refractive) stepped lens, first proposed by Count Buffon[3] and independently reinvented by Fresnel, is used in screen magnifiers and in condenser lenses for overhead projectors.

By expressing Huygens' principle of secondary waves and Young's principle of interference in quantitative terms, and supposing that simple colors consist of 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.[4] By further supposing that light waves are purely 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 and reflection coefficients at a boundary between transparent 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 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, 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.

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.

Inevitably, after the wave theory of light was subsumed by Maxwell's electromagnetic theory in the 1860s and '70s, 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, 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."[5]

Early life

Family

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 (1755–1805)[6] and his wife Augustine, née Mérimée (1755?–1833).[7] In 1790, following the Revolution, Broglie became part of the département of Eure. The family moved twice — in 1790 to Cherbourg,[8] and in 1794[9]: 166  to Jacques' home town of Mathieu, where Madame Fresnel remained as a widow,[10]: 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.[7] The third, Léonor (1790–1869),[6] followed Augustin into civil engineering, succeeded him as Secretary of the Lighthouse Commission,[11] and helped to edit his collected works (Fresnel, Oeuvres complètes, 1866–70). The fourth, Fulgence Fresnel (1795–1855), became a noted linguist, diplomat, and orientalist, and occasionally assisted Augustin with negotiations.[12]

Their mother's brother Léonor Mérimée (1757–1836),[7] father of the writer Prosper Mérimée (1803–1870), was a painter who studied 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 French scientific establishment (see below).

Education

Augustin and his brothers were initially home-schooled by their mother. Augustin was considered the slow one, not 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 were too dangerous to play with, provoking a crackdown from his elders.

e have a tradition that, at the age of eight could not read well and had difficulty in remembering new words. There was no laziness there : all his life, Fresnel was to loath the simplest exercises of memory

591: It seems he went on experimenting in ballistics till his weapons became so effective that a deputation of frenzied farmers had to wait upon the schoolmaster ; the supposedly slow-witted boy was then aged ten.

In October 1803, Louis is examined in the annual competition for entry into the École Poly- technique and accepted : we shall not hear again of poor Louis, who perishes at twenty-two under Badajoz. In 1804, Augustin in his turn is accepted. In some subjects he has barely passed, but in Geometry his answers have surprised and delighted the examiner, already a well-known man : Legendre.

592: Since the École's records, still preserved, begin in 1808, we know next to nothing of Fresnel's life there. Health didn't improve though it does not appear he ever had to stop attending. seems to have excelled in the graphic arts and geometry. few or no friends.

His early progress in learning was slow, and when eight years old he was still unable to read. At the age of thirteen he entered the École Centrale in Caen, and at sixteen and a half the École Polytechnique, where he acquitted himself with distinction. Thence he went to the École des Ponts et Chaussées. He served as an engineer successively in the departments of Vendée, Drôme and Ille-et-Vilaine; but his espousal of the cause of the Bourbons in 1814 occasioned, on Napoleon’s reaccession to power, the loss of his appointment. On the second restoration he obtained a post as engineer in Paris.[13]

In his 17th year he entered the polytechnic school, where he gained the applause of Legen- dre by a peculiar solution of a question in geometry.[14]

Religious views

Fresnel's parents were Roman Catholics of the Jansenist sect, characterized by an extreme Augustinian view of original sin. In the early home-schooling that the four boys received from their mother, religion took first place. In 1802, Mme Fresnel wrote to Louis concerning Augustin:

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.[15]: 147 

Augustin Fresnel indeed regarded his intellectual talents as a gift from God, and considered it his duty to use them for the benefit of others. Plagued by poor health, and determined to do his duty before death thwarted him, he shunned pleasures and worked himself to exhaustion.[9]: 166  According to his fellow engineer Alphonse Duleau, who helped to nurse him through his final illness, Fresnel saw the study of nature as 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."[15]: 148–9n  Although Jansenism is considered 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."[1]

Engineering assignments

After graduating, he su- perintended the engineering operations of the government in the department of Vendee for eight years.??[14]

During the Hundred Days he was persona non grata, but after Waterloo he returned to Paris to his former occupation.[16]

Contributions to physical optics

Historical context

chisholm-1911-brewster:

The most important subjects of his inquiries are enumerated by Forbes under the following five heads:—(1) The laws of polarization by reflection and refraction, and other quantitative laws of phenomena; (2) The discovery of the polarizing structure induced by heat and pressure; (3) The discovery of crystals with two axes of double refraction, and many of the laws of their phenomena, including the connexion of optical structure and crystalline forms; (4) The laws of metallic reflection; (5) Experiments on the absorption of light. In this line of investigation the prime importance belongs to the discovery (1) of the connexion between the refractive index and the polarizing angle, (2) of biaxial crystals, and (3) of the production of double refraction by irregular heating.

In 1819 Brewster undertook further editorial work by establishing, in conjunction with Robert Jameson (1774-1854), the Edinburgh Philosophical Journal, which took the place of the Edinburgh Magazine. The first ten volumes (1819-1824) were published under the joint editorship of Brewster and Jameson, the remaining four volumes (1825-1826) being edited by Jameson alone. After parting company with Jameson, Brewster started the Edinburgh Journal of Science in 1824, sixteen volumes of which appeared under his editorship during the years 1824-1832, with very many articles from his own pen. To the transactions of various learned societies he contributed from first to last between three and four hundred papers, and few of his contemporaries wrote so much for the various reviews. In the North British Review alone seventy-five articles of his appeared.

Quarterly Review

Forbes:—"His scientific glory is different in kind from that of Young and Fresnel; but the discoverer of the law of polarization of biaxial crystals, of optical mineralogy, and of double refraction by compression, will always occupy a foremost rank in the intellectual history of the age."

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.[1]

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.[17]

Polarization

Partial reflection

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°.[13]

Double refraction

and by modeling the medium as an array of particles subject to 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.[14]

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.[18] 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.[19] Further samples followed at Howth Baily, North Foreland, and at least four other locations.[18] But much of the light was wasted by absorption in the glass.

1: Cross-section of Buffon/Fresnel lens. 2: Cross-section of conventional plano-convex lens of equivalent power. (Buffon's version was biconvex.[20])

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, Count Buffon proposed grinding such prisms as steps in a single piece of glass.[3] In 1790[21] (although secondary sources give the date as 1773[22]: 609  or 1788[23]), 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.[24][25] These designs were intended not for lighthouses,[3] but for burning glasses.[22]: 609  Brewster, however, proposed a system similar to Condorcet's in 1811,[3][14][23] and by 1820 was advocating its use in British lighthouses.[26]

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.[24] The Commission had been established by Napoleon in 1811, and placed under the Corps des ponts — Fresnel's employer.[27]

On 29 August 1819, unaware of the Buffon-Condorcet-Brewster proposal,[14][24] 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.[28] 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".[29] But, whereas Buffon's version was biconvex and in one piece, Fresnel's was 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 Count Rumford[30]: 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.[31]

(Fresnel acknowledged the British lenses and Buffon's invention in a memoir published in 1822.[30]: 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;[26] but the text makes it clear that Fresnel's involvement began no later than 1819.[30]: 1 )

Fresnel's innovations

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 by Saint-Gobain,[32], 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.[33] 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.[30]: 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 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.[34] It was about this time that Fresnel started coughing up blood.Cite error: A <ref> tag is missing the closing </ref> (see the help page). He was also an examiner at the École Polytechnique (since 1821),[1] but poor health soon induced him to resign that post and save his energy for his lighthouse work.[35] The following year 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.[36]

Also in 1825, Fresnel extended his fixed design by adding a rotating array outside the fixed array.[24] Each panel of the rotating array refracted part of the fixed light from a horizontal fan into a narrow beam.

First-order rotating catadioptric Fresnel lens, dated 1870, on display 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.

To reduce the loss of light in the reflecting elements, Fresnel proposed to replace the mirrors with catadioptric prisms, through which the light would pass by two refractions and one total internal reflection.[37] 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,[38] 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 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.[39]

Close-up view of a thin plastic Fresnel lens.

Later developments

Production of one-piece stepped lenses (roughly as envisaged by Buffon) eventually became profitable. By the 1870s, in the USA, such lenses were made of pressed glass and used with small lights on ships and piers.[14] Similar lenses, with finer steps, serve as condensers in overhead projectors. Still finer steps can be found in low-cost plastic "sheet" magnifiers.

Honors

In May 1824, he was appointed secretary of the commission of light- houses. He was at the same time engineer of the pavements of Paris and one of the exami- ners of the polytechnic school.[14]

But, as he wrote to Young in 1824, in him "that sensibility, or that vanity, which people call love of glory" had been blunted. "All the compliments," he says, "that I have received from Arago, Laplace and Biot never gave me so much pleasure as the discovery of a theoretic truth, or the confirmation of a calculation by experiment."[13]

In 1823 he was unanimously elected a member of the Academy.[13][1][14]

In 1827 he received the Rumford Medal.[16][13]

In 1824,[40] he was made a chevalier de la Légion d'honneur (Knight of the Legion of Honour).[41]

Decline and death

Fresnel's grave at Père Lachaise Cemetery, Paris, photographed in 2014. The inscription on the headstone is partly eroded away.

Rumford medal, which was presented to him upon his deathbed by his friend and collaborator Arago.[14]

Unfinished business

Ether models

Conical refraction

Legacy

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.[42]

With a century after Fresnel's initial proposal, more than 10,000 lights with Fresnel lenses marked coastlines around the world.[43] The numbers of lives saved can only be guessed at. Concerning the other benefits, 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 becamed linked into the world economy.[44]

In the history of physical optics, Fresnel's successful revival of the wave theory seems to identify him as the pivotal figure between Newton, who held that light consisted of corpuscles, and Maxwell, who established that light waves are electromagnetic. Whereas Einstein described Maxwell's work as "the most profound and the most fruitful that physics has experienced since the time of Newton,"[45] 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".[46]: 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 Science Association, he wrote: "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."[47]: 382  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."[5] 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",[48] which appeared in the same year as Maxwell's Treatise on Electricity and Magnetism (1873).
  • 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:

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 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.[49]: 370-71 

Bust of Fresnel by David d'Angers.

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 quanta, which were eventually identified with particles called 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

  1. ^ a b c d e H.M. Brock, "Fresnel, Augustin-Jean", Catholic Encyclopedia, 1907–12, v.6 (1909).
  2. ^ Darrigol, 2012, pp. 220–23
  3. ^ a b c d H. Chisholm (ed.), "Lighthouse", Encyclopedia Britannica, 11th Ed., 1911.
  4. ^ Darrigol, 2012, p.205
  5. ^ a b H. Lloyd, Lectures on the Wave-theory of Light, Dublin: Milliken, 1841, Part II, Lecture III, p.26.
  6. ^ a b J.H. Favre, "Augustin Fresnel", gw.geneanet.org, accessed 30 August 2017.
  7. ^ a b c 'jeanelie' (author), "Augustine Charlotte Marie Louise Merimee" and "Louis Jacques Fresnel", gw.geneanet.org, accessed 30 August 2017.
  8. ^ Levitt, 2013, p.23.
  9. ^ a b R.H. Silliman, "Fresnel, Augustin Jean", Complete Dictionary of Scientific Biography, Detroit: Charles Scribner's Sons, 2008, v.5, pp. 165–71. (The version at encyclopedia.com lacks the diagram and equations.)
  10. ^ Cite error: The named reference boutry was invoked but never defined (see the help page).
  11. ^ Levitt, 2013, p.99.
  12. ^ Levitt, 2013, p.72.
  13. ^ a b c d e H. Chisholm (ed.), "Fresnel, Augustin Jean", Encyclopedia Britannica, 11th Ed., 1911.
  14. ^ a b c d e f g h i G. Ripley & C.A. Dana (ed.), "Fresnel, Augustin Jean", American Cyclopedia, v.7, pp.486–9.
  15. ^ a b K.A. Kneller (tr. T.M. Kettle), 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.
  16. ^ a b G.E. Rines (ed.), "Fresnel, Augustin Jean", Encyclopedia Americana, 1918–20, v.12 (1919), p.93. (Note: 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.)
  17. ^ A. Fresnel, "Mémoire sur la diffraction de la lumière" (deposited 1818, "crowned" 1819), in Oeuvres complètes, v.1, pp. 247–364; partly translated as "Fresnel's prize memoir on the diffraction of light", in 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.)
  18. ^ a b T. Tag, "Lens use prior to Fresnel", U.S. Lighthouse Society, accessed 12 August 2017; archived 20 May 2017.
  19. ^ Levitt, 2013, p.57.
  20. ^ Levitt, 2013, p.59.
  21. ^ Nicolas de Condorcet, Éloge de M. le Comte de Buffon, Paris: Chez Buisson, 1790, pp. 11–12.
  22. ^ a b D. Appleton & Co., "Sea-lights", Dictionary of Machines, Mechanics, Engine-work, and Engineering, 1861, v.2.
  23. ^ a b T. Tag, "Chronology of Lighthouse Events", U.S. Lighthouse Society, accessed 22 August 2017; archived 8 April 2017.
  24. ^ a b c d T. Tag, "The Fresnel lens", U.S. Lighthouse Society, accessed 12 August 2017; archived 22 July 2017.
  25. ^ Levitt, 2013, p.71.
  26. ^ a b H. Chisholm (ed.), "Brewster, Sir David", Encyclopedia Britannica, 11th Ed., 1911, v.4, pt.3.
  27. ^ Levitt, 2013, pp. 49–50.
  28. ^ Levitt, 2013, pp. 56,58.
  29. ^ Levitt, 2013, p.59.
  30. ^ a b c d A. Fresnel, "Mémoire sur un nouveau système d'éclairage des phares", read at the Académie des Sciences, 29 July 1822; translated by T. Tag as "Memoir Upon A New System Of Lighthouse Illumination", U.S. Lighthouse Society, accessed 26 August 2017; archived 19 August 2016.
  31. ^ Levitt, 2013, pp. 59–66.
  32. ^ Levitt, 2013, p.71.
  33. ^ D. Gombert, photograph of the Optique de Cordouan in the collection of the Musée des Phares et Balises, Ouessant, France, 23 March 2017.
  34. ^ Levitt, 2013, pp. 72–3.
  35. ^ Levitt, 2013, p.97.
  36. ^ Levitt, 2013, pp. 83–4.
  37. ^ Levitt, 2013, pp. 79–80.
  38. ^ Musée national de la Marine, "Appareil catadioptrique, Appareil du canal Saint-Martin", accessed 26 August 2017; archived 26 August 2017.
  39. ^ Levitt, 2013, pp. 108–10, 113–16.
  40. ^ Levitt, 2013, p.77.
  41. ^ Académie des sciences, Membres… "Augustin Fresnel", accessed 21 August 2017; archived 15 February 2017.
  42. ^ Phare de Cordouan, "The lighting systems of the Cordouan Lighthouse", accessed 26 August 2017; archived 22 September 2016.
  43. ^ Levitt, 2013, p.19.
  44. ^ Levitt, 2013, p.8.
  45. ^ James Clerk Maxwell Foundation, "Who was James Clerk Maxwell?", accessed 6 August 2017; archived 30 June 2017.
  46. ^ J. MacCullagh, "On the Double Refraction of Light in a Crystallized Medium, according to the Principles of Fresnel", Transactions of the Royal Irish Academy, v.16 (1830), pp. 65–78; jstor.org/stable/30079025.
  47. ^ H. Lloyd, "Report on the progress and present state of physical optics", 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.
  48. ^ H. Lloyd, Elementary Treatise on the Wave-theory of Light, 3rd Ed., London: Longmans, Green, & Co., 1873, p.167. (Cf. 2nd Ed., 1857, p.136.)
  49. ^ W. Whewell, History of the Inductive Sciences: From the Earliest to the Present Time, 3rd Ed., London: John W. Parker & Son, 1857, v.2.

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Bibliography

  • O. Darrigol, A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford, 2012.
  • A. Fresnel (ed. H. de Senarmont, E. Verdet, L. Frenel), Oeuvres complètes d'Augustin Fresnel (3 vols.), Paris: Imprimerie impériale, 1866–70; v.1 (1866), v.2 (1868), v.3 (1870).
  • T.H. Levitt, A Short Bright Flash: Augustin Fresnel and the Birth of the Modern Lighthouse, New York: W.W. Norton, 2013.

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