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1501 | later, on 22 March. Arago's verification of Poisson's counter-intuitive prediction passed into folklore as if it had decided the prize. That view, however, is not supported by the judges' report, which gave the matter only two sentences in the penultimate paragraph. Neither did Fresnel's triumph immediately convert Laplace, Biot, and Poisson to the wave theory, for at least four reasons. First, although the professionalization of science in France had established common standards, it was one thing to acknowledge a piece of research as meeting those standards, and another thing to regard it as conclusive. Second, it was possible to interpret | "Augustin-Jean Fresnel" | [
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1502 | Fresnel's integrals as rules for combining "rays". Arago even encouraged that interpretation, presumably in order to minimize resistance to Fresnel's ideas. Even Biot began teaching the Huygens-Fresnel principle without committing himself to a wave basis. Third, Fresnel's theory did not explain the mechanism of generation of secondary waves or why they had any significant angular spread; this issue particularly bothered Poisson. Fourth, the question that most exercised optical physicists at that time was not diffraction, but polarization — on which Fresnel had been working, but was yet to make his critical breakthrough. An "emission" theory of light was one that | "Augustin-Jean Fresnel" | [
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1503 | regarded the propagation of light as the transport of some kind of matter. While the corpuscular theory was obviously an emission theory, the converse did not follow: in principle, one could be an emissionist without being a corpuscularist. This was convenient because, beyond the ordinary laws of reflection and refraction, emissionists never managed to make testable quantitative predictions from a theory of forces acting on corpuscles of light. But they "did" make quantitative predictions from the premises that rays were countable objects, which were conserved in their interactions with matter (except absorbent media), and which had particular orientations with respect | "Augustin-Jean Fresnel" | [
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1504 | to their directions of propagation. According to this framework, polarization and the related phenomena of double refraction and partial reflection involved altering the orientations of the rays and/or selecting them according to orientation, and the state of polarization of a beam (a bundle of rays) was a question of how many rays were in what orientations: in a fully polarized beam, the orientations were all the same. This approach, which Jed Buchwald has called "selectionism", was pioneered by Malus and diligently pursued by Biot. Fresnel, in contrast, decided to introduce polarization into interference experiments. In the summer of 1816, Fresnel | "Augustin-Jean Fresnel" | [
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] |
1505 | discovered that when a birefringent crystal produced two images of a single slit, he could "not" obtain the usual two-slit interference pattern, even if he compensated for the different propagation times. A more general experiment, suggested by Arago, found that if the two beams of a double-slit device were separately polarized, the interference pattern appeared and disappeared as the polarization of one beam was rotated, giving full interference for parallel polarizations, but no interference for perpendicular polarizations . These experiments, among others, were eventually reported in a brief memoir published in 1819 and later translated into English. In a memoir | "Augustin-Jean Fresnel" | [
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1506 | drafted on 30 August 1816 and revised on 6 October, Fresnel reported an experiment in which he placed two matching thin laminae in a double-slit apparatus — one over each slit, with their optic axes perpendicular — and obtained two interference patterns offset in opposite directions, with perpendicular polarizations. This, in combination with the previous findings, meant that each lamina split the incident light into perpendicularly polarized components with different velocities — just like a normal (thick) birefringent crystal, and contrary to Biot's "mobile polarization" hypothesis. Accordingly, in the same memoir, Fresnel offered his first attempt at a wave theory | "Augustin-Jean Fresnel" | [
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1507 | of chromatic polarization. When polarized light passed through a crystal lamina, it was split into ordinary and extraordinary waves (with intensities described by Malus's law), and these were perpendicularly polarized and therefore did not interfere, so that no colors were produced (yet). But if they then passed through an "analyzer" (second polarizer), their polarizations were brought into alignment (with intensities again modified according to Malus's law), and they would interfere. This explanation, by itself, predicts that if the analyzer is rotated 90°, the ordinary and extraordinary waves simply switch roles, so that if the analyzer takes the form of a | "Augustin-Jean Fresnel" | [
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1508 | calcite crystal, the two images of the lamina should be of the same hue (this issue is revisited below). But in fact, as Arago and Biot had found, they are of complementary colors. To correct the prediction, Fresnel proposed a phase-inversion rule whereby "one" of the constituent waves of "one" of the two images suffered an additional 180° phase shift on its way through the lamina. This inversion was a weakness in the theory relative to Biot's, as Fresnel acknowledged, although the rule specified which of the two images had the inverted wave. Moreover, Fresnel could deal only with special | "Augustin-Jean Fresnel" | [
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] |
1509 | cases, because he had not yet solved the problem of superposing sinusoidal functions with arbitrary phase differences due to propagation at different velocities through the lamina. He solved that problem in a "supplement" signed on 15 January 1818 (mentioned above). In the same document, he accommodated Malus's law by proposing an underlying law: that if polarized light is incident on a birefringent crystal with its optic axis at an angle "θ" to the "plane of polarization", the ordinary and extraordinary vibrations (as functions of time) are scaled by the factors cos"θ" and sin"θ", respectively. Although modern readers easily interpret these | "Augustin-Jean Fresnel" | [
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1510 | factors in terms of perpendicular components of a "transverse" oscillation, Fresnel did not (yet) explain them that way. Hence he still needed the phase-inversion rule. He applied all these principles to a case of chromatic polarization not covered by Biot's formulae, involving "two" successive laminae with axes separated by 45°, and obtained predictions that disagreed with Biot's experiments (except in special cases) but agreed with his own. Fresnel applied the same principles to the standard case of chromatic polarization, in which "one" birefringent lamina was sliced parallel to its axis and placed between a polarizer and an analyzer. If the | "Augustin-Jean Fresnel" | [
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1511 | analyzer took the form of a thick calcite crystal with its axis in the plane of polarization, Fresnel predicted that the intensities of the ordinary and extraordinary images of the lamina were respectively proportional to where formula_5 is the angle from the initial plane of polarization to the optic axis of the lamina, formula_6 is the angle from the initial plane of polarization to the plane of polarization of the final ordinary image, and formula_7 is the phase lag of the extraordinary wave relative to the ordinary wave due to the difference in propagation times through the lamina. The terms | "Augustin-Jean Fresnel" | [
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1512 | in formula_7 are the frequency-dependent terms and explain why the lamina must be "thin" in order to produce discernible colors: if the lamina is too thick, formula_9 will pass through too many cycles as the frequency varies through the visible range, and the eye (which divides the visible spectrum into only three bands) will not be able to resolve the cycles. From these equations it is easily verified that formula_10 for all formula_11 so that the colors are complementary. Without the phase-inversion rule, there would be a "plus" sign in front of the last term in the second equation, so | "Augustin-Jean Fresnel" | [
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1513 | that the formula_7-dependent term would be the same in both equations, implying (incorrectly) that the colors were of the same hue. These equations were included in an undated note that Fresnel gave to Biot, to which Biot added a few lines of his own. If we substitute then Fresnel's formulae can be rewritten as which are none other than Biot's empirical formulae of 1812, except that Biot interpreted formula_17 and formula_18 as the "unaffected" and "affected" selections of the rays incident on the lamina. If Biot's substitutions were accurate, they would imply that his experimental results were more fully explained | "Augustin-Jean Fresnel" | [
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1514 | by Fresnel's theory than by his own. Arago delayed reporting on Fresnel's works on chromatic polarization until June 1821, when he used them in a broad attack on Biot's theory. In his written response, Biot protested that Arago's attack went beyond the proper scope of a report on the nominated works of Fresnel. But Biot also claimed that the substitutions for formula_17 and formula_20 and therefore Fresnel's expressions for formula_21 and formula_22 were empirically wrong because when Fresnel's intensities of spectral colors were mixed according to Newton's rules, the squared cosine and sine functions varied too smoothly to account for | "Augustin-Jean Fresnel" | [
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1515 | the observed sequence of colors. That claim drew a written reply from Fresnel, who disputed whether the colors changed as abruptly as Biot claimed, and whether the human eye could judge color with sufficient objectivity for the purpose. On the latter question, Fresnel pointed out that different observers may give different names to the same color. Furthermore, he said, a single observer can only compare colors side-by-side; and even if they are judged to be the same, the identity is of sensation, not necessarily of composition. Fresnel's oldest and strongest point — that thin crystals were subject to the same | "Augustin-Jean Fresnel" | [
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1516 | laws as thick ones and did not need or allow a separate theory — Biot left unanswered. Arago and Fresnel were seen to have won the debate. Moreover, by this time Fresnel had a new, simpler derivation of his equations on chromatic polarization. In the draft memoir of 30 August 1816, Fresnel mentioned two hypotheses — one of which he attributed to Ampère — by which the non-interference of orthogonally-polarized beams could be explained if polarized light waves were "partly" transverse. But Fresnel could not develop either of these ideas into a comprehensive theory. According to his later account, both | "Augustin-Jean Fresnel" | [
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1517 | he and Ampère realized as early as September 1816 that the non-interference of orthogonally-polarized beams, together with the phase-inversion rule in chromatic polarization, would be most easily explained if the waves were "purely" transverse. But that would raise a new difficulty: as natural light seemed to be "un"polarized and its waves were therefore presumed to be longitudinal, one would need to explain how the longitudinal component of vibration disappeared on polarization, and why it did not reappear when polarized light was reflected or refracted obliquely by a glass plate. Independently, on 12 January 1817, Young wrote to Arago (in English) | "Augustin-Jean Fresnel" | [
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1518 | noting that a transverse vibration would constitute a polarization, and that if two longitudinal waves crossed at a significant angle, they could not cancel without leaving a residual transverse vibration. Young repeated this idea in an article published in a supplement to the "Encyclopædia Britannica" in February 1818, in which he added that Malus's law would be explained if polarization consisted in a transverse motion. Thus Fresnel, by his own testimony, may not have been the first person to suspect that light waves could have a transverse "component", or that "polarized" waves were exclusively transverse. And it was Young, not | "Augustin-Jean Fresnel" | [
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1519 | Fresnel, who first "published" the idea that polarization depends on the orientation of a transverse vibration. But these incomplete theories had not reconciled the nature of polarization with the apparent existence of "unpolarized" light; that achievement was to be Fresnel's alone. In a note that Buchwald dates in the summer of 1818, Fresnel entertained the idea that unpolarized waves could have vibrations of the same energy and obliquity, with their orientations distributed uniformly about the wave-normal, and that the degree of polarization was the degree of "non"-uniformity in the distribution. Two pages later he noted, apparently for the first time | "Augustin-Jean Fresnel" | [
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1520 | in writing, that his phase-inversion rule and the non-interference of orthogonally-polarized beams would be easily explained if the vibrations of fully polarized waves were "perpendicular to the normal to the wave" — that is, purely transverse. But if he could account for "lack" of polarization by averaging out the transverse component, he did not also need to assume a longitudinal component. It was enough to suppose that light waves are "purely" transverse, hence "always" polarized in the sense of having a particular transverse orientation, and that the "unpolarized" state of natural or "direct" light is due to rapid and random | "Augustin-Jean Fresnel" | [
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1521 | variations in that orientation, in which case two "coherent" portions of "unpolarized" light will still interfere because their orientations will be synchronized. It is not known exactly when Fresnel made this last step, because there is no relevant documentation from 1820 or early 1821 (perhaps because he was too busy working on lighthouse-lens prototypes; see below). But he first "published" the idea in a paper on ""Calcul des teintes…"" ("calculation of hues…"), serialized in Arago's "Annales" for May, June, and July 1821. In the first installment, Fresnel described "direct" (unpolarized) light as "the rapid succession of systems of waves polarized | "Augustin-Jean Fresnel" | [
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1522 | in all directions", and gave the modern explanation of chromatic polarization. In the second installment, he revealed the suspicion that he and Ampère had harbored since 1816, and the difficulty it raised. He continued: According to this new view, he wrote, ""the act of polarization consists not in creating transverse motions, but in decomposing them in two fixed, mutually perpendicular directions, and in separating the two components"". While selectionists could insist on interpreting Fresnel's diffraction integrals in terms of discrete, countable rays, they could not do the same with his theory of polarization. For a selectionist, the state of polarization | "Augustin-Jean Fresnel" | [
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1523 | of a beam concerned the distribution of orientations over the "population" of rays, and that distribution was presumed to be static. For Fresnel, the state of polarization of a beam concerned the variation of a displacement over "time". That displacement might be constrained but was "not" static, and rays were geometric constructions, "not" countable objects. The conceptual gap between the wave theory and selectionism had become unbridgeable. The other difficulty posed by pure transverse waves, of course, was the apparent implication that the aether was an elastic solid (!) but, unlike other elastic solids, incapable of transmitting "longitudinal" waves. The | "Augustin-Jean Fresnel" | [
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1524 | wave theory was cheap on assumptions, but its latest assumption was expensive on credulity. If that assumption was to be widely entertained, its explanatory power would need to be impressive. In the second installment of "Calcul des teintes" (June 1821), Fresnel supposed, by analogy with sound waves, that the density of the aether in a refractive medium was inversely proportional to the square of the wave velocity, and therefore directly proportional to the square of the refractive index. For reflection and refraction at the surface between two isotropic media of different indices, Fresnel decomposed the transverse vibrations into two perpendicular | "Augustin-Jean Fresnel" | [
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1525 | components, now known as the "s" and "p" components, which are parallel to the "surface" and the "plane" of incidence, respectively; in other words, the "s" and "p" components are respectively "square" and "parallel" to the plane of incidence. For the "s" component, Fresnel supposed that the interaction between the two media was analogous to an elastic collision, and obtained a formula for what we now call the "reflectivity": the ratio of the reflected intensity to the incident intensity. The predicted reflectivity was non-zero at all angles. The third installment (July 1821) was a short "postscript" in which Fresnel announced | "Augustin-Jean Fresnel" | [
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1526 | that he had found, by a "mechanical solution", a formula for the reflectivity of the "p" component, which predicted that "the reflectivity was zero at the Brewster angle". So polarization by reflection had been accounted for — but with the proviso that the direction of vibration in Fresnel's model was "perpendicular" to the plane of polarization as defined by Malus. (On the ensuing controversy, see "Plane of polarization".) For other angles of incidence, the technology of the time did not allow the "s" and "p" reflectivities to be measured accurately enough to test Fresnel's formulae. But the formulae could be | "Augustin-Jean Fresnel" | [
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1527 | rewritten in terms of what we now call the "reflection coefficient": the signed ratio of the reflected amplitude to the incident amplitude. Then, if the plane of polarization of the incident ray was at 45° to the plane of incidence, the tangent of the corresponding angle for the reflected ray was obtainable from the "ratio" of the two reflection coefficients, and this angle could be measured. Fresnel measured it for a range of angles of incidence, for glass and water, and the agreement between the calculated and measured angles was better than 1.5° in all cases. Fresnel gave details of | "Augustin-Jean Fresnel" | [
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1528 | the "mechanical solution" in a memoir read to the Académie des Sciences on 7 January 1823. Conservation of energy was combined with continuity of the "tangential" vibration at the interface. The resulting formulae for the reflection coefficients and reflectivities became known as the "Fresnel equations". The reflection coefficients for the "s" and "p" polarizations are most succinctly expressed as where formula_5 and formula_26 are the angles of incidence and refraction; these equations are known respectively as "Fresnel's sine law" and "Fresnel's tangent law". By allowing the coefficients to be "complex", Fresnel even accounted for the different phase shifts of the | "Augustin-Jean Fresnel" | [
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1529 | "s" and "p" components due to total internal reflection. This success inspired James MacCullagh and Augustin-Louis Cauchy, beginning in 1836, to analyze reflection from metals by using the Fresnel equations with a complex refractive index. The same technique is applicable to non-metallic opaque media. With these generalizations, the Fresnel equations can predict the appearance of a wide variety of objects under illumination — for example, in computer graphics . In a memoir dated 9 December 1822, Fresnel coined the terms "linear polarization" (French: "polarisation rectiligne") for the simple case in which the perpendicular components of vibration are in phase or | "Augustin-Jean Fresnel" | [
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1530 | 180° out of phase, "circular polarization" for the case in which they are of equal magnitude and a quarter-cycle (±90°) out of phase, and "elliptical polarization" for other cases in which the two components have a fixed amplitude ratio and a fixed phase difference. He then explained how optical rotation could be understood as a species of birefringence. Linearly-polarized light could be resolved into two circularly-polarized components rotating in opposite directions. If these components propagated at slightly different speeds, the phase difference between them — and therefore the direction of their linearly-polarized resultant — would vary continuously with distance. These | "Augustin-Jean Fresnel" | [
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1531 | concepts called for a redefinition of the distinction between polarized and unpolarized light. Before Fresnel, it was thought that polarization could vary in direction, and in degree (e.g., due to variation in the angle of reflection off a transparent body), and that it could be a function of color (chromatic polarization), but not that it could vary in "kind". Hence it was thought that the degree of polarization was the degree to which the light could be suppressed by an analyzer with the appropriate orientation. Light that had been converted from linear to elliptical or circular polarization (e.g., by passage | "Augustin-Jean Fresnel" | [
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1532 | through a crystal lamina, or by total internal reflection) was described as partly or fully "depolarized" because of its behavior in an analyzer. "After" Fresnel, the defining feature of polarized light was that the perpendicular components of vibration had a fixed ratio of amplitudes and a fixed difference in phase. By that definition, elliptically or circularly polarized light is "fully" polarized although it cannot be fully suppressed by an analyzer alone. The conceptual gap between the wave theory and selectionism had widened again. By 1817 it had been discovered by Brewster, but not adequately reported, that plane-polarized light was partly | "Augustin-Jean Fresnel" | [
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1533 | depolarized by total internal reflection if initially polarized at an acute angle to the plane of incidence. Fresnel rediscovered this effect and investigated it by including total internal reflection in a chromatic-polarization experiment. With the aid of his "first" theory of chromatic polarization, he found that the apparently depolarized light was a mixture of components polarized parallel and perpendicular to the plane of incidence, and that the total reflection introduced a phase difference between them. Choosing an appropriate angle of incidence (not yet exactly specified) gave a phase difference of 1/8 of a cycle (45°). Two such reflections from the | "Augustin-Jean Fresnel" | [
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1534 | "parallel faces" of "two coupled prisms" gave a phase difference of 1/4 of a cycle (90°). These findings were contained in a memoir submitted to the Académie on 10 November 1817 and read a fortnight later. An undated marginal note indicates that the two coupled prisms were later replaced by a single "parallelepiped in glass" — now known as a "Fresnel rhomb". This was the memoir whose "supplement", dated January 1818, contained the method of superposing sinusoidal functions and the restatement of Malus's law in terms of amplitudes. In the same supplement, Fresnel reported his discovery that optical rotation could | "Augustin-Jean Fresnel" | [
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1535 | be imitated by passing the polarized light through a Fresnel rhomb (still in the form of "coupled prisms"), followed by an ordinary birefringent lamina sliced parallel to its axis, with the axis at 45° to the plane of reflection of the Fresnel rhomb, followed by a second Fresnel rhomb at 90° to the first. In a further memoir read on 30 March, Fresnel reported that if polarized light was fully "depolarized" by a Fresnel rhomb — now described as a parallelepiped — its properties were not further modified by a subsequent passage through an optically rotating medium or device. The | "Augustin-Jean Fresnel" | [
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1536 | connection between optical rotation and birefringence was further explained in 1822, in the memoir on elliptical and circular polarization. This was followed by the memoir on reflection, read in January 1823, in which Fresnel quantified the phase shifts in total internal reflection, and thence calculated the precise angle at which a Fresnel rhomb should be cut in order to convert linear polarization to circular polarization. For a refractive index of 1.51, there were two solutions: about 48.6° and 54.6°. When light passes through a slice of calcite cut perpendicular to its optic axis, the difference between the propagation times of | "Augustin-Jean Fresnel" | [
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1537 | the ordinary and extraordinary waves has a second-order dependence on the angle of incidence. If the slice is observed in a highly convergent cone of light, that dependence becomes significant, so that a chromatic-polarization experiment will show a pattern of concentric rings. But most minerals, when observed in this manner, show a more complicated pattern of rings involving two foci and a lemniscate curve, as if they had "two" optic axes. The two classes of minerals naturally become known as "uniaxal" and "biaxal" — or, in later literature, "uniaxial" and "biaxial". In 1813, Brewster observed the simple concentric pattern in | "Augustin-Jean Fresnel" | [
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1538 | "beryl, emerald, ruby &c." The same pattern was later observed in calcite by Wollaston, Biot, and Seebeck. Biot, assuming that the concentric pattern was the general case, tried to calculate the colors with his theory of chromatic polarization, and succeeded better for some minerals than for others. In 1818, Brewster belatedly explained why: seven of the twelve minerals employed by Biot had the lemniscate pattern, which Brewster had observed as early as 1812; and the minerals with the more complicated rings also had a more complicated law of refraction. In a uniform crystal, according to Huygens' theory, the secondary wavefront | "Augustin-Jean Fresnel" | [
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1539 | that expands from the origin in unit time is the "ray-velocity surface" — that is, the surface whose "distance" from the origin in any direction is the ray velocity in that direction. In calcite, this surface is two-sheeted, consisting of a sphere (for the ordinary wave) and an oblate spheroid (for the extraordinary wave) touching each other at opposite points of a common axis — touching at the north and south poles, if we may use a geographic analogy. But according to Malus's "corpuscular" theory of double refraction, the ray velocity was proportional to the reciprocal of that given by | "Augustin-Jean Fresnel" | [
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] |
1540 | Huygens' theory, in which case the velocity law was of the form where formula_28 and formula_29 were the ordinary and extraordinary ray velocities "according to the corpuscular theory", and formula_30 was the angle between the ray and the optic axis. By Malus's definition, the plane of polarization of a ray was the plane of the ray and the optic axis if the ray was ordinary, or the perpendicular plane (containing the ray) if the ray was extraordinary. In Fresnel's model, the direction of vibration was normal to the plane of polarization. Hence, for the sphere (the ordinary wave), the vibration | "Augustin-Jean Fresnel" | [
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1541 | was along the lines of latitude (continuing the geographic analogy); and for the spheroid (the extraordinary wave), the vibration was along the lines of longitude. On 29 March 1819, Biot presented a memoir in which he proposed simple generalizations of Malus's rules for a crystal with "two" axes, and reported that both generalizations seemed to be confirmed by experiment. For the velocity law, the squared sine was replaced by the "product" of the sines of the angles from the ray to the two axes ("Biot's sine law"). And for the polarization of the ordinary ray, the plane of the ray | "Augustin-Jean Fresnel" | [
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1542 | and the axis was replaced by the plane bisecting the dihedral angle between the two planes each of which contained the ray and one axis ("Biot's dihedral law"). Biot's laws meant that a biaxial crystal with axes at a small angle, cleaved in the plane of those axes, behaved nearly like a uniaxial crystal at near-normal incidence; this was fortunate because gypsum, which had been used in chromatic-polarization experiments, is biaxial. Until Fresnel turned his attention to biaxial birefringence, it was assumed that one of the two refractions was ordinary, even in biaxial crystals. But, in a memoir submitted on | "Augustin-Jean Fresnel" | [
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1543 | 19 November 1821, Fresnel reported two experiments on topaz showing that "neither refraction" was ordinary in the sense of satisfying Snell's law; that is, neither ray was the product of spherical secondary waves. The same memoir contained Fresnel's first attempt at the biaxial velocity law. For calcite, if we interchange the equatorial and polar radii of Huygens' oblate spheroid while preserving the polar direction, we obtain a "prolate" spheroid touching the sphere at the equator. A plane through the center/origin cuts this prolate spheroid in an ellipse whose major and minor semi-axes give the magnitudes of the extraordinary and ordinary | "Augustin-Jean Fresnel" | [
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1544 | ray velocities in the direction normal to the plane, and (said Fresnel) the directions of their respective vibrations. The direction of the optic axis is the normal to the plane for which the ellipse of intersection reduces to a "circle". So, for the biaxial case, Fresnel simply replaced the prolate spheroid with a triaxial ellipsoid, which he called the "ellipsoid of elasticity", to be sectioned by a plane in the same way. In general there would be "two" planes passing through the center of the ellipsoid and cutting it in a circle, and the normals to these planes would give | "Augustin-Jean Fresnel" | [
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] |
1545 | "two" optic axes. From the geometry, Fresnel deduced Biot's sine law (with the ray velocities replaced by their reciprocals). The "ellipsoid of elasticity" indeed gave the correct ray velocities, although the initial experimental verification was only approximate. But it did not give the correct directions of vibration, for the biaxial case or even for the uniaxial case, because the vibrations in Fresnel's model were tangential to the wavefront, which is "not" generally normal to the ray (for an extraordinary ray). This mistake was corrected in an "extract" that Fresnel read to the Académie a week later, on 26 November. Starting | "Augustin-Jean Fresnel" | [
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1546 | with Huygens' spheroid, Fresnel obtained the 4th-degree "surface of elasticity" which, when sectioned by a plane as above, would yield the "wave-normal velocities" for a wavefront in that plane, together with their vibration directions. For the biaxial case, he generalized the surface to allow three unequal principal dimensions. But he retained the former "ellipsoid of elasticity" as an approximation, from which he deduced Biot's dihedral law. Fresnel's initial derivation of the "surface of elasticity" had been purely geometric, and not deductively rigorous. His first attempt at a "mechanical" derivation, contained in a "supplement" dated 13 January 1822, assumed that (i) | "Augustin-Jean Fresnel" | [
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1547 | there were three mutually perpendicular directions in which a displacement produced a reaction in the same direction, (ii) the reaction was otherwise a linear function of the displacement, and (iii) the radius of the surface in any direction was the square root of the component, "in that direction", of the reaction to a unit displacement in that direction. The last assumption recognized the requirement that if a wave was to maintain a fixed direction of propagation and a fixed direction of vibration, the reaction must not be outside the plane of those two directions. In the same supplement, Fresnel considered | "Augustin-Jean Fresnel" | [
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1548 | how he might find, for the biaxial case, the secondary wavefront that expands from the origin in unit time — that is, the surface that reduces to Huygens' sphere and spheroid in the uniaxial case. He noted that this "wave surface" ("surface de l'onde") is tangential to all possible plane wavefronts that could have crossed the origin one unit of time ago, and he listed the mathematical conditions that it must satisfy. But he doubted the feasibility of deriving the surface "from" those conditions. In a "second supplement", Fresnel eventually exploited two related facts: (i) the "wave surface" was also | "Augustin-Jean Fresnel" | [
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1549 | the ray-velocity surface, which could be obtained by sectioning what he had mistakenly called the "ellipsoid of elasticity"; and (ii) the "wave surface" intersected each plane of symmetry of the ellipsoid in two curves: a circle and an ellipse. Thus he found that the "wave surface" is described by the 4th-degree equation where formula_32 and formula_33 are the propagation speeds in directions normal to the coordinate axes for vibrations along the axes (the ray and wave-normal speeds being the same in those special cases). Later commentators put the equation in the more compact and memorable form Earlier in the "second | "Augustin-Jean Fresnel" | [
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1550 | supplement", Fresnel modeled the medium as an array of point-masses and found that the force-displacement relation was described by a symmetric matrix, confirming the existence of three mutually perpendicular axes on which the displacement produced a parallel force. Later in the document, he noted that in a biaxial crystal, unlike a uniaxial crystal, the directions in which there is only one wave-normal velocity are not the same as those in which there is only one ray velocity. Nowadays we refer to the former directions as the "optic" axes or "binormal" axes, and the latter as the "ray" axes or "biradial" | "Augustin-Jean Fresnel" | [
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1551 | axes . Fresnel's "second supplement" was signed on 31 March 1822 and submitted the next day — less than a year after the publication of his pure-transverse-wave hypothesis, and just less than a year after the demonstration of his prototype eight-panel lighthouse lens . Fresnel still wanted a mechanical foundation for the ray-velocity surface and Biot's dihedral law. He attended to these matters in his "second memoir" on double refraction, published in the "Recueils" of the Académie des Sciences for 1824, which was not actually printed until late 1827, a few months after his death. Having confirmed the three perpendicular | "Augustin-Jean Fresnel" | [
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1552 | axes on which a displacement produced a parallel reaction, and thence constructed the surface of elasticity, he showed that Biot's dihedral law is exact provided that the binormals are taken as the optic axes, and the wave-normal direction as the direction of propagation. As early as 1822, Fresnel discussed his perpendicular axes with Cauchy. Acknowledging Fresnel's influence, Cauchy went on to develop the first rigorous theory of elasticity of non-isotropic solids (1827), hence the first rigorous theory of transverse waves therein (1830) — which he promptly tried to apply to optics. The ensuing difficulties drove a long competitive effort to | "Augustin-Jean Fresnel" | [
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1553 | find an accurate mechanical model of the aether. Fresnel's own model was not dynamically rigorous; for example, it considered only the displacement of one particle while all others were fixed, and it simply "assumed" that the relation between the stiffness and the wave-normal velocity was analogous to that for longitudinal sound waves. But it was enough to enable the wave theory to do what selectionist theory could not: generate testable formulae covering a comprehensive range of optical phenomena, from "mechanical" assumptions. In 1815, Brewster reported that colors appear when a slice of isotropic material, placed between crossed polarizers, is mechanically | "Augustin-Jean Fresnel" | [
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1554 | stressed. Brewster himself immediately and correctly attributed this phenomenon to stress-induced birefringence — now known as "photoelasticity". In a memoir read in September 1822, Fresnel announced that he had verified Brewster's diagnosis more directly, by compressing a combination of glass prisms so severely that one could actually see a double image through it. In his experiment, Fresnel lined up seven 45°-90°-45° prisms, short side to short side, with their 90° angles pointing in alternating directions. Two half-prisms were added at the ends to make the whole assembly rectangular. The prisms were separated by thin films of turpentine ("térébenthine") to suppress | "Augustin-Jean Fresnel" | [
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1555 | internal reflections, allowing a clear line of sight along the row. When the four prisms with similar orientations were compressed in a vise, from apex to base across the line of sight, an object viewed through the assembly produced two images with perpendicular polarizations, with an apparent spacing of 1.5mm at one metre. At the end of that memoir, Fresnel predicted that one could use an analogous arrangement of prisms, without compression, to verify that optical rotation is a form of birefringence. If the prisms were cut from monocrystalline quartz with their optic axes aligned along the row, and with | "Augustin-Jean Fresnel" | [
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1556 | alternating directions of optical rotation, an object seen by looking along the common optic axis would give two images, which would seem unpolarized if viewed through an analyzer alone; but if viewed through a Fresnel rhomb, they would be polarized at ±45° to the plane of reflection (because they would initially be circularly polarized in opposite directions). In the memoir of December 1822, in which he introduced the term "circular polarization", he reported that he had confirmed this prediction. To obtain a visible separation of the images, he needed only one 14°-152°-14° prism and two half-prisms; he merely remarked in | "Augustin-Jean Fresnel" | [
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1557 | passing that one could increase the separation by increasing the number of prisms. For the supplement to Riffault's translation of Thomson's "System of Chemistry", Fresnel was chosen to contribute the article on light. The resulting 137-page essay, titled "De la Lumière" ("On Light"), was apparently finished in June 1821 and published by February 1822. With sections covering the nature of light, diffraction, thin-film interference, reflection and refraction, double refraction and polarization, chromatic polarization, and modification of polarization by reflection, it made a comprehensive case for the wave theory to a readership that was not restricted to physicists. To examine Fresnel's | "Augustin-Jean Fresnel" | [
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1558 | first memoir and supplements on double refraction, the Académie des Sciences appointed Ampère, Arago, Fourier, and Poisson. Their report, of which Arago was clearly the main author, was delivered at the meeting of 19 August 1822. Then, in the words of Émile Verdet, as translated by Ivor Grattan-Guinness: Whether Laplace was announcing his conversion to the wave theory — at the age of 73 — is uncertain. Grattan-Guinness entertained the idea. Buchwald, noting that Arago failed to explain that the "ellipsoid of elasticity" did not give the correct planes of polarization, suggests that Laplace may have merely regarded Fresnel's theory | "Augustin-Jean Fresnel" | [
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1559 | as a successful generalization of Malus's ray-velocity law, embracing Biot's laws. In the following year, Poisson, who did not sign Arago's report, disputed the possibility of transverse waves in the aether. Starting from assumed equations of motion of a fluid medium, he noted that they did not give the correct results for partial reflection and double refraction — as if that were Fresnel's problem rather than his own — and that the predicted waves, even if they were initially transverse, became more longitudinal as they propagated. In reply Fresnel noted, "inter alia", that the equations in which Poisson put so | "Augustin-Jean Fresnel" | [
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] |
1560 | much faith did not even predict viscosity. The implication was clear: given that the behavior of light had not been satisfactorily explained except by transverse waves, it was not the responsibility of the wave-theorists to abandon transverse waves in deference to pre-conceived notions about the aether; rather, it was the responsibility of the aether modelers to produce a model that accommodated transverse waves. According to Eugene Frankel, Poisson eventually accepted the wave theory in the late 1830s. Among the French, Poisson's reluctance was an exception. According to Frankel, "in Paris no debate on the issue seems to have taken place | "Augustin-Jean Fresnel" | [
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1561 | after 1825. Indeed, almost the entire generation of physicists and mathematicians who came to maturity in the 1820s — Pouillet, Savart, Lamé, Navier, Liouville, Cauchy — seem to have adopted the theory immediately." Fresnel's other prominent French opponent, Biot, appeared to take a neutral position in 1830, and eventually accepted the wave theory — possibly by 1846 and certainly by 1858. In 1826, the British astronomer John Herschel, who was working on a book-length article on light for the "Encyclopædia Metropolitana", addressed three questions to Fresnel concerning double refraction, partial reflection, and their relation to polarization. The resulting article, titled | "Augustin-Jean Fresnel" | [
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1562 | simply "Light", was highly sympathetic to the wave theory, although not entirely free of selectionist language. It was circulating privately by 1828 and was published in 1830. Meanwhile, Young's translation of Fresnel's "De la Lumière" was published in installments from 1827 to 1829. George Biddell Airy, the former Lucasian Professor at Cambridge and future Astronomer Royal, unreservedly accepted the wave theory by 1831. In 1834 he famously calculated the diffraction pattern of a circular aperture from the wave theory, thereby explaining the limited angular resolution of a perfect telescope . By the end of the 1830s, the only prominent British | "Augustin-Jean Fresnel" | [
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1563 | physicist who held out against the wave theory was Brewster, whose objections included the difficulty of explaining photochemical effects and (in his opinion) dispersion. A German translation of "De la Lumière" was published in installments in 1825 and 1828. The wave theory was adopted by Fraunhofer in the early 1820s and by Franz Ernst Neumann in the 1830s, and then began to find favor in German textbooks. The economy of assumptions under the wave theory was emphasized by William Whewell in his "History of the Inductive Sciences", first published in 1837. In the corpuscular system, "every new class of facts | "Augustin-Jean Fresnel" | [
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1564 | requires a new supposition," whereas in the wave system, a hypothesis devised in order to explain one phenomenon is then found to explain or predict others. In the corpuscular system there is "no unexpected success, no happy coincidence, no convergence of principles from remote quarters"; but in the wave system, "all tends to unity and simplicity." Hence, in 1850, when Foucault and Fizeau found by experiment that light travels more slowly in water than in air, in accordance with the wave explanation of refraction and contrary to the corpuscular explanation, the result came as no surprise. Fresnel was not the | "Augustin-Jean Fresnel" | [
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1565 | first person to focus a lighthouse beam using a lens. That distinction apparently belongs to the London glass-cutter Thomas Rogers, who proposed the idea to Trinity House in 1788. 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. Further samples followed at Howth Baily, North Foreland, and at least four other locations. But much of the light was wasted by absorption in the glass. Nor was Fresnel the first to suggest replacing a convex lens with a series of concentric annular prisms, to reduce | "Augustin-Jean Fresnel" | [
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1566 | weight and absorption. In 1748, Count Buffon proposed grinding such prisms as steps in a single piece of glass. In 1790 (although secondary sources give the date as 1773 or 1788), 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. These designs were intended not for lighthouses, but for burning glasses. Brewster, however, proposed a system similar to Condorcet's in 1811, and by 1820 was advocating its use in British lighthouses. Meanwhile, on 21 June 1819, Fresnel was temporarily | "Augustin-Jean Fresnel" | [
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1567 | seconded 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. The Commission had been established by Napoleon in 1811, and placed under the Corps des Ponts — Fresnel's employer. On 29 August 1819, unaware of the Buffon-Condorcet-Brewster proposal, 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. One of the assembled commissioners, Jacques Charles, recalled Buffon's suggestion. | "Augustin-Jean Fresnel" | [
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1568 | Fresnel was disappointed to discover that he had again "broken through an open door". 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), and accidentally discovered that fish glue was heat-resistant, making it suitable for use in the lens. | "Augustin-Jean Fresnel" | [
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1569 | 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. Fresnel's next lens was a rotating apparatus with eight "bull's-eye" panels, made in annular arcs by Saint-Gobain, giving eight rotating beams — to be seen | "Augustin-Jean Fresnel" | [
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1570 | 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. 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. 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 | "Augustin-Jean Fresnel" | [
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1571 | on the unfinished "Arc de Triomphe" on 20 August 1822, was witnessed by the Commission — and by Louis 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. It was about this time that Fresnel started coughing up blood. In May 1824, Fresnel was promoted to Secretary of the "Commission des Phares", becoming the first member of that body to draw a salary. He was also an examiner (not a teacher) at | "Augustin-Jean Fresnel" | [
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1572 | the École Polytechnique since 1821; but poor health, long hours during the examination season, and anxiety about judging others induced him to resign that post in late 1824, to save his energy for his lighthouse work. In the same year he designed the first "fixed" lens — for spreading light evenly around the horizon while minimizing waste above or below. This had the familiar reflecting (catoptric) rings above and below the refracting (dioptric) parts. But the curved refracting surfaces were segments of toroids about a common vertical axis, so that the dioptric panel looked like a cylindrical drum and the | "Augustin-Jean Fresnel" | [
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1573 | entire apparatus looked like a beehive. In 1825 he unveiled the "Carte des Phares" (Lighthouse Map), calling for a system of 51 lighthouses plus smaller harbor lights, in a hierarchy of lens sizes (called "orders", the first order being the largest), with different characteristics to facilitate recognition: a constant light (from a fixed lens), one flash per minute (from a rotating lens with eight panels), and two per minute (sixteen panels). On 1 February 1825, the second lighthouse Fresnel lens entered service: a third-order fixed lens at Dunkirk. Also in 1825, Fresnel extended his fixed design by adding a rotating | "Augustin-Jean Fresnel" | [
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1574 | array outside the fixed array. Each panel of the rotating array refracted part of the fixed light from a horizontal fan into a narrow beam. 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. 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, but he did not live | "Augustin-Jean Fresnel" | [
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1575 | 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 catadioptric rings (made in segments) were one metre in diameter. The first-order Skerryvore lens, installed in 1844, was only partly catadioptric; 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 | "Augustin-Jean Fresnel" | [
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1576 | 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". Production of one-piece stepped lenses (roughly as envisaged by Buffon) eventually became profitable. By the 1870s, in the United States, such lenses were made of pressed glass and used with small lights on ships and piers. Similar lenses are used in "Fresnel lanterns" for stage lighting. Lenses | "Augustin-Jean Fresnel" | [
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1577 | with finer steps serve as condensers in overhead projectors. Still finer steps can be found in low-cost plastic "sheet" magnifiers. Fresnel was elected to the "Société Philomathique de Paris" in April 1819, and in 1822 became one of the editors of the Société's "Bulletin des Sciences". As early as May 1817, at Arago's suggestion, Fresnel applied for membership of the Académie des Sciences, but received only one vote. 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 | "Augustin-Jean Fresnel" | [
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1578 | 1823 by Pierre Louis Dulong, with 36 votes to Fresnel's 20. But in May 1823, after another vacancy was left by the death of Jacques Charles, Fresnel's election was unanimous. In 1824, Fresnel was made a "chevalier de la Légion d'honneur" (Knight of the Legion of Honour). Meanwhile, in Britain, the wave theory was yet to take hold; Fresnel wrote to Thomas Young in November 1824, saying in part: But "the praise of English scholars" soon followed. On 9 June 1825, Fresnel was made a Foreign Member of the Royal Society of London. In 1827 he was awarded the Society's | "Augustin-Jean Fresnel" | [
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1579 | Rumford Medal for the year 1824, "For his Development of the Undulatory Theory as applied to the Phenomena of Polarized Light, and for his various important discoveries in Physical Optics." The monument to Fresnel at his birthplace was dedicated on 14 September 1884 with a speech by , Permanent Secretary of the Académie des Sciences. "" is among the 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 | "Augustin-Jean Fresnel" | [
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] |
1580 | he had made safer. The lunar features "Promontorium Fresnel" and "Rimae Fresnel" were later named after him. Fresnel's health, which had always been poor, deteriorated in the winter of 1822-3, increasing the urgency of his original research, and causing him to turn down an invitation from Young to write an article on double refraction for the "Encyclopædia Britannica". The memoirs on circular and elliptical polarization and optical rotation, and on the detailed derivation of the Fresnel equations and their application to total internal reflection, date from this period. In the spring he recovered enough, in his own view, to supervise | "Augustin-Jean Fresnel" | [
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1581 | the lens installation at Cordouan. Soon afterwards, it became clear that his condition was tuberculosis. 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 first radiometer and attributed the observed repulsive force to a temperature difference. Although his fundamental research ceased, his advocacy did not; as late as August or September 1826, he | "Augustin-Jean Fresnel" | [
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1582 | found the time to answer Herschel's queries on the wave theory. It was Herschel who recommended Fresnel for the Royal Society's Rumford Medal. Fresnel's cough worsened in the winter of 1826-7, leaving him too ill to return to Mathieu in the spring. In early June he was carried to Ville-d'Avray, 12km 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 | "Augustin-Jean Fresnel" | [
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1583 | the Royal Society. He died eight days later, on Bastille Day. He is buried at Père Lachaise Cemetery, Paris. The is partly eroded away; the legible part says, when translated, "To the memory of Augustin Jean Fresnel, member of the Institute of France." Fresnel's "second memoir" on double refraction was not printed until late 1827, a few months after his death. Until then, the best published source on his work on double refraction was an extract of that memoir, printed in 1822. His final treatment of partial reflection and total internal reflection, read to the Académie in January 1823, was | "Augustin-Jean Fresnel" | [
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] |
1584 | thought to be lost until it was rediscovered among the papers of the deceased Joseph 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, read in March 1818, was mislaid until 1846. 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 — were not published in full until his "Oeuvres complètes" ("complete works") began to appear in 1866. The | "Augustin-Jean Fresnel" | [
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] |
1585 | "supplement" of July 1816, proposing the "efficacious ray" and reporting the famous double-mirror experiment, met the same fate, as did the "first memoir" on double refraction. Publication of Fresnel's collected works was itself delayed by the deaths of successive editors. The task was initially entrusted to Félix Savary, who died in 1841. It was restarted twenty years later by the Ministry of Public Instruction. Of the three editors eventually named in the "Oeuvres", Sénarmont died in 1862, Verdet in 1866, and Léonor Fresnel in 1869, by which time only two of the three volumes had appeared. At the beginning of | "Augustin-Jean Fresnel" | [
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1586 | vol.3 (1870), the completion of the project is described in a long footnote by "J. Lissajous." Not included in the "Oeuvres" are two short notes by Fresnel on magnetism, which were discovered among Ampère's manuscripts. In response to Ørsted's discovery of electromagnetism in 1820, Ampère initially supposed that the field of a permanent magnet was due to a macroscopic circulating current. Fresnel suggested instead that there was a "microscopic" 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 | "Augustin-Jean Fresnel" | [
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1587 | 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. He was not to know that the fundamental units of permanent magnetism are even smaller than molecules . The two notes, together with Ampère's acknowledgment, were eventually published in 1885. Fresnel's essay "Rêveries" of 1814 has not survived. While its content would have been interesting to historians, its quality may perhaps be gauged from the fact that Fresnel | "Augustin-Jean Fresnel" | [
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1588 | himself never referred to it in his maturity. More disturbing is the fate of the late 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 journal "European Review". This work seems to have been similar in scope to the essay "De la Lumière" of 1821/22, except that Fresnel's views on double refraction, circular and elliptical polarization, optical rotation, and total internal reflection had developed since then. The manuscript was received by the publisher's agent in Paris in early September | "Augustin-Jean Fresnel" | [
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] |
1589 | 1824, and promptly forwarded to London. But the journal failed before Fresnel's contribution could be published. Fresnel tried unsuccessfully to recover the manuscript. The editors of his collected works were also unable to find it, and admitted that it was probably lost. 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, on the hypothesis that if an object with refractive index formula_35 moved at velocity formula_36 relative | "Augustin-Jean Fresnel" | [
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1590 | to the external aether (taken as stationary), then the velocity of light inside the object gained the additional component formula_37. 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 formula_38, of which the excess, namely formula_39, was dragged along at velocity formula_36, whence the "average" velocity of the internal aether was formula_37. The factor in parentheses, which Fresnel originally expressed in terms of wavelengths, became known as the "Fresnel drag coefficient". In his analysis of double refraction, Fresnel supposed that the different refractive indices | "Augustin-Jean Fresnel" | [
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1591 | in different directions within the "same 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 of "different media" were due to different aether densities, not different elasticities. The latter decision is puzzling in the context of double refraction, but makes sense in the earlier context of aether drag. In 1846, George Gabriel Stokes pointed out that there was no need to divide the aether inside a moving object into two portions; all of | "Augustin-Jean Fresnel" | [
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1592 | it could be considered as moving at a common velocity. Then, if the aether was conserved while its density changed in proportion to formula_38, the resulting velocity of the aether inside the object was equal to Fresnel's additional velocity component. Conversely, Fresnel could have started with the required additional velocity component, equated it to aether drag, combined that with conservation of aether, and arrived at the relation between refractive index and aether density, thereby justifying his choice in the case of partial reflection. The analogy between light waves and transverse waves in elastic solids does not predict "dispersion" — that | "Augustin-Jean Fresnel" | [
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] |
1593 | is, the frequency-dependence of the speed of propagation, which enables prisms to produce spectra and causes lenses to suffer from chromatic aberration. Fresnel, in "De 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. 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. But no such note appeared in print, and | "Augustin-Jean Fresnel" | [
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] |
1594 | 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. One obvious possibility is that the explanation of the formula was given in the appended note, which should be counted as another lost work. In the 1830s, Fresnel's suggestion was taken up by Cauchy, Powell, and Kelland, and it was indeed found to be tolerably consistent with the variation of refractive indices with wavelength over the visible spectrum, for a variety of transparent media . These investigations were | "Augustin-Jean Fresnel" | [
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1595 | enough to show that the wave theory was at least "compatible" with dispersion. However, 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 . 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 by William Rowan Hamilton in 1832. Hamilton went further, establishing two properties of the surface that Fresnel, in the short time given to him, had | "Augustin-Jean Fresnel" | [
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1596 | overlooked: (i) at each of the four points where the inner and outer sheets of the surface make contact, the surface has a tangent cone (tangential to both sheets), hence a cone of normals, indicating that a cone of wave-normal directions corresponds to a single ray-velocity vector; and (ii) around each of these points, the outer sheet has a circle of contact with a tangent plane, indicating that a cone of ray directions corresponds to a single wave-normal velocity vector. As Hamilton noted, these properties respectively imply that (i) a narrow beam propagating inside the crystal in the direction of | "Augustin-Jean Fresnel" | [
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1597 | the single ray velocity will, on exiting the crystal through a flat surface, break into a hollow cone ("external conical refraction"), and (ii) a narrow beam striking a flat surface of the crystal in the appropriate direction (corresponding to that of the single internal wave-normal velocity) will, on entering the crystal, break into a hollow cone ("internal conical refraction"). Thus a new pair of phenomena, "qualitatively" different from anything previously observed or suspected, had been predicted by mathematics as consequences of Fresnel's theory. The prompt experimental confirmation of those predictions by Humphrey Lloyd brought Hamilton a prize that had never | "Augustin-Jean Fresnel" | [
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] |
1598 | come to Fresnel: immediate fame. 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. Concerning the other benefits, the science historian Theresa H. Levitt has remarked: In the history of physical optics, Fresnel's successful revival of the wave theory nominates him as the pivotal figure between Newton, who held that light consisted of corpuscles, and James Clerk Maxwell, who established that light waves are electromagnetic. Whereas Albert Einstein described Maxwell's work as "the most profound and the most fruitful that physics has experienced since the time | "Augustin-Jean Fresnel" | [
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1599 | of Newton," commentators of the era between Fresnel and Maxwell made similarly strong statements about Fresnel: 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, | "Augustin-Jean Fresnel" | [
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1600 | which photons do not. Neither 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, the phenomena studied by Fresnel are still most easily explained in terms of waves. In these respects, his edifice still stands. Augustin-Jean Fresnel Augustin-Jean Fresnel ( , ; ; 10 May 178814 July 1827) | "Augustin-Jean Fresnel" | [
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-0.6380347609519958,
0.41186830401420593,
-0.12622332572937012,
0.18964187800884247,
-0.07696031033992767,
0.4794831871986389,
-0.12959237396717072
] |
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