Newton, 1730, Opticks: or, a Treatise of the Reflections, Refractions, Inflections, and Colours of Light, 4th Ed.

(London: William Innys, 1730; Project Gutenberg, 2010); republished with Foreword by A. Einstein and Introduction by E.T. Whittaker (London: George Bell & Sons, 1931); reprinted with additional Preface by I.B. Cohen and Analytical Table of Contents by D.H.D. Roller, Mineola, NY: Dover, 1952, 1979 (with revised preface), 2012.

Translations of his papers were published in France in 1803, and apparently came to the attention of Pierre-Simon Laplace. According to Laplace's elaboration of Newton's theory of refraction, a corpuscle incident on a plane interface between two homogeneous isotropic media was subject to a force field that was symmetrical about the interface.

Laplace's theory further predicted a relationship between refractive index and density for a given substance. In 1807, Laplace's theory was tested experimentally by his protégé, Étienne-Louis Malus.

In 1811, François Arago discovered that polarized light was apparently "depolarized" in an orientation-dependent and color-dependent manner when passed through a slice of doubly-refractive crystal: the emerging light showed colors when viewed through an analyzer (second polarizer).

Chromatic polarization, as this phenomenon came to be called, was more thoroughly investigated in 1812 by Jean-Baptiste Biot.

In 1813, Biot established that one case studied by Arago, namely quartz cut perpendicular to its optic axis, was actually a gradual rotation of the plane of polarization with distance. In 1816, Fresnel offered his first attempt at a wave-based theory of chromatic polarization.

Theodoric's work was forgotten until it was rediscovered by Giovanni Battista Venturi in 1814. Theodoric having fallen into obscurity, the discovery of TIR was generally attributed to Johannes Kepler, who published his findings in his Dioptrice in 1611.

In 1813, Biot established that one case studied by Arago, namely quartz cut perpendicular to its optic axis, was actually a gradual rotation of the plane of polarization with distance. In 1816, Fresnel offered his first attempt at a wave-based theory of chromatic polarization.

Hence, speaking loosely, we tend to say that the evanescent wave amplitude is significant within "a few wavelengths" of the interface. === Phase shifts === Between 1817 and 1823, Augustin-Jean Fresnel discovered that total internal reflection is accompanied by a non-trivial phase shift (that is, a phase shift that is not restricted to 0° or 180°), as the Fresnel reflection coefficient acquires a non-zero imaginary part.

In 1817 he noticed that plane-polarized light seemed to be partly depolarized by total internal reflection, if initially polarized at an acute angle to the plane of incidence.

These findings were reported in a memoir submitted and read to the French Academy of Sciences in November 1817. In 1821, Fresnel derived formulae equivalent to his sine and tangent laws Eqs.() and (), above by modeling light waves as transverse elastic waves with vibrations perpendicular to what had previously been called the plane of polarization.

These findings were reported in a memoir submitted and read to the French Academy of Sciences in November 1817. In 1821, Fresnel derived formulae equivalent to his sine and tangent laws Eqs.() and (), above by modeling light waves as transverse elastic waves with vibrations perpendicular to what had previously been called the plane of polarization.

The derivation combined conservation of energy with continuity of the tangential vibration at the interface, but failed to allow for any condition on the normal component of vibration. Meanwhile, in a memoir submitted in December 1822, Fresnel coined the terms linear polarization, circular polarization, and elliptical polarization.

The explanation of this effect by Augustin-Jean Fresnel, in 1823, added to the evidence in favor of the wave theory of light. The phase shifts are utilized by Fresnel's invention, the Fresnel rhomb, to modify polarization.

Hence, speaking loosely, we tend to say that the evanescent wave amplitude is significant within "a few wavelengths" of the interface. === Phase shifts === Between 1817 and 1823, Augustin-Jean Fresnel discovered that total internal reflection is accompanied by a non-trivial phase shift (that is, a phase shift that is not restricted to 0° or 180°), as the Fresnel reflection coefficient acquires a non-zero imaginary part.

Fresnel himself, in 1823, gave a formula for .

Details of the derivation were given later, in a memoir read to the Academy in January 1823.

For circular polarization, the two perpendicular components were a quarter-cycle (±90°) out of phase. The new terminology was useful in the memoir of January 1823, containing the detailed derivations of the sine and tangent laws: in that same memoir, Fresnel found that for angles of incidence greater than the critical angle, the resulting reflection coefficients were complex with unit magnitude.

Lloyd, 1834, "Report on the progress and present state of physical optics", Report of the Fourth Meeting of the British Association for the Advancement of Science (held at Edinburgh in 1834), London: J. Murray, 1835, pp.295–413. I.

Lloyd, 1834, "Report on the progress and present state of physical optics", Report of the Fourth Meeting of the British Association for the Advancement of Science (held at Edinburgh in 1834), London: J. Murray, 1835, pp.295–413. I.

Meanwhile, Fresnel's 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.

Whewell, 1857, History of the Inductive Sciences: From the Earliest to the Present Time, 3rd Ed., London: J.W. Parker & Son, vol.2. E.

H. de Senarmont, E. Verdet, and L. Fresnel), Oeuvres complètes d'Augustin Fresnel, Paris: Imprimerie Impériale (3 vols., 1866–70), vol.1 (1866). E.

The imaginary part of the complex index represents absorption. The term critical angle, used for convenience in the above narrative, is anachronistic: it apparently dates from 1873. In the 20th century, quantum electrodynamics reinterpreted the amplitude of an electromagnetic wave in terms of the probability of finding a photon.

Huygens, 1690, Traité de la Lumière (Leiden: Van der Aa), translated by S.P. Thompson as Treatise on Light, University of Chicago Press, 1912; Project Gutenberg, 2005.

(Cited page numbers match the 1912 edition and the Gutenberg HTML edition.) F.A.

(London: William Innys, 1730; Project Gutenberg, 2010); republished with Foreword by A. Einstein and Introduction by E.T. Whittaker (London: George Bell & Sons, 1931); reprinted with additional Preface by I.B. Cohen and Analytical Table of Contents by D.H.D. Roller, Mineola, NY: Dover, 1952, 1979 (with revised preface), 2012.

Stratton, 1941, Electromagnetic Theory, New York: McGraw-Hill. W.

(London: William Innys, 1730; Project Gutenberg, 2010); republished with Foreword by A. Einstein and Introduction by E.T. Whittaker (London: George Bell & Sons, 1931); reprinted with additional Preface by I.B. Cohen and Analytical Table of Contents by D.H.D. Roller, Mineola, NY: Dover, 1952, 1979 (with revised preface), 2012.

Boyer, 1959, The Rainbow: From Myth to Mathematics, New York: Thomas Yoseloff. J.Z.

Wolf, 1970, Principles of Optics, 4th Ed., Oxford: Pergamon Press. C.B.

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Rutten and M.A.M.van Venrooij, 1988 (fifth printing, 2002), Telescope Optics: A Comprehensive Manual for Amateur Astronomers, Richmond,VA: Willmann-Bell, . J.A.

Buchwald, 1989, The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century, University of Chicago Press, . O.

Hecht, 2002, Optics, 4th Ed., Addison Wesley, . C.

Rutten and M.A.M.van Venrooij, 1988 (fifth printing, 2002), Telescope Optics: A Comprehensive Manual for Amateur Astronomers, Richmond,VA: Willmann-Bell, . J.A.

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Darrigol, 2012, A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford, . R.

Fitzpatrick, 2013, Oscillations and Waves: An Introduction, Boca Raton, FL: CRC Press, . R.

Fitzpatrick, 2013a, "Total Internal Reflection", University of Texas at Austin, accessed 14 March 2018. A.

Levitt, 2013, A Short Bright Flash: Augustin Fresnel and the Birth of the Modern Lighthouse, New York: W.W. Norton, . H.

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