A quantitative analysis of these effects is based on the Fresnel equations, but with additional calculations to account for interference. The transfer-matrix method, or the recursive Rouard method can be used to solve multiple-surface problems. ==History== In 1808, Étienne-Louis Malus discovered that when a ray of light was reflected off a non-metallic surface at the appropriate angle, it behaved like one of the two rays emerging from a doubly-refractive calcite crystal.
He later coined the term polarization to describe this behavior. In 1815, the dependence of the polarizing angle on the refractive index was determined experimentally by David Brewster.
But the reason for that dependence was such a deep mystery that in late 1817, Thomas Young was moved to write: In 1821, however, Augustin-Jean Fresnel derived results equivalent to his sine and tangent laws (above), by modeling light waves as transverse elastic waves with vibrations perpendicular to what had previously been called the plane of polarization.
But the reason for that dependence was such a deep mystery that in late 1817, Thomas Young was moved to write: In 1821, however, Augustin-Jean Fresnel derived results equivalent to his sine and tangent laws (above), by modeling light waves as transverse elastic waves with vibrations perpendicular to what had previously been called the plane of polarization.
The experimental confirmation was reported in a "postscript" to the work in which Fresnel first revealed his theory that light waves, including "unpolarized" waves, were purely transverse. Details of Fresnel's derivation, including the modern forms of the sine law and tangent law, were given later, in a memoir read to the French Academy of Sciences in January 1823.
The first derivation from electromagnetic principles was given by Hendrik Lorentz in 1875. In the same memoir of January 1823, Fresnel found that for angles of incidence greater than the critical angle, his formulas for the reflection coefficients ( and ) gave complex values with unit magnitudes.
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. W.
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. W.
Whewell, 1857, History of the Inductive Sciences: From the Earliest to the Present Time, 3rd Ed., London: J.W. Parker & Son, vol.2. E.
de Senarmont, E. Verdet, and L. Fresnel), Oeuvres complètes d'Augustin Fresnel, Paris: Imprimerie Impériale (3 vols., 1866–70), vol.1 (1866). E.
The first derivation from electromagnetic principles was given by Hendrik Lorentz in 1875. In the same memoir of January 1823, Fresnel found that for angles of incidence greater than the critical angle, his formulas for the reflection coefficients ( and ) gave complex values with unit magnitudes.
Whittaker, 1910, A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century, London: Longmans, Green, & Co. ==Further reading== Encyclopaedia of Physics (2nd Edition), R.G.
Collin, 1966, Foundations for Microwave Engineering, Tokyo: McGraw-Hill. O.
Wolf, 1970, Principles of Optics, 4th Ed., Oxford: Pergamon Press. J.Z.
White, 1976, Fundamentals of Optics, 4th Ed., New York: McGraw-Hill, . H.
Hecht, 1987, Optics, 2nd Ed., Addison Wesley, . E.
Buchwald, 1989, The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century, University of Chicago Press, . R.E.
Trigg, VHC publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1, ISBN (VHC Inc.) 0-89573-752-3 McGraw Hill Encyclopaedia of Physics (2nd Edition), C.B.
Hecht, 2002, Optics, 4th Ed., Addison Wesley, . F.A.
Darrigol, 2012, A History of Optics: From Greek Antiquity to the Nineteenth Century, Oxford, . A.
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