Ewald–Oseen extinction theorem

In optics, the Ewald–Oseen extinction theorem, sometimes referred to as just "extinction theorem", is a theorem that underlies the common understanding of refraction. It is named after Paul Peter Ewald and Carl Wilhelm Oseen, who proved the theorem in crystalline and isotropic media, respectively, in 1916 and 1915.[1]

Overview

An important part of optical physics theory is starting with microscopic physics—the behavior of atoms and electrons—and using it to derive the familiar, macroscopic, laws of optics. In particular, there is a derivation of how the refractive index works and where it comes from, starting from microscopic physics. The Ewald–Oseen extinction theorem is one part of that derivation (as is the Lorentz–Lorenz equation etc.).

When light traveling in vacuum enters a transparent medium like glass, the light slows down, as described by the index of refraction. Although this fact is famous and familiar, it is actually quite strange and surprising when you think about it microscopically. After all, according to the superposition principle, the light in the glass is a superposition of:

(Remember, light has an electric field that pushes atoms back and forth, which causes the atoms to emit dipole radiation.)

Individually, each of these waves travels at the speed of light in vacuum, not at the (slower) speed of light in glass. Yet when the waves are added up, they surprisingly create only a wave that travels at the slower speed.

The Ewald–Oseen extinction theorem says that the light emitted by the atoms has a component traveling at the speed of light in vacuum, which exactly cancels out ("extinguishes") the original light wave. Additionally, the light emitted by the atoms has a component which looks like a wave traveling at the slower speed of light in glass. Altogether, the only wave in the glass is the slow wave, consistent with what we expect from basic optics.

A more complete description can be found in Classical Optics and its Applications, by Masud Mansuripur.[2] A classic proof of the theorem can be found in Principles of Optics, by Born and Wolf.[1]

Extinction lengths and tests of special relativity

The characteristic "extinction length" of a medium is the distance after which the original wave can be said to have been completely replaced. For visible light, traveling in air at sea level, this distance is approximately 1 mm.[3] In interstellar space, the extinction length for light is 2 light years[4] At very high frequencies, the electrons in the medium can't "follow" the original wave into oscillation, which lets that wave travel much further: for 0.5 MeV gamma rays, the length is 19 cm of air and 0.3 mm of Lucite, and for 4.4 GeV, 1.7 m in air, and 1.4 mm in carbon.[5]

Special relativity predicts that the speed of light in vacuum is independent of the velocity of the source emitting it. This widely-believed prediction has been occasionally tested using astronomical observations.[3][4] For example, in a binary star system, the two stars are moving in opposite directions, and one might test the prediction by analyzing their light. (See, for instance, the De Sitter double star experiment.) Unfortunately, the extinction length of light in space nullifies the results of any such experiments using visible light, especially when taking account of the thick cloud of stationary gas surrounding such stars.[3] However, experiments using X-rays emitted by binary pulsars, with much longer extinction length, have been successful.[4]

References

  1. 1 2 Born, Max; Wolf, Emil (1999), Principles of Optics (7th ed.), Cambridge: Cambridge University Press, p. 106
  2. ↑ Mansuripur, Masud (2009), Classical Optics and its Applications (2nd ed.), Cambridge: Cambridge University Press, p. 209, doi:10.1017/CBO9780511803796.019
  3. 1 2 3 Fox, J.G. (1962), "Experimental Evidence for the Second Postulate of Special Relativity", American Journal of Physics 30 (1): 297–300, Bibcode:1965AmJPh..33....1F, doi:10.1119/1.1941992.
  4. 1 2 3 Brecher, K. (1977). "Is the speed of light independent of the velocity of the source". Physical Review Letters 39 (17): 1051–1054. Bibcode:1977PhRvL..39.1051B. doi:10.1103/PhysRevLett.39.1051.
  5. ↑ Filippas, T.A.; Fox, J.G. (1964). "Velocity of Gamma Rays from a Moving Source". Physical Review 135 (4B): B1071–1075. Bibcode:1964PhRv..135.1071F. doi:10.1103/PhysRev.135.B1071.
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