Plane of polarization: Difference between revisions

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Indeed, that is the convention used in the online ''Encyclopædia Britannica'',{{r|luntz}} and in [[Richard Feynman|Feynman]]'s lecture on polarization.{{r|feynman-1963}} In the latter case one must infer the convention from the context: Feynman keeps emphasizing the direction of the ''electric'' ('''E''') vector and leaves the reader to presume that the "plane of polarization" contains that vector — and this interpretation indeed fits the examples he gives. The same vector is used to describe the polarization of radio signals and [[antenna (radio)#Polarization|antennas]] (Fig.{{nnbsp}}3).<ref name="auto">Stratton, 1941, p.{{hsp}}280.</ref>

If the medium is magnetically isotropic but electrically ''non''-isotopicisotropic (like a [[birefringence|doubly-refracting]] crystal), the magnetic vectors '''B''' and '''H''' are still parallel, and the electric vectors '''E''' and '''D''' are still perpendicular to both, and the ray direction is still perpendicular to '''E''' and the magnetic vectors, and the wave-normal direction is still perpendicular to '''D''' and the magnetic vectors; but there is generally a small angle between the electric vectors '''E''' and '''D''', hence the same angle between the ray direction and the wave-normal direction (Fig.{{nnbsp}}1).{{r|lunney-weaire-2006}}<ref>Born & Wolf, 1970, p.{{hsp}}668.</ref>{{tsp}} Hence '''D''', '''E''', the wave-normal direction, and the ray direction are all in the same plane, and it is all the more natural to define that plane as the "plane of polarization".

This "natural" definition, however, depends on the theory of EM waves developed by [[James Clerk Maxwell]] in the 1860s — whereas the word ''polarization'' was coined about 50 years earlier, and the associated mystery dates back even further.

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[[File:Calcite and polarizing filter.gif|frame|'''Fig.{{nnbsp}}4''':{{big|&nbsp;}}Printed label seen through a doubly-refracting calcite crystal{{hsp}} and a modern polarizing filter (rotated to show the different polarizations of the two images).]]

Polarization was discovered — but not named or understood — by [[Christiaan Huygens]], as he investigated the [[birefringence|double refraction]] of "Iceland crystal" (transparent [[calcite]], now called [[Iceland spar]]). The essence of his discovery, published in his ''Treatise on Light'' (1690), was as follows. When a ray (meaning a narrow beam of light) passes through two similarly oriented calcite crystals at normal incidence, the ordinary ray emerging from the first crystal suffers only the ordinary refraction in the second, while the extraordinary ray emerging from the first suffers only the extraordinary refraction in the second. But when the second crystal is rotated 90° about the incident rays, the roles are interchanged, so that the ordinary ray emerging from the first crystal suffers only the extraordinary refraction in the second, and vice versa. At intermediate positions of the second crystal, each ray emerging from the first is doubly refracted by the second, giving four rays in total; and as the crystal is rotated from the initial orientation to the perpendicular one, the brightnesses of the rays vary, giving a smooth transition between the extreme cases in which there are only two final rays.<ref>Huygens, 1690, tr.&nbsp;Thompson, pp.{{nnbsp}}92–4.</ref>

Huygens defined a ''principal section'' of a calcite crystal as a plane normal to a natural surface and parallel to the axis of the obtuse solid angle.<ref>Huygens, 1690, tr.&nbsp;Thompson, pp.{{nnbsp}}55–6.</ref> This axis was parallel to the axes of the [[spheroid]]al [[Huygens–Fresnel principle|secondary waves]] by which he (correctly) explained the directions of the extraordinary refraction.