Plane of polarization: Difference between revisions

Revision as of 11:15, 3 June 2019

Revision as of 02:44, 4 June 2019

Line 61:

Fresnel himself found this implication inconvenient; later that year he wrote:

::Adopting this hypothesis, it would have been more natural to have called the plane of polarisation that in which the oscillations are supposed to be made: but I&nbsp;wished to avoid making any change in the received appellations.<ref name=fy406/><ref group=Note>The actual writing of this treatise (Fresnel, 1822) was apparently completed by mid 1821; see I.&nbsp;Grattan-Guinness, ''Convolutions in French Mathematics, 1800–1840'', Basel: Birkhäuser, 1990, vol.{{tsp}}2, p.{{nnbsp}}884.</ref>

But he soon felt obliged to make a less radical change. In his successful model of double refraction, the displacement of the medium was constrained to be tangential to the wavefront, while the force was allowed to deviate from the displacement and from the wavefront.<ref>Aldis, 1879, pp.{{nnbsp}}8–9.</ref> Hence, if the vibrations were perpendicular to the plane of polarization, then the plane of polarization contained the wave-normal but not necessarily the ray.<ref>Aldis, 1879, pp.{{nnbsp}}9,{{hsp}}20.</ref> In his "Second Memoir" on double refraction, Fresnel formally adopted this new definition, acknowledging that it agreed with the old definition in an isotropic medium such as air, but not in a birefringent crystal.<ref name=fh318/>

Line 70:

=== "Plane of vibration" ===

The principle that refractive index depended on the density of the aether was essential to Fresnel's [[aether drag hypothesis]].<ref>Darrigol, 2012, pp.{{nnbsp}}258–60.</ref> But it could not be extended to birefringent crystals — in which at least one refractive index varies with direction — because density is not directional. Hence his explanation of refraction required a directional variation in [[stiffness]] of the aether ''within'' a birefringent medium, plus a variation in density ''between'' media.<ref>Whittaker, 1910, pp.{{nnbsp}}127,{{tsp}}132–5.</ref>

[[James MacCullagh]] and [[Franz Ernst Neumann]] avoided this complication by supposing that a higher refractive index corresponded always to the same density but a greater elastic ''compliance'' (lower stiffness). To obtain results that agreed with observations on partial reflection, they had to suppose, contrary to Fresnel, that the vibrations were ''within'' the plane of polarization.<ref>Powell, 1856, pp.{{nnbsp}}4–5; Whittaker, 1910, p.{{nnbsp}}149.</ref>

Line 76:

[[File:Portrait of George Gabriel Stokes (1819-1903), Physicist and Mathematician (2551115803).jpg|thumb|left|<div style="text-align: center;">George Gabriel Stokes (1819–1903).</div>]]

The question called for a directan experimental determination of the direction of vibration, and the challenge was answered by [[Sir George Stokes, 1st Baronet|George Gabriel Stokes]]. He defined the ''plane of vibration'' as "the plane passing through the ray and the direction of vibration"{{r|stokes-1849}} (in agreement with Fig.{{nnbsp}}1). Now suppose that a fine [[diffraction grating]] is illuminated at normal incidence. At large angles of diffraction, the grating will appear somewhat edge-on, so that the directions of vibration will be crowded towards the direction parallel to the plane of the grating. If the planes of polarization coincide with the planes of vibration (as MacCullagh and Neumann said), they will be crowded in the same direction; and if the planes of polarization are ''normal'' to the planes of vibration (as Fresnel said), the planes of polarization will be crowded in the normal direction. To find the direction of the crowding, one could vary the polarization of the incident light in equal steps, and determine the planes of polarization of the diffracted light in the usual manner. Stokes performed such an experiment in 1849, and it found in favor of Fresnel.{{r|stokes-1849}}<ref>Powell, 1856, pp.{{nnbsp}}19–20; Whittaker, 1910, pp.{{nnbsp}}168–9.</ref>

In 1852, Stokes noted a much simpler experiment that leads to the same conclusion. Sunlight scattered from a patch of blue sky 90° from the sun is found, by the methods of Malus, to be polarized in the plane containing the line of sight and the sun. But it is obvious from the geometry that the vibrations of that light can only be perpendicular to that plane.<ref>Whittaker, 1910, pp.{{nnbsp}}169–70.</ref>