Plane of polarization: Difference between revisions

Revision as of 16:15, 28 December 2017

Revision as of 12:20, 31 December 2017

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The modern implication of Malus's definition — that the plane of polarization contains the ''magnetic'' vectors — survives in the online Merriam-Webster dictionary.{{r|merriamW}}

In 1821, [[Augustin-Jean Fresnel]], having already explained [[diffraction]] in terms of the [[wave theory of light]], announced his hypothesis that light waves are exclusively ''[[transverse wave|transverse]]'' and therefore ''always'' polarized in the sense of having a particular transverse orientation, and that what we call "''unpolarized"'' light is in fact light whose polarizationorientation is rapidly and randomly changing.{{r|buchwald-1989|p=227–9}} On that hypothesis, he proceeded to explain nearly all the remaining optical phenomena known at that time.{{r|frankel-1976|p=169}}

In deriving his [[Fresnel equations|eponymous equations]] for the reflection and transmission coefficients at the interface between two transparent media, Fresnel thought in terms of [[s-wave|shear waves]] in [[elasticity (physics)|elastic solids]], and supposed that a higher [[refractive index]] corresponded to a higher [[density]] of the [[luminiferous aether]]. But,This asidea [[Jamescould MacCullagh]]not laterbe pointedextended out, that supposition does not work forto double-refracting crystals (in which at least one refractive index varies with direction), because density is not directional;. underThus Fresnel's analogy, a complete explanation of refraction would requirerequired a directional variation in [[stiffness]] of the aether ''within'' one medium, plus a variation in density ''between'' media. To avoid this complication, [[James MacCullagh]] supposed that a higher refractive index corresponded always to the same density but a greater elastic ''compliance'' (lower stiffness). Fresnel's suppositionanalogies led to results that agreed with observation (on partial reflection and transmission), if he further supposed that the vibrations were ''normal'' to the plane of polarization. So began the distinction between the "plane of vibration" and the "plane of polarization". MacCullagh, in contrast, had to suppose that the two planes were the same — i.e., that the vibrations were ''within'' the plane of polarization. (This storyhistory was recounted in 1856 by [[Baden Powell (mathematician)|Baden Powell]]. in 1856,{{r|powell-1856}} and by [[E. T. Whittaker|E.T. Whittaker]] in 1910.{{r|whittaker-1910|p=132–5,{{hsp}}149}})

Thus attention was focused on whether the plane of vibration could be determined experimentally with the technology of the time. Consider a fine [[diffraction grating]] 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 (''à la'' MacCullagh), they will be crowded in the same direction; and if the planes of polarization are ''normal'' to the planes of vibration (''à la'' Fresnel), the planes of polarization will be crowded in the normal direction. To measure 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. Such an experiment was devised, and performed in 1849, by [[Sir George Stokes, 1st Baronet|George Gabriel Stokes]], and it found in favor of Fresnel.{{r|powell-1856|p=19–20;{{hsp}}}}{{r|stokes-1849|p=4–5}}

ThisIt isremains surprisingto inexplain viewhow ofthis MacCullagh'sresult pointcan thatbe densityreconciled iswith notthe directionalnon-directionality of density. If we attempt an analogy between shear waves in a non-isotropic elastic solid and EM waves in a magnetically isotropic but electrically non-isotropic crystal, the density must correspond to the magnetic [[permeability (electromagnetism)|permeability]] (both being non-directional), and the compliance must correspond to the electric [[permittivity]] (both being directional). The result is that the velocity of the solid corresponds to the '''H''' field,{{r|carcione-cavallini-1995}} so that the mechanical vibrations of the shear wave are in the direction of the ''magnetic'' vibrations of the EM wave. But Stokes's experiment was bound to detect the ''electric'' vibrations, because those were the vibrations that interacted with the grating (and with most other objects). In short, MacCullagh's "vibrations" were the ones that had a mechanical analog, but Fresnel's were the ones that were going to be detected in optical experiments. But that clarification raises another difficulty: the analogy between permeability and aether density allows very little variation in aether density among non-magnetic media and is therefore incompatible with Fresnel's hypothesis that aether density is the main criterion of refractive index.{{r|analogies}}

== History meets physics ==

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<ref name=frankel-1976>E. Frankel, "Corpuscular optics and the wave theory of light: The science and politics of a revolution in physics", ''Social Studies of Science'', Vol.{{nnbsp}}6, No.{{hsp}}2 (May&nbsp;1976), pp.{{nnbsp}}141–84.</ref>

<ref name=huygens-1690>C. Huygens, ''Traité de la Lumière'' (Leiden: Van der Aa, 1690), translated by S.P. &nbsp;Thompson as ''[http://www.gutenberg.org/ebooks/14725 Treatise on Light]'', University of Chicago Press, 1912.</ref>

<ref name=jenkins-white-1976>Cf.&nbsp; F.A. Jenkins and H.E. White, ''Fundamentals of Optics'', 4th&nbsp;Ed., New&nbsp;York: McGraw-Hill, 1976, Fig.{{nnbsp}}26{{serif|I}} (p.{{hsp}}554).</ref>

<ref name=lunney-weaire-2006> J.G. Lunney and D. Weaire, "The ins and outs of conical refraction", ''Europhysics News'', Vol.{{nnbsp}}37, No.{{hsp}}3 (May–June&nbsp;2006), pp.{{nnbsp}}26–9; [https://dx.doi.org/10.1051/epn:2006305 doi.org/10.1051/epn:2006305].</ref>

<ref name=luntz>M. Luntz (?) et al., [https://www.britannica.com/science/radiation/The-structure-and-properties-of-matter#ref398787 "Double refraction"], ''Encyclopædia Britannica'', accessed 15&nbsp;September 2017.</ref>

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<ref name=stokes-1849>G.G. Stokes, [https://archive.org/stream/transactionsofca09camb#page/n15/mode/2up "On the dynamical theory of diffraction"] (read 26&nbsp;November 1849), ''Transactions of the Cambridge Philosophical Society'', Vol.{{nnbsp}}9, Part&nbsp;1 (1851), pp.{{nnbsp}}1–62.</ref>

<ref name=whittaker-1910>E.T. Whittaker, [https://archive.org/details/historyoftheorie00whitrich ''A History of the Theories of Aether and Electricity: From the age of Descartes to the close of the nineteenth century''], Longmans, Green, &amp; Co., 1910.</ref>

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