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The term ''plane of polarization'' refers to the direction of
polarization Polarization or polarisation may refer to: Mathematics *Polarization of an Abelian variety, in the mathematics of complex manifolds *Polarization of an algebraic form, a technique for expressing a homogeneous polynomial in a simpler fashion by ...
of ''
linearly-polarized In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. The term ''linear polarizat ...
'' light or other
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible ...
. Unfortunately the term is used with two contradictory meanings. As originally defined by Étienne-Louis Malus in 1811,Buchwald, 1989, p.54. the plane of polarization coincided (although this was not known at the time) with the plane containing the direction of propagation and the ''magnetic'' vector. In modern literature, the term ''plane of polarization'', if it is used at all, is likely to mean the plane containing the direction of propagation and the ''electric'' vector, because the electric field has the greater propensity to interact with matter.Born & Wolf, 1970, p.28. For waves in a
birefringent Birefringence is the optics, optical property of a material having a refractive index that depends on the Polarization (waves), polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or ...
(doubly-refractive) crystal, under the old definition, one must also specify whether the direction of propagation means the ray direction or the wave- normal direction, because these directions generally differ and are both perpendicular to the magnetic vector (Fig.1). Malus, as an adherent of the
corpuscular theory of light In optics, the corpuscular theory of light states that light is made up of small discrete particles called " corpuscles" (little particles) which travel in a straight line with a finite velocity and possess impetus. This was based on an alternate ...
, could only choose the ray direction. But
Augustin-Jean Fresnel Augustin-Jean Fresnel (10 May 1788 â€“ 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theo ...
, in his successful effort to explain double refraction under the
wave theory In historical linguistics, the wave model or wave theory (German ''Wellentheorie'') is a model of language change in which a new language feature (innovation) or a new combination of language features spreads from its region of origin, affecting ...
(1822 onward), found it more useful to choose the wave-normal direction, with the result that the supposed vibrations of the medium were then consistently perpendicular to the plane of polarization.Fresnel, 1827, tr. Hobson, p.318. In an isotropic medium such as air, the ray and wave-normal directions are the same, and Fresnel's modification makes no difference. Fresnel also admitted that, had he not felt constrained by the received terminology, it would have been more natural to define the plane of polarization as the plane containing the vibrations and the direction of propagation.Fresnel, 1822, tr. Young, part 7
p.406
That plane, which became known as the plane of ''vibration'', is perpendicular to Fresnel's "plane of polarization" but identical with the plane that modern writers tend to call by that name! It has been argued that the term ''plane of polarization'', because of its historical ambiguity, should be avoided in original writing. One can easily specify the orientation of a particular field vector; and even the term ''plane of vibration'' carries less risk of confusion than ''plane of polarization''.


Physics of the term

For electromagnetic (EM) waves in an ''isotropic'' medium (that is, a medium whose properties are independent of direction), the electric field vectors (E and D) are in one direction, and the
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...
vectors (B and H) are in another direction, perpendicular to the first, and the direction of propagation is perpendicular to both the electric and the magnetic vectors. In this case the direction of propagation is both the ''ray'' direction and the ''wave-normal'' direction (the direction perpendicular to the
wavefront In physics, the wavefront of a time-varying ''wave field'' is the set ( locus) of all points having the same '' phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal fre ...
). For a ''linearly''-polarized wave (also called a ''plane''-polarized wave), the orientations of the field vectors are fixed (Fig.2). Because innumerable materials are
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the m ...
s or conductors while comparatively few are ferromagnets, the reflection or
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...
of EM waves (including
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...
) is more often due to differences in the ''electric'' properties of media than to differences in their magnetic properties. That circumstance tends to draw attention to the ''electric'' vectors, so that we tend to think of the direction of polarization as the direction of the electric vectors, and the "plane of polarization" as the plane containing the electric vectors and the direction of propagation. Indeed, that is the convention used in the online ''Encyclopædia Britannica'', and in
Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superflu ...
's lecture on polarization. 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
antennas In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies a ...
(Fig.3).Stratton, 1941, p.280. If the medium is magnetically isotropic but electrically ''non''-isotopic (like a 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.1). 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 James Clerk Maxwell (13 June 1831 â€“ 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
in the 1860s — whereas the word ''polarization'' was coined about 50 years earlier, and the associated mystery dates back even further.


History of the term


Three candidates

Whether by accident or by design, the plane of polarization has always been defined as the plane containing a field vector and a direction of propagation. In Fig.1, there are three such planes, to which we may assign numbers for ease of reference: :(1)  the plane containing both electric vectors and both propagation directions  (i.e., the plane normal to the magnetic vectors); :(2a)  the plane containing the magnetic vectors and the wave-normal  (i.e., the plane normal to D); :(2b)  the plane containing the magnetic vectors and the ray  (i.e., the plane normal to E). In an isotropic medium, E and D have the same direction,This conclusion does not follow if the medium is optically rotating (see e.g. Darrigol, 2012, pp.253n,257n); however, throughout this article, the existence of a stable plane of polarization requires the absence of optical rotation. so that the ray and wave-normal directions merge, and the planes (2a) and (2b) become one: :(2)  the plane containing both magnetic vectors and both propagation directions  (i.e., the plane normal to the electric vectors).


Malus's choice

Polarization was discovered — but not named or understood — by
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists ...
, as he investigated the
double refraction Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or birefractive). The birefringe ...
of "Iceland crystal" (transparent
calcite Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate (CaCO3). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on the Mohs scale of mineral hardness, based on scra ...
, 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. 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. This axis was parallel to the axes of the
spheroid A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has ...
al secondary waves by which he (correctly) explained the directions of the extraordinary refraction. The term ''polarization'' was coined by Étienne-Louis Malus in 1811.  In 1808, in the midst of confirming Huygens' geometric description of double refraction (while disputing his physical explanation), Malus had discovered that when a ray of light is reflected off a non-metallic surface at the appropriate angle, it behaves like ''one'' of the two rays emerging from a calcite crystal.The angle of reflection at which this modification occurs became known as '' Brewster's angle'', after its dependence on the refractive index was determined experimentally by
David Brewster Sir David Brewster KH PRSE FRS FSA Scot FSSA MICE (11 December 178110 February 1868) was a British scientist, inventor, author, and academic administrator. In science he is principally remembered for his experimental work in physical optic ...
in 1815.
As this behavior had previously been known only in connection with double refraction, Malus described it in that context. In particular, he defined the ''plane of polarization'' of a polarized ray as the plane, containing the ray, in which a principal section of a calcite crystal must lie in order to cause only ''ordinary'' refraction. This definition was all the more reasonable because it meant that when a ray was polarized by reflection (off an isotopic medium), the plane of polarization was the
plane of incidence In describing reflection and refraction in optics, the plane of incidence (also called the incidence plane or the meridional plane) is the plane which contains the surface normal and the propagation vector of the incoming radiation. (In wave o ...
and reflection — that is, the plane containing the incident ray, the normal to the reflective surface, and the polarized reflected ray. But, as we now know, this plane happens to contain the ''magnetic'' vectors of the polarized ray, not the electric vectors. The plane of the ray and the magnetic vectors is the one numbered (2b) above. The implication that the plane of polarization contains the ''magnetic'' vectors is still found in the definition given in the online Merriam-Webster dictionary. Even Julius Adams Stratton, having said that "It is customary to define the polarization in terms of E", promptly adds: "In optics, however, the orientation of the vectors is specified traditionally by the 'plane of polarization,' by which is meant the plane normal to E containing both H and the axis of propagation." That definition is identical with Malus's.


Fresnel's choice

In 1821,
Augustin-Jean Fresnel Augustin-Jean Fresnel (10 May 1788 â€“ 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theo ...
announced his hypothesis that light waves are exclusively ''
transverse Transverse may refer to: *Transverse engine, an engine in which the crankshaft is oriented side-to-side relative to the wheels of the vehicle *Transverse flute, a flute that is held horizontally * Transverse force (or ''Euler force''), the tangen ...
'' 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 orientation is rapidly and randomly changing. Supposing that light waves were analogous to shear waves in elastic solids, and that a higher
refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, o ...
corresponded to a higher
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''Ï'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
of the
luminiferous aether Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), s ...
, he found that he could account for the partial reflection (including polarization by reflection) at the interface between two transparent isotropic media, provided that the vibrations of the aether were perpendicular to the plane of polarization. Thus the polarization, according to the received definition, was "in" a certain plane if the vibrations were ''perpendicular'' to that plane! 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 wished to avoid making any change in the received appellations.The actual writing of this treatise (Fresnel, 1822) was apparently completed by mid 1821; see I. Grattan-Guinness, ''Convolutions in French Mathematics, 1800–1840'', Basel: Birkhäuser, 1990, vol.2, p.884. 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. 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. 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. The vibrations normal to Malus's plane of polarization are electric, and the electric vibration tangential to the wavefront is D (Fig.1). Thus, in terms of the above numbering, Fresnel changed the "plane of polarization" from (2b) to (2a). Fresnel's definition remains compatible with the Merriam-Webster definition, which fails to specify the propagation direction. And it remains compatible with Stratton's definition, because that is given in the context of an isotropic medium, in which planes (2a) and (2b) merge into
(2) ''(2)'' is the eighteenth studio album by British-Australian pop singer Olivia Newton-John, released on 12 November 2002 in Australia. A duets album, the majority of tracks are with Australian artists, along with two American performers (Richa ...
. What Fresnel called the "more natural" choice was a plane containing D and a direction of propagation. In Fig.1, the only plane meeting that specification is the one labeled "Plane of vibration" and later numbered (1) — that is, the one that ''modern'' authors tend to identify with the "plane of polarization". We might therefore wish that Fresnel had been less deferential to his predecessors. That scenario, however, is less realistic than it may seem, because even after Fresnel's transverse-wave theory was generally accepted, the direction of the vibrations was the subject of continuing debate.


"Plane of vibration"

The principle that refractive index depended on the density of the aether was essential to Fresnel's aether drag hypothesis. 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 Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a b ...
of the aether ''within'' a birefringent medium, plus a variation in density ''between'' media. James MacCullagh and
Franz Ernst Neumann Franz Ernst Neumann (11 September 1798 – 23 May 1895) was a German mineralogist, physicist and mathematician. Biography Neumann was born in Joachimsthal, Margraviate of Brandenburg, near Berlin. In 1815 he interrupted his studies at Berlin to ...
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. The question called for an experimental determination of the direction of vibration, and the challenge was answered by
George Gabriel Stokes Sir George Gabriel Stokes, 1st Baronet, (; 13 August 1819 – 1 February 1903) was an Irish English physicist and mathematician. Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the Luc ...
. He defined the ''plane of vibration'' as "the plane passing through the ray and the direction of vibration" (in agreement with Fig.1). Now suppose that a fine
diffraction grating In optics, a diffraction grating is an optical component with a periodic structure that diffracts light into several beams travelling in different directions (i.e., different diffraction angles). The emerging coloration is a form of structural ...
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. 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. There was, however, a sense in which MacCullagh and Neumann were correct. 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 (both being non-directional), and the compliance must correspond to the electric
permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more i ...
(both being directional). The result is that the velocity of the solid corresponds to the H field, so that the mechanical vibrations of the shear wave are in the direction of the ''magnetic'' vibrations of the EM wave. But Stokes's experiments were bound to detect the ''electric'' vibrations, because those have the greater propensity to interact with matter. In short, the MacCullagh-Neumann vibrations were the ones that had a mechanical analog, but Fresnel's vibrations were the ones that were more likely to be detected in experiments.Concerning the limitations of elastic-electromagnetic analogies, see (e.g.) Born & Wolf, 1970, pp.xxiv–xxv; Darrigol, 2012, pp.227–32.


Modern practice

The electromagnetic theory of light further emphasized the ''electric'' vibrations because of their interactions with matter, whereas the old "plane of polarization" contained the ''magnetic'' vectors. Hence the electromagnetic theory would have reinforced the convention that the vibrations were normal to the plane of polarization — provided, of course, that one was familiar with the historical definition of the plane of polarization. But if one was influenced by physical considerations ''alone'', then, as Feynman and the ''Britannica'' illustrate, one would pay attention to the electric vectors and assume that the "plane" of polarization (if one needed such a concept) contained those vectors. However, it is not clear that a "plane of polarization" is needed at all: knowing what field vectors are involved, one can specify the polarization by specifying the orientation of a particular vector, or, as
Born Born may refer to: * Childbirth * Born (surname), a surname (see also for a list of people with the name) * ''Born'' (comics), a comic book limited series Places * Born, Belgium, a village in the German-speaking Community of Belgium * Born, Luxe ...
and
Wolf The wolf (''Canis lupus''; : wolves), also known as the gray wolf or grey wolf, is a large canine native to Eurasia and North America. More than thirty subspecies of ''Canis lupus'' have been recognized, and gray wolves, as popularly u ...
suggest, by specifying the "plane of vibration" of that vector.  Hecht also prefers the term ''plane of vibration'' (or, more usually, ''plane-of-vibration''), which he defines as the plane of E and the wave-normal, in agreement with Fig.1 above.


Remaining uses

In an optically ''
chiral Chirality is a property of asymmetry important in several branches of science. The word ''chirality'' is derived from the Greek (''kheir''), "hand", a familiar chiral object. An object or a system is ''chiral'' if it is distinguishable from i ...
'' medium — that is, one in which the direction of polarization gradually rotates as the wave propagates — the choice of definition of the "plane of polarization" does not affect the existence or direction ("handedness") of the rotation. This is one context in which the ambiguity of the term ''plane of polarization'' causes no further confusion. There is also a context in which the original definition might still suggest itself. In a non-magnetic non-chiral crystal of the '' biaxial'' class (in which there is no ordinary refraction, but both refractions violate
Snell's law Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
), there are three mutually perpendicular planes for which the speed of light is isotropic within the plane provided that the electric vectors are normal to the plane. This situation naturally draws attention to a plane normal to the vibrations as envisaged by Fresnel, and that plane is indeed the plane of polarization as defined by Fresnel or Malus. In most contexts, however, the concept of a "plane of polarization" distinct from a plane containing the electric "vibrations" has arguably become redundant, and has certainly become a source of confusion. In the words of Born & Wolf, "it is… better not to use this term."Born & Wolf, 1970, p.43.


Notes


References


Bibliography

* W.S. Aldis, 1879
''A Chapter on Fresnel's Theory of Double Refraction''
2nd Ed., Cambridge: Deighton, Bell, & Co. / London: George Bell & Sons. * M. Born and E. Wolf, 1970, ''
Principles of Optics ''Principles of Optics'', colloquially known as ''Born and Wolf'', is an optics textbook written by Max Born and Emil Wolf that was initially published in 1959 by Pergamon Press. After going through six editions with Pergamon Press, the book wa ...
'', 4th Ed., Oxford: Pergamon Press. * J.Z. Buchwald, 1989, ''The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century'', University of Chicago Press, . * O. Darrigol, 2012, ''A History of Optics: From Greek Antiquity to the Nineteenth Century'', Oxford, . * A. Fresnel, 1822, ''De la Lumière'' (''On Light''), in J. Riffault (ed.)
''Supplément à la traduction française de la cinquième édition du "Système de Chimie" par Th.Thomson''
Paris: Chez Méquignon-Marvis, 1822, pp.1–137,535–9; reprinted in Fresnel, 1866–70, vol.2
pp.3–146
translated by T. Young as "Elementary view of the undulatory theory of light", ''Quarterly Journal of Science, Literature, and Art'', vol.22 (Jan.–Jun.1827), p
127–41441–54
vol.23 (Jul.–Dec.1827), p
113–35431–48
vol.24 (Jan.–Jun.1828), p
198–215
vol.25 (Jul.–Dec.1828), p
168–91389–407
vol.26 (Jan.–Jun.1829), p
159–65
* A. Fresnel, 1827, "Mémoire sur la double réfraction", ''Mémoires de l'Académie Royale des Sciences de l'Institut de France'', vol. (for 1824, printed 1827)
pp.45–176
reprinted as "Second mémoire…" in Fresnel, 1866–70, vol.2
pp.479–596
translated by A.W. Hobson a
"Memoir on double refraction"
in R.Taylor (ed.), ''Scientific Memoirs'', vol. (London: Taylor & Francis, 1852), pp.238–333. (Cited page numbers are from the translation.) * A. Fresnel (ed. H. de Senarmont, E. Verdet, and L. Fresnel), 1866–70, ''Oeuvres complètes d'Augustin Fresnel'' (3 volumes), Paris: Imprimerie Impériale
vol.1 (1866)vol.2 (1868)vol.3 (1870)
* E. Hecht, 2017, ''Optics'', 5th Ed., Pearson Education, . * C. Huygens, 1690, ''Traité de la Lumière'' (Leiden: Van der Aa), translated by S.P. Thompson as
Treatise on Light
', University of Chicago Press, 1912; Project Gutenberg, 2005. (Cited page numbers match the 1912 edition and the Gutenberg HTML edition.) * B. Powell (July 1856)
"On the demonstration of Fresnel's formulas for reflected and refracted light; and their applications"
''Philosophical Magazine and Journal of Science'', Series 4, vol.12, no.76, pp.1–20. * J.A. Stratton, 1941, ''Electromagnetic Theory'', New York: McGraw-Hill. * E. T. 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. {{Authority control Light Optics Physical optics Polarization (waves) Electromagnetic radiation Antennas (radio) History of physics