On the other hand, if the emergent streams overlap and the
common part be examined, it is found to have all the properties
of common light. To this phenomenon E. T. Malus gave the
name of polarization, as he attributed it, on the emission theory
of light, to a kind of polarity of the light-corpuscles. This
term has been retained and the ordinary stream is said to be
plane polarized in the principal plane of the face of entry into
the rhomb, and the extraordinary stream to be plane polarized
in the perpendicular plane.
The phenomenon of polarization observed by Huygens remained an isolated fact for over a century, until Malus in 1808 discovered that polarization can be produced independently of double refraction, and must consequently be something closely connected with the nature of light itself. Examining the light reflected from the windows of the Luxemburg palace with a doubly refracting prism, he was led to infer (though more refined experiments have shown that this is not strictly the case) that light reflected at a certain angle, called the polarizing angle, from the surface of transparent substances has the same properties with respect to the plane of incidence as those of the ordinary stream in Iceland spar with respect to the principal plane of the crystal. Thus in accordance with the definition, it is polarized in the plane of incidence. Further, if polarized light fall at the polarizing angle on a reflecting surface, the intensity of the reflected stream depends upon the azimuth of the plane of incidence, being proportional to the square of the cosine of the angle between this plane and the plane of the polarization. At angles other than the polarizing angle common light gives a reflected stream that behaves as a mixture of common light with light polarized in the plane of incidence, and is accordingly said to be partially polarized in that plane. The refracted light, whatever be the angle of incidence, is found to be partially polarized in a plane perpendicular to the plane of incidence, and D. F. J. Arago showed that at all angles of incidence the reflected and refracted streams contain equal quantities of polarized light. The polarizing angle varies from one transparent substance to another, and Sir David Brewster in 1815 enunciated the law that the tangent of the polarizing angle is equal to the refractive index of the substance. It follows then that if a stream of light be incident at the polarizing angle on a pile of parallel transparent plates of the same nature, each surface in turn will be met by the light at the polarizing angle and will give rise to a reflected portion polarized in the plane of incidence. Hence the total reflected light will be polarized in this plane and will of necessity have a greater intensity than that produced by a single surface. The polarization of the light transmitted by the pile is never complete, but tends to become more nearly so as the number of the plates is increased and at the same time the angle of incidence for which the polarization is a maximum approaches indefinitely the polarizing angle (Sir G. G. Stokes, Math. and Phys. Papers, iv 145).
In order to isolate a polarized pencil of rays with a rhomb of Iceland spar, it is necessary to have a crystal of such a thickness that the emergent streams are separated, so that one may be stopped by a screen. There are, however, certain crystals that with a moderate thickness give an emergent stream of light that is more or less completely polarized. The polarizing action of such crystals is due to the unequal absorption that they exert on polarized streams. Thus a plate of tourmaline of from 1 mm. to 2 mm. in thickness with its faces perpendicular to the optic axis is nearly opaque to light falling normally upon it, and a plate of this thickness parallel to the axis permits of the passage of a single stream polarized in a plane perpendicular to the principal section. Such a plate acts in the same way on polarized light, stopping it or allowing it to pass, according as the plane of polarization is parallel or perpendicular to the principal section. Certain artificial salts, e.g. iodo-sulphate of quinine, act in a similar manner.
From the above instances we see that an instrumental appliance that polarizes a beam of light may be used as a means of detecting and examining polarization. This latter process is termed analysation, and an instrument is called a polarizer or an analyser according as it is used for the first or the second of these purposes.
In addition to the above facts of polarization mention may be made of the partial polarization, in a plane perpendicular to that of emission, of the light emitted in an oblique direction from a white-hot solid, and of the polarization produced by diffraction. Experiments with gratings have been instituted by Sir G. Gabriel Stokes, C. H. A. Holtzmann, F. Eisenlohr and others, with the view of determining the direction of the vibrations in polarized light (vide infra), but the results have not been consistent, and H. Fizeau and G. H. Quincke have shown that they depend upon the size and form of the apertures and upon the state of the surface on which they are traced. The polarization of the light reflected from a glass grating has also been investigated by I. Frohlich, while L. G. Gouy has studied the more simple case of diffraction at a straight edge. The polarization of the light scattered by small particles has been examined by G. Govi, J. Tyndall, L. Soret and A. Lallemand, and in the case of ultra microscopic particles by H. Siedentopf and R. Zsigmondy (Drude Ann. 1903, x. 1); an interesting cast of this phenomenon is the polarization of the light from the sky—a subject that has been treated theoretically by Lord Rayleigh in an important series of papers (See Sky, Colour of, and Rayleigh, Scientific Works, i. 87, 104, 518, iv. 397).
An important addition to the knowledge of polarization was made in 1816 by Augustin J. Fresnel and D. F. J. Arago, who summed up the results of a searching series of experiments in the following laws of the interference of polarized light: (1) Under the same conditions in which two streams of common light interfere, two streams polarized at right angles are without mutual influence. (2) Two streams polarized in parallel planes give the same phenomena of interference as common light. (3) Two streams polarized at right angles and coming from a stream of common light can be brought to the same plane of polarization without thereby acquiring the faculty of interfering. (4) Two streams polarized at right angles and coming from a stream of polarized light interfere as common light, when brought to the same plane of polarization. (5) In calculating the conditions of interference in the last case, it is necessary to add a half wave-length to the actual difference of path of the streams, unless the primitive and final planes of polarization lie in the same angle between the two perpendicular planes.
The lateral characteristics of a polarized stream lead at once to the conclusion that the stream may be represented by a vector, and since this vector must indicate the direction in which the light travels as well as the plane of polarization, it is natural to infer that it is transverse to the direction of propagation. That this is actually the case is proved by experiments on the interference of polarized light, from which it may be deduced that the polarization-vector of a train of plane waves of plane polarized light executes rectilinear vibrations in the plane of the waves. By symmetry the polarization-vector must be either parallel or perpendicular to the plane of polarization: which of these directions is assumed depends upon the physical characteristic that is attributed to the vector. In fact, whatever theory of light be adopted, there are two vectors to be considered, that are at right angles to one another and connected by purely geometrical relations.
The general expressions for the rectangular components of a vector transverse to the direction of propagation (z) in the case of waves of length λ travelling with speed v are:—
where . The path of the extremity of the vector is then in general an ellipse, traversed in a right-handed direction to an observer receiving the light when α−β is between 0 and π, or between −π and −2π, and in a left-handed direction if this angle be between π and 2π, or between 0 and −π. In conformity with the form of the path, the light is said to be elliptically polarized, right- or left-handedly as the case may be, and the axes of the elliptic path are determined by the planes of
