We may for convenience in considering the effect of reflection on a beam of light regard it as made up of two sets of rectilinear vibrations, equal and at right angles to each other; and that one of these sets of vibrations is in the plane of incidence. When the ray reaches the surface of the glass obliquely the component which is vibrating at right angles to the plane of incidence will have its motion parallel to the surface, while the other vibration will penetrate the surface of the glass. One of these will pass on into the glass while the other will be reflected. The result of reflection, there fore, will be to separate the beam of unpolarized light into two parts and the reflected ray will vibrate in a single fixed plane. Light modified in this way is said to be plane polarized. The complete separation of the two components by reflection occurs only at a certain angle of in cidence, called the angle of polarization. Brew ster Transactions,' 1815) discovered that this angle varied with different substances and that tan a.= n, where a is the angle of polar ization and n is the index of refraction. This relation is fulfilled whenever in a given case the refracted ray makes an angle of 90 degrees with the reflected ray (see Fig. 1). When the polarized beam reaches the second mirror it will be freely reflected provided the planes of incidence of the two mirrors coincide. When the second mirror is turned so that these planes are at right angles, the ray will penetrate the glass without reflection.
When the theory of light was first developed at the hands of Fresnel, Neumann and numer ous other mathematicians, it seemed difficult to determine positively which component of the unpolarized incident ray at the first reflection would be transmitted and which would be re flected. It became customary, therefore, to speak of the plane of polarization rather than of the plane of vibration of the polarized ray; leaving it undetermined whether polarized light vibrated in the plane of polarization or at right angles to the same. The plane of polarization is defined as the plane of incidence. According to the assumptions made by Fresnel, the plane of vibration is perpendicular to the plane of polarization so that it is the component of the incident ray whose vibrations are parallel to the glass, which is reflected.
Some remarkable experiments which afford direct experimental evidence concerning the plane of vibration of polarized light were made in 1890 (Wiedemann's ol. 40, page 203). Wiener was able to locate by photographic means the position of the nodes of a standing system of light-waves produced by the interference within a collodion film on glass of the incident and the reflected ray. His interpretation of the results led him to the con clusion that the plane of vibration of polarized light is, as Fresnel had assumed, perpendicular to the plane of polarization.
Polarization by Double Refraction.—An other method by which it is possible to separate a beam of unpolarized light into two polarized components consists in causing the beam to pass through a doubly refracting medium. Many crystals have a structure such that the velocity at which light-waves are transmitted by them depends upon the plane of vibration.
A beam of light entering such a .crystal is in general resolved into two components, one of which vibrates in the direction which will per mit the light to travel with the maximum ve locity, the other at right angles to the same. These two polarized beams travel through the crystal independently, the latter being more re tarded than the former. If the light enters the crystal obliquely the index of refraction for the two components will differ. The component (0) which is most retarded will be more bent from its original path than the other (E) and will take a somewhat different direction through the crystal (see Fig. 3). If the two polarized beams thus produced by the action of the tal leave the crystal through a face parallel to that at which they entered, both will be restored to their original direction and instead of one beam of unpolarized light we then have two beams traveling along parallel paths. The distance between them will depend upon the thickness of the crystal, the angle of in cidence and the extent to which the crystal is doubly refracting. If, for example, in the path of a beam of unpolarized light a diaphragm with a circular opening be placed and between this and a screen a lens be mounted in such a position as to produce an image of the dia phragm upon the screen we shall have a circular spot of light at that point on the screen where the image falls. If now in the path of the ray we interpose a rhomb of calcite (Iceland spar) the surfaces of which form an oblique angle with the path of the ray, the latter upon enter ing the crystal will be bent from its course and divided into two as already described. These upon reaching the screen will form two images of the diaphragm. One of these polarized rays is spoken of as the ordinary and the other as the extraordinary ray.
To obtain a single beam of polarized light by means of the action of a doubly refracting crystal it is only necessary to interpose a screen which will intercept one and not the other of the two polarized components, or what is more convenient, to devise some way of intercepting one of these rays within the crystal itself. The device usually employed for this purpose was invented by Nicol (1828). The so-called Nicol prism consists of a rhomb of calcite of the form shown in Fig. 4. The rhomb is cut through diagonally at CD and is then cemented together by means of a layer of Canada balsam. The extraordinary ray meets the interface thus pro duced at an angle which permits its passage while the ordinary ray which is more bent from its course is totally reflected at 0 and passes out through the side of the prism. In this way a single ray of polarized light the plane of polarization of which is known is obtained. This method of producing polarization has the advantage over the method of reflection that the intensity of the polarized light is nearly half of that of the unpolarized ray. The intensity would be exactly 50 per cent but for the slight losses by' reflection at the surfaces and by the absorption within the crystal. Various modifi cations of the Nicol prism have since been de vised by Foucault, Glan, Thompson and others.