CHAPTER VIII.

POLARIZATION OF LIGHT.

(139) IN the various phenomena which take place when a ray of light encounters the surface of a new medium, it has been supposed that the direction and intensity of the several portions into which it is subdivided will continue the same, on whatever side of the ray the surface is presented, provided that the angle and the plane of incidence continue unchanged. In other words, it was taken for granted that a ray of light had no relation to space, with the exception of that dependent on its direction; that, around that direction, its properties were on all sides alike; and that, if the ray be made to revolve round that line as an axis, the resulting phenomena would be unaltered.

Huygens was the first to observe that this was not always the case. In the course of his researches on the law of double refraction, he found that when a ray of solar light is received upon a rhomb of Iceland crystal, in any but one direction, it is always subdivided into two of equal intensity. But, on transmitting these rays through a second rhomb, he was surprised to observe that the two portions, into which each of them was subdivided, were no longer equally intense; that their relative brightness depended on the position of the second rhomb with regard to the first; and that there were two such positions in which one of the rays vanished altogether.

On analyzing the phenomenon, it is found that these two positions are those in which the principal sections of the two crystals are parallel or perpendicular. When these sections are parallel, the ray which has undergone ordinary refraction by the first crystal will be also refracted ordinarily by the second;

and the ray which has been extraordinarily refracted by the first will be also extraordinarily refracted by the second. On the contrary, when the principal sections of the two crystals are perpendicular, the ray which has suffered ordinary refraction by the first crystal will undergo extraordinary refraction by the second; and the extraordinary ray of the first will be refracted according to the ordinary law in the second. In the intermediate positions of the two principal sections, each of the rays refracted by the first crystal will be divided into two by the second; and these two pencils are in general different in intensity, their intensities being measured by the square of the cosine of the distance from the position of greatest intensity.

(140) From this "wonderful phenomenon," as Huygens justly called it, it appears that each of the rays refracted by the first rhomb has acquired properties which distinguish it altogether from solar light. It has, in fact, acquired sides; and it is evident that the phenomena of refraction depend, in some unknown manner, on the relation of these sides to certain planes within the crystal. Such was the conclusion of Newton. "This argues," says he, "a virtue or disposition in those sides of the rays, which answers to, and sympathizes with, that virtue or disposition of the crystal, as the poles of two magnets answer to one another."

Although the phenomenon discovered by Huygens was one of such importance, in the mind of Newton, as to force him to admit the existence of properties in the rays of light which, until then, had never been imagined, yet the result remained, for more than 100 years, a unique fact in science; and the kindred phenomena-the properties which light acquires in a greater or less degree in almost every modification which it undergoes remained unnoticed until the beginning of the present century.

(141) In the year 1808, while Malus was engaged in the

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experimental researches by which he established the Huygenian law of double refraction, he happened to turn a doublerefracting prism towards the windows of the Luxembourg palace, which then reflected the rays of the setting sun. turning round the prism, he was astonished to find that the ordinary image of the window nearly disappeared in two opposite positions of the prism; while in two other positions, at right angles to the former, the extraordinary image nearly vanished. Struck with the analogy of this phenomenon to that which is observed when light is transmitted through two rhomboids of Iceland spar, Malus at first ascribed it to some property which the light had acquired in its passage through the atmosphere: but he soon abandoned this idea, and found that this new property was impressed upon the light by reflexion at the surface of the glass.

Pursuing the subject, he was led to the important discovery, that when a ray of light is reflected from the surface of glass, or water, or any other transparent medium, at certain angles, the reflected ray acquires all the characters which belong to the light which has undergone double refraction. When received upon a rhomb of Iceland spar, or a doublerefracting prism, one of the two pencils into which it is divided vanishes in two positions of the rhomb,—namely, when the principal section of the crystal is parallel or perpendicular to the plane of reflexion; while, in intermediate positions, these pencils vary in intensity through every possible gradation.

A ray, then, may acquire sides or poles-may, in short, be polarized by reflexion at the surface of a transparent medium, as well as by double refraction. The plane of polarization is the plane of reflexion at which the effect is produced; and it is experimentally known by its relation to the principal section of a double-refracting crystal,—the ray undergoing ordinary refraction only, when the principal section is parallel to the plane of polarization.

(142) But a polarized ray possesses other characters. When a ray of light, proceeding directly from a self-luminous body, is received upon a reflecting surface at a given angle, the intensity of the reflected beam will be unaltered, whether the surface be above or below, on the right or on the left of the incident beam. The case, however, is different, if, instead of the direct light of a self-luminous body, we submit to the same trial light which has been already polarized. It is then no longer indifferent on what side of the ray the new surface is presented. The inclination of the reflected or transmitted ray will, indeed, remain unaltered, on whatever side the surface be presented, but its intensity will be very different; and a ray which is reflected most intensely when the new surface is presented at one side, under a certain angle, will be wholly transmitted when it is offered to another, all other circumstances being identical.

It is evident then, that the ray which has suffered reflexion at the first surface, in this experiment, has in consequence acquired properties wholly distinct from the original light. The latter is equally reflected in every azimuth of the plane of reflexion; while, on the other hand, the intensity of the twice-reflected ray diminishes, as the angle between the reflecting planes increases; and it vanishes altogether, and the ray is wholly transmitted, when the plane of reflexion at the second surface is perpendicular to that at the first. These sides, or poles, once acquired, are retained by the ray in all its future course, provided it undergoes no further modification by reflexion or refraction; for, whether the plates be an inch or a mile asunder, the phenomena are the same.

(143) A polarized ray, then, is distinguished by the following characters:—

I. It is not divided into two pencils by a double-refracting crystal, in two positions of the principal section with respect to the ray; being refracted ordinarily, when the plane of

polarization coincides with the principal section, and extraordinarily when it is perpendicular to it. In other cases it gives rise to two pencils, which vary in intensity according to the position of the principal section.

II. It suffers no reflexion at the polished surface of a transparent medium, when this surface is presented to it at a certain angle, and in a plane of incidence perpendicular to the plane of polarization; while it is partially reflected, when the reflecting surface is presented in other planes of incidence, or under different angles.

The apparatus best fitted for the exhibition of these phenomena is that devised by M. Biot. It consists of a tube, furnished at its extremities with two graduated rings, which are capable of revolving in a plane perpendicular to its axis. Each of these rings carries a plate of glass set in a frame, and held by two projecting arms. These plates are capable of revolving round a transverse axis, so that their inclination to the axis of the tube may be varied at pleasure; and a small graduated circle, attached to one of the arms, measures the inclination. The whole apparatus is connected with a vertical pillar, by a moveable joint, so that the tube may be inclined to the horizon at any angle. In this form of the apparatus, it is arranged to exhibit the properties of polarized light dependent on reflexion: in order to show the other properties, one of the glass plates may be removed, and a double-refracting prism, or a plate of tourmaline, substituted in its place.

(144) The angles of incidence at which light is polarized are called the angles of polarization. They are in general different for different substances: thus the angle of polarization of glass is 57°, and that of water, 53°.

The connexion between the polarizing angles and the other properties of substances with regard to light was discovered by Sir David Brewster, In the year 1811 he commenced