§ 1. In an ordinary ray of light the vibrations of the particies of ether take place successively in all possible directions perpendicular to its axis. Fig. 1 shows a transverse section of a ray, projected on a vertical plane.

Fig. 1.

Fig. 2.

By certain means it is possible to restrict the vibrations to some one particular direction (Fig. 2). The ray is then called a linear polarized ray. Its behaviour is no longer identically the same all around its axis, as in an ordinary ray; on the contrary, it displays two distinct sides, one in the plane of its vibrations, the other in a plane at right angles thereto.

§ 2. This conversion of common into polarized light may be effected, first, by reflection, for which purpose a glass mirror, inclined to the perpendicular at a certain angle (35° 25′), as L M (Figs. 3 and 4), will be found best. Rays falling in the direction a b, so as to make an angle of 55° with the normal x y, are reflected in the direction bc, and at the same time are polarized. This becomes manifest when the reflected rays meet the mirror P Q, which has a rotatory movement about be as an axis. When the second mirror is parallel to the first, as in Fig. 3, the ray bc is wholly reflected in the direction c d; but as the mirror turns on its axis, the intensity of the light reflected from it diminishes, until at 90° from the starting-point there is no longer any reflection, and the mirror appears dark. Continuing the rotation, we find that at 180°, нь

B

i.e., when the mirrors are inclined, so that the planes a b c and b c d are again coincident, as in Fig. 4, there is another maximum of reflection, and, lastly, at 270° another minimum. Thus the ray

behaves differently in two different directions at right angles to each other, one direction being in the plane of incidence or reflection, abc, the other in a plane at right angles therewith. The ray is polarized, and the former of the two planes is its plane of polarization.

We can therefore recognize a ray as polarized, and determine the position of its plane of polarization, by permitting it to fall upon a glass mirror at an angle of 55°. If the mirror be turned about the ray as an axis, light and darkness will alternate at intervals of 90°, and if the mirror be set so that the light emitted by it is at its brightest, the plane passing through it and the incident polarized ray is the plane of polarization of the latter. Again, if the mirror is at its darkest, the plane at right angles to the plane of incidence of the polarized ray is coincident with the plane of polarization.

By the undulatory theory of light it can be proved that the plane of polarization is either the plane in which the vibrations of ether take place, or a plane at right angles thereto. Which of these is really the case is still an open question among physicists; but for simplicity's sake we shall adopt the former view, and in these pages assume that the planes of vibration and polarization are coincident.

§ 3. But a pencil of light can also be polarized by repeated

b

single refractions or by double refraction in certain crystals, as of calc-spar-the latter being the most suitable means.

Fig. 5.

с

g

In a natural rhombohedron of Iceland spar (Fig. 5), the principal axis lies in the line joining the points d and f, where three obtuse angles meet. Suppose a plane to pass through the shorter diagonals of two opposite faces of the rhomb, i.e., either d g, a f, or d b, hf, or de, cf, it will invariably contain the principal axis df. Any such plane, and all planes parallel thereto, are called principal sections of the prism. If a pencil of light, m n (Fig. 6), falls on one face, as a b c d (of which d b h f represents the principal section), it will, on entering the crystal, divide into two refracted rays unequally bent. Both are polarized, and application of the mirror will show that the plane of polarization (or plane of vibration) of the less refracted or extraordinary ray n q is perpendicular to the principal section d b hf, while that of the

Fig. 6.

31

તે

h

more highly refracted or ordinary ray n p coincides with the plane of the said section.

For polariscopic purposes it is best to give exit to one only of the two polarized rays; that, namely, in the direction of the incident light, and to eliminate the other ray. This can be done in various ways, but most completely by converting the calc-spar into a Nicol's prism.1

For this purpose a piece of Iceland spar is split up into an elongated rhombohedron, as in Fig. 7, in which the plane passing through the points a b c d represents a principal section. The natural ends of the prism af be and d g ch, the former of which is inclined to a d and the latter to c b at an angle of 71°, are ground so as to reduce these angles to 68° (see Fig. 8). The prism is then divided in the direction b'd, which is perpendicular to a b' and cď, and the halves? -after polishing the faces of the section—are united as before with

1 For other forms of calc-spar polarizing prisms (Sénarmont's, Foucault's, and "achromatized" prism) see Wüllner's Lehrbuch der Physik, 3 Aufl. 2, 528–530.

2. Smaller Nicols may be prepared by grinding two separate crystals.

Canada balsam. Finally, the sides are blackened and the Nicol (Fig. 9) is fixed with cork into a brass case. The principal section of this prism passes through the shorter diagonals of the two rhombic ends. If a pencil of light, I m (Fig. 10), parallel to the edges of the longer side, falls on the face a b', it divides into two rays, which are polarized at right angles to one another. The less refracted (or extraordinary) ray, m p q, traverses the film of balsam at p, and emerges in the direction q s, parallel to 7 m. The more refracted (or ordinary) ray, m o, meets the balsam at o, which, from

its being a medium of so much feebler refractive power, causes total reflection of the ray in the direction or, whereby it becomes absorbed by the case of the prism. The other ray emerges in the direction of the incident pencil, but possesses only half of its luminous power. The plane of polarization (and vibration) of this ray is at right angles to the principal section, and therefore passes through the longer diagonals of the end faces of the prism.

§ 4. We have next to consider the behaviour of a polarized ray from a fixed Nicol, in passing through a second Nicol having a movement of rotation about its longitudinal axis. The first prism we will call the polarizer, the second the analyzer.