produce this result increasing as the incidence is more removed from the polarizing angle.

(173) It remains to describe the modification which light undergoes in refraction.

When common light is suffered to fall upon a plate of glass, a portion of it in all cases enters the plate, and is refracted; and this refracted portion is found to be partially polarized. The quantity of polarized light in the refracted pencil increases with the incidence, being nothing at a perpendicular incidence, and greatest when the incidence is most oblique. The plane of polarization is not (as in the case of reflected light) coincident with the plane of incidence, but perpendicular to it.

The connexion between the light thus polarized, and that polarized by reflexion, is very intimate, the two portions being always of equal intensity. This remarkable law was discovered by Arago, and may be thus enunciated—“ When an unpolarized ray is partly reflected at, and partly transmitted through a transparent surface, the reflected and transmitted portions contain equal quantities of polarized light; and their planes of polarization are at right angles to each other."

(174) If the transmitted light be received upon a second plate parallel to the first, the portion of common light which it contains undergoes a new subdivision; and so continually, whatever be the number of plates. Hence, when that number is sufficiently great, the transmitted light will be, as to sense, completely polarized, the plane of polarization being perpendicular to the plane of incidence. These facts were discovered by Malus.

It is a remarkable consequence of these principles, that when a ray is incident upon a pile of parallel plates at the polarizing angle, after passing a certain number the intensity

of the transmitted light will undergo no further diminution. For the light becoming wholly polarized in the plane perpendicular to the plane of incidence, no portion of it will be reflected by any of the succeeding plates; it is therefore transsmitted without diminution through them, whatever be their number. The case is different, when the light is incident on the pile at any other than the polarizing angle; and it follows therefore that the intensity of the light transmitted through a thick pile is greatest, when it is incident at the polarizing angle.

(175) There are certain crystals which, like the pile of transparent plates, possess the property of polarizing the transmitted light. This property depends upon a peculiarity in the absorbing powers of double-refracting crystals,namely, that the absorption of a polarized ray varies with the position of its plane of polarization with respect to the crystal. Thus, tourmaline absorbs a polarized ray more rapidly when the plane of polarization is parallel to the axis, than when it is perpendicular to it. Now a ray of common light, which falls upon a plate of this crystal cut parallel to the axis, may be resolved into two, one polarized in a plane passing through the axis, and the other in a plane perpendicular to it; and the former of these being absorbed more rapidly than the latter, the transmitted light will be partially polarized in the plane perpendicular to the axis of the crystal. When the plate is sufficiently thick, the latter portion alone will be sensible, and the ray emerges wholly polarized in the perpendicular plane.

The tourmaline, accordingly, is of much use in experiments on polarized light, not only in affording a ready test of polarization, but also in producing a polarized beam. It has the disadvantages, however, that the polarization of the

M

emergent light is never perfect, and that its intensity is much weakened by absorption-both the rays being absorbed in their passage through the crystal, although with unequal energies.

The polarization produced by double refraction is the most complete of any; while the intensity of the polarized pencils is greater than in any other case, being very nearly one-half of the intensity of the original light. The intensity of the light reflected from a plate of glass, at the polarizing angle, is not more than the one-twelfth part of that of the incident light.

(176) From the foregoing it would appear that the most effective mode of producing a polarized ray of strong intensity is, to transmit a ray of common light through a rhomb of Iceland spar, and to shut off one of the two refracted pencils by means of an opaque plate on the second surface of the rhomb. Here however there is a difficulty. The two rays will overlap, unless the aperture by which the light is admitted to the first surface of the rhomb is very small, or the thickness of the rhomb is very considerable. The former condition reduces the quantity of the light; the latter is difficult of attainment, on account of the rarity of large specimens of the crystal of sufficient purity.

These difficulties may be evaded, by receiving the light upon a lens of short focus, placed immediately behind the rhomb. The rays which have passed through the lens and the rhomb will converge to two foci, one of which may be covered by a diaphragm, and the rays diverging from the other suffered to proceed alone. These rays may be reduced to parallelism, when required, by receiving them upon a second lens, placed at its own focal distance from the point of divergence. The aperture of this lens will determine the breadth of the beam. It will be convenient to employ a

plano-convex as the first lens, and to cement it with Canada balsam to the rhomb.

(177) A more usual method is to stop one of the pencils by total reflexion. A long rhomb of Iceland spar is taken, and cut obliquely, in such manner that the refracting edges of the two resulting prisms shall be parallel to the axis of the crystal. The cut faces are then polished, and reunited in their original positions by Canada balsam. Now the index of refraction of Canada balsam is less than that of the ordinary ray of Iceland spar, while it is greater than that of the extraordinary ray. Hence, when the incidence is sufficiently oblique, the ordinary ray will be totally reflected, while the extraordinary ray is transmitted. The transmitted light is therefore polarized.

The angle of incidence at which total reflexion takes place is easily calculated. The refractive index of the ordinary ray in Iceland spar = 1.654; and that of Canada balsam 1.549. Hence the ratio of the sines of incidence and refraction from the crystal into the balsam, for that ray, 1.549

=

1.653

=

=

0.937. Accordingly, when the refracted ray just grazes the surface, the sine of incidence 0.937; and the corresponding angle = 69° 30′. The ordinary ray therefore will be wholly reflected, when it is incident on the separating surface at this or any greater angle, or when that surface is inclined to the axis of the prism at any angle less than 20° 30′. This ingenious contrivance is denominated, after the inventor, Nicol's prism.

The foregoing arrangement has been much improved by M. Foucault, by dispensing with the Canada balsam altogether, and shortening the rhomb. The sines of the angles of total reflexion in passing from the crystal into

and the cor

Hence, if the

responding angles are 37° 14′ and 42° 23'. length of the compound prism be so adjusted that the ray shall fall upon the bounding surface at an incidence intermediate to these two angles, the ordinary ray will be wholly reflected, while the extraordinary ray will be transmitted. It is obvious that the length of the rhomb which will give this incidence is much shorter than in Nicol's prism.

(178) M. Haidinger has observed a remarkable phenomenon of polarized light, by which it may be recognised by the naked eye, and its plane of polarization ascertained. This phenomenon consists in the appearance of two brushes, of a pale orange-yellow colour, the axis of which coincides always with the trace of the plane of polarization; these are accompanied, on either side, by two patches of light, of a complementary or violet tint. In order to see them, the plane of polarization of the light must be turned quickly from one position to another, so as to shift the position of the brushes. Thus they may be observed by looking for a few moments at one of the images of a circular aperture, formed by a rhomb of Iceland spar, and then at the other, and so alternately. They gradually disappear when the eye continues directed to them in the same position; but they may be made to reappear by shifting that position, or the plane of polarization on which it depends.

The most probable explanation of this phenomenon seems to be that given by M. Jamin, in which it is ascribed to the refracting coats of the eye. When polarized light falls upon a pile of parallel plates, the proportion of the refracted to the incident light varies with the plane of polarization, being a