of reflection. It is found by experience that this polarized ray is incapable of a second reflection at certain angles and in certain positions of the incident plane. For if another pane of plate-glass having one surface blackened, be so placed as to make an angle of 33° with the reflected ray, the image of the first pane will be reflected in its surface, and will be alternately illuminated and obscured at every quarter revolution of the blackened pane, according as the plane of reflection is parallel or perpendicular to the plane of polarization. Since this happens by whatever means the light has been polarized, it evinces another general property of polarized light, which is, that it is incapable of reflection in a plane at right angles to the plane of polarization.

All reflecting surfaces are capable of polarizing light, but the angle of incidence at which it is completely polarized is different in each substance (N. 205). It appears that the angle for plate-glass is 57°; in crownglass it is 56° 55', and no ray will be completely polarized by water, unless the angle of incidence be 53° 11'. The angles at which different substances polarize light are determined by a very simple and elegant law, discovered by Sir David Brewster, "That the tangent of the polarizing angle for any medium is equal to the sine of the angle of incidence divided by the sine of the angle of refraction of that medium." Whence also the refractive power even of an opaque body is known when its polarizing angle has been determined.

Metallic substances, and such as are of high refractive powers, like the diamond, polarize imperfectly.

If a ray polarized by refraction or by reflection from any substance not metallic, be viewed through a piece of Iceland spar, each image will alternately vanish and reappear at every quarter revolution of the spar, whether it revolves from right to left, or from left to right; which shows that the properties of the polarized ray are symmetrical on each side of the plane of polarization.

Although there be only one angle in each substance at which light is completely polarized by one reflection, yet it may be polarized at any angle of incidence by a sufficient number of reflections. For if a ray falls upon the upper surface of a pile of plates of glass at an angle

greater or less than a polarizing angle, a part only of the reflected ray will be polarized, but a part of what is transmitted will be polarized by reflection at the surface of the second plate, part at the third, and so on till the whole is poralized. This is the best apparatus; but one plate of glass having its inferior surface blackened, or even a polished table, will answer the purpose.

SECTION XXII.

Phenomena exhibited by the passage of Polarized Light through Mica and Sulphate of Lime-The Colored Images produced by Polarized Light passing through Crystals having one and two Optic Axes-Circular Polarization-Elliptical Polarization-Discoveries of MM. Biot, Fresnel, and Professor Airy-Colored Images produced by the Interference of Polarized Rays.

SUCH is the nature of polarized light and of the laws it follows. But it is hardly possible to convey an idea of the splendor of the phenomena it exhibits under circumstances which an attempt will now be made to describe.

If light polarized by reflection from a pane of glass be viewed through a plate of tourmaline, with its longitudinal section vertical, an obscure cloud, with its center totally dark, will be seen on the glass. Now let a plate of mica, uniformly about the thirtieth of an inch in thickness, be interposed between the tourmaline and the glass; the dark spot will instantly vanish, and instead of it, a succession of the most gorgeous colors will appear, varying with every inclination of the mica, from the richest reds, to the most vivid greens, blues, and purples (N. 206). That they may be seen in perfection, the mica must revolve at right angles to its own plane. When the mica is turned round in a plane perpendicular to the polarized ray, it will be found that there are two lines in it where the colors entirely vanish. These are the optic axes of the mica, which is a doubly refracting substance, with two optic axes, along which light is refracted in one pencil.

No colors are visible in the mica, whatever its position may be with regard to the polarized light, without the aid of the tourmaline, which separates the transmitted ray into two pencils of colored light complementary to

one another, that is, which taken together would make white light. One of these it absorbs, and transmits the other; it is therefore called the analyzing plate. The truth of this will appear more readily, if a film of sulphate of lime between the twentieth and sixtieth of an inch thick be used instead of the mica. When the film is of uniform thickness, only one color will be seen when it is placed between the analyzing plate and the reflecting glass; as, for example, red. But when the tourmaline revolves, the red will vanish by degrees till the film is colorless; then it will assume a green hue, which will increase and arrive at its maximum when the tourmaline has turned through ninety degrees; after that the green will vanish and the red will reappear, alternating at each quadrant. Thus the tourmaline separates the light which has passed through the film into a red and a green pencil; in one position it absorbs the green and lets the red pass, and in another it absorbs the red and transmits the green. This is proved by analyzing the ray v with Iceland spar instead of tourmaline; for since the spar does not absorb the light, two images of the sulphate of lime will be seen, one red and the other green, and these exchange colors every quarter revolution of the spar, the red becoming green, and the green red; and where the images overlap, the color is white, proving the red and green to be complementary to each other. The tint depends on the thickness of the film. Films of sulphate of lime, the 0·00124 and 0.01818 of an inch respectively, give white light in whatever position they may be held, provided they be perpendicular to the polarized ray; but films of intermediate thickness will give all colors. Consequently, a wedge of sulphate of lime, varying in thickness between the 0.00124 and the 0.01818 of an inch, will appear to be striped with all colors when polarized light is transmitted through it. A change in the inclination of the film, whether of mica or sulphate of lime, is evidently equivalent to a variation in thickness.

When a plate of mica, held as close to the eyes as possible at such an inclination as to transmit the polarized ray along one of its optic axes, is viewed through the tourmaline with its axis vertical, a most splendid appear

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ance is presented. The cloudy spot in the direction of the optic axis is seen surrounded by a set of vividly colored rings of an oval form, divided into two unequal parts by a black curved band passing through the cloudy spot about which the rings are formed. The other optic axis of the mica exhibits a similar image (N. 207).

When the two optic axes of a crystal make a small angle with one another, as in nitre, the two sets of rings touch externally; and if the plate of nitre be turned round in its own plane, the black transverse bands undergo a variety of changes, till at last the whole richly colored image assumes the form of the figure 8, traversed by a black cross (N. 208). Substances with one optic axis have but one set of colored circular rings, with a broad black cross passing through its center, dividing the rings into four equal parts. When the analyzing plate revolves, this figure recurs at every quarter revolution; but in the intermediate positions it assumes the complementary colors, the black cross becoming white.

It is in vain to attempt to describe the beautiful phenomena exhibited by innumerable bodies, which undergo periodic changes in form and color when the analyzing plate revolves, but not one of them shows a trace of color without the aid of tourmaline or something equivalent to analyze the light, and as it were to call these beautiful phantoms into existence. Tourmaline has the disadvantage of being itself a colored substance; but that inconvenience may be obviated by employing a reflecting surface as an analyzing plate. When polarized light is reflected by a plate of glass at the polarizing angle, it will be separated into two colored pencils; and when the analyzing plate is turned round in its own plane, it will alternately reflect each ray at every quarter revolution, so that all the phenomena that have been described will be seen by reflection on its surface.

Colored rings are produced by analyzing polarized light transmitted through glass melted and suddenly or unequally cooled; also through thin plates of glass bent with the hand, jelly indurated or compressed, &c. &c. In short, all the phenomena of colored rings may be produced, either permanently or transiently, in a variety of substances, by heat and cold, rapid cooling,

compression, dilatation, and induration; and so little apparatus is necessary for performing the experiments, that, as Sir John Herschel says, a piece of windowglass or a polished table to polarize the light, a sheet of clear ice to produce the rings, and a broken fragment of plate-glass placed near the eye to analyze the light, are alone requisite to produce one of the most splendid of optical exhibitions.

It has been observed, that when a ray of light, polarized by reflection from any surface not metallic, is analyzed by a doubly refracting substance, it exhibits properties which are symmetrical both to the right and left of the plane of reflection, and the ray is then said to be polarized according to that plane. This symmetry is not destroyed when the ray, before being analyzed, traverses the optic axis of a crystal having but one optic axis, as evidently appears from the circular forms of the colored rings already described. Regularly crystalized quartz, however, forms an exception. In it, even though the rays should pass through the optic axis itself, where there is no double refraction, the primitive symmetry of the ray is destroyed, and the plane of primitive polarization deviates either to the right or left of the observer, by an angle proportional to the thickness of the plate of quartz. This angular motion, or true rotation of the plane of polarization, which is called circular polarization, is clearly proved by the phenomena. The colored rings produced by all crystals having but one optic axis are circular, and traversed by a black cross concentric with the rings; so that the light entirely vanishes throughout the space inclosed by the interior ring, because there is neither double refraction nor polarization along the optic axis. But in the system of rings produced by a plate of quartz, whose surfaces are perpendicular to the axis of the crystal, the part within the interior ring, instead of being void of light, is occupied by a uniform tint of red, green, or blue, according to the thickness of the plate (N. 209). Suppose the plate of quartz to be of an inch thick, which will give the red tint to the space within the interior ring; when the analyzing plate is turned in its own plane through an angle of 1710, the