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having unequal 'tensions, whether from unequal temperature or pressure, possess the property of doubling the image or appearance of an object seen through them in certain directions; because à ray of natural light falling upon them is refracted into two pencils which move with different velocities, and are more or less separated, according to the nature of the body and the direction of the incident ray. Iceland spar, a carbonate of lime, which, by its natural cleavage, may be split into the form of a rhombohedron, possesses this property in an eminent degree, as may be seen by passing a piece of paper, with a large pin hole in it, on the side of the spar farthest from the eye. The hole will appear double when held to the light. One of these pencils is refracted according to the same law, as in glass or water, never quitting the plane perpendicular to the refracting surface, and therefore called the ordinary ray; but the other does quit that plane, being refracted according to a different and much more complicated law, and on that account is called the extraordinary ray. For the same reason one image is called the ordinary, and the other the extraordinary image. When the spar is turned round in the same plane, the extraordinary image of the hole revolves about the ordinary image which remains fixed, both being equally bright. But if the spar be kept in one position, and viewed through a plate of tourmaline, it will be found that, as the tourmaline revolves, the images vary in their relative brightness--one increases in intensity till it arrives at a maximum, at the same time that the other diminishes till it vanishes, and so on alternately at each quarter revolution, proving both rays to be polarized ; for in one position the tourmaline transmits the ordinary ray, and reflects the extraordinary, and after revolving 90°, the extraordinary ray is transmitted, and the ordinary ray is reflected. Thus another property of polarized light is, that it cannot be divided into two equal pencils by double refraction, in positions of the doubly refracting bodies, in which a ray of common light would be so divided.
Were tourmaline like other doubly refracting bodies, each of the transmitted rays would be double, but that mineral, when of a certain thickness, after separating the light into two polarized pencils, absorbs one of them, and consequently shows only one image of an object.
The pencils of light, on leaving a doubly refracting substance, are parallel; and it is clear, from the preceding experiments, that they are polarized in planes at right angles to each other. But that will be better understood by considering the change produced in common light by the action of the polarizing body. It has been shown that the undulations of ether, which produce the sensation of common light, are performed in every possible plane, at right angles to the direction in which the ray is moving; but the case is very different after the ray has passed through a doubly refracting substance, like Iceland spar. The light then proceeds in two parallel pencils, whose undula tions are still, indeed, transverse to the direction of the rays, but they are accomplished in planes at right angles to one another, analogous to two parallel stretched cords, one of which performs its undulations only in a horizontal plane, and the other in a vertical, or upright plane. Thus the polarizing action of Iceland spar, and of all doubly refracting substances, is, to separate a ray of common light whose waves, or undulations, are in every plane, into two parallel rays, whose waves or undulations lie in planes at right angles to each other. The ray of common light may be assimilated to a round rod, whereas the two polarized rays are like two parallel long flat rulers, one of which is laid horizontally on its broad surface, and the other horizontally on its edge. The alternate transmission and obstruction of one of these flattened beams by the tourmaline is similar to the facility with which a thin sheet of paper, or a card, may be passed between the bars of a grating, or wires of a cage, if presented edgeways, and the
impossibility of its passing in a direction transverse to the openings of the bars or wires.
Although it generally happens that a ray of light, in passing through Iceland spar, is separated into two polarized rays; yet there is one direction along which it is refracted in one ray only, and that according to the ordinary law. This direction is called the optic axis. Many crystals and other substances have two optic axes, inclined to each other, along which a ray of light is transmitted in one pencil by the law of ordinary refraction. The extraordinary ray is sometimes refracted towards the optic axis, as in quartz, zircon, ice, &c., which are, therefore, said to be positive crystals; but when it is bent from the optic axis, as in Iceland spar, tourmaline, eme-. rald, beryl, &c., the crystals are negative, which is the most numerous class. The ordinary ray moves with uniform velocity within a doubly refracting substance, but the velocity of the extraordinary ray varies with the position of the ray relatively to the optic axis, being a maximum when its motion within the crystal is at right angles to the optic axis, and a minimum when parallel to it. Between these extremes its velocity varies according to a determinate law.
It had been inferred from the action of Iceland spar on light, that, in all doubly refracting sub
stances, one only of the two rays is turned aside from the plane of ordinary refraction, while the other follows the ordinary law; and the great difficulty of observing the phenomena tended to confirm that opinion. M. Fresnel, however, proved, by a most profound mathematical inquiry, à priori, that the extraordinary ray must be wanting in glass and other uncrystallized substances, and that it must necessarily exist in carbonate of lime, quartz, and other bodies having one optic axis, but that, in the numerous class of substances which possess two optic axes, both rays must undergo extraordinary refraction, and consequently that both must deviate from their original plane; and these results have been perfectly confirmed by subsequent experiments. This theory of refraction, which, for generalization, is perhaps only inferior to the law of gravitation, has enrolled the name of Fresnel among those which pass not away, and make his early loss a subject of deep regret to all who take an interest in the higher paths of scientific research.
Panes of glass, if sufficiently numerous, will give a polarized beam by refraction. It appears that, when a beam of common light is partly reflected at, and partly transmitted through, a transparent surface, the reflected and refracted pencils contain equal quantities of polarized light, and