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as fluids, gases, glass, &c., and a few regularly crystallized minerals, it is refracted into a single pencil of light by the laws of ordinary refraction, according to which the ray, passing through the refracting surface from the object to the eye, never quits a plane perpendicular to that surface. Almost all other bodies, such as the greater number of crystallized minerals, animal and vegetable substances, gums, resins, jellies, and all solid bodies 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 a 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. Whenever a ray of natural light is thus divided into two pencils in its passage through a substance, both of the transmitted rays are polarized. Iceland spar, a carbonate of lime, which by its natural cleavage may be split into the form of a rhombohedron, possesses the property of double refraction in an eminent degree, as may be seen by pasting 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 (N. 205). 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 is therefore called the ordinary ray. But the other does quit the 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 that which undergoes ordinary refraction, and consequently shows only one image of an object. On this account tourmaline is peculiarly fitted for analyzing polarized light, which shows nothing remarkable till viewed through it or something equivalent.
The pencils of light, on leaving a double refracting substance, are parallel; and it is clear, from the preceding experiments, that they are polarized in planes at right angles to each other (N. 206). 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. light then proceeds in two parallel pencils, whose undulations 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 (N. 206). 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. By a simple mechanical law each vibratory motion of the first is resolved into two vibratory motions at right angles to one another. 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 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 transverse direction.
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 (N. 207). 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, emerald, 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 substances one only of 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 a 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 makes his early loss a subject of deep regret to all who take an interest in the higher paths of scientific research.
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 their planes of polarization are at right angles to one another hence, a pile of panes of glass will give a polarized beam by refraction. For, if a ray of common light pass through them, part of it will be polarized by the first plate, the second plate will polarize a part of what passes through it, and the rest will do the same in succession, till the whole beam is polarized, except what is lost by reflection at the different surfaces, or by absorption. This beam is polarized in a plane at right angles to the plane of reflection, that is, at right angles to the plane passing through the incident and reflected ray (N. 208).
By far the most convenient way of polarizing light is by reflection. A plane of plate-glass laid upon a piece of black cloth, on a table at an open window, will appear of a uniform brightness from the reflection of the sky or clouds. But if it be viewed through a plate of tourmaline, having its axis vertical, instead of being illuminated as before, it will be obscured by a large cloudy spot, having its centre quite dark, which will readily be found by elevating or depressing the eye, and will only be visible when the angle of incidence is 57°, that is, when the line from the eye to the centre of the black spot makes an angle of 33° with the surface of the reflector (N. 209). When the tourmaline is turned round in its own plane, the dark cloud will diminish, and entirely vanish when the axis of the tourmaline is horizontal, and then every part of the surface of the glass will be equally illuminated. As the tourmaline revolves, the cloudy spot will appear and vanish alternately at every quarter revolution. Thus, when a ray of light is incident on a pane of plate-glass at an angle of 57°, the reflected ray is rendered incapable of penetrating a plate of tourmaline whose axis is in the plane of incidence. Consequently it has acquired the same character as if it had been polarized by transmission through a plate of tourmaline, with its axis at right angles to the plane 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 plateglass, 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. 210). It appears that the angle for plateglass is 570; in crown-glass 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.
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 polarized. This is the best apparatus; but one plate of glass having its inferior surface blackened, or even a polished table, will answer the purpose.