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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 570, 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 57°; 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.
Phenomena exhibited by the Passage of Polarized Light through Mica and
Sulphate of Lime - The Coloured 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 Coloured Images produced by the Interference of
Polarized Rays — Fluorescence. Such is the nature of polarized light and of the laws it follows. But it is hardly possible to convey an idea of the splendour 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 centre 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 colours will appear, varying with every inclination of the mica, from the richest reds, to the most vivid greens, blues, and purples (N. 211). 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 colours 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 colours 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 coloured 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 colour 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 colourless; then it will assume a green hue, which will increase and arrive at its maxi. mum 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 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 colours every quarter revolution of the spar, the red becoming green, and the green red; and, where the images overlap, the colour 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 colours. 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 colours 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 eye 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 appearance is presented. The cloudy spot in the direction of the optic axis is seen surrounded by a set of vividly coloured 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. 212).
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;