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/:„ p< • c >• c
/.> By rotating the analyzer the reverse happens: C Oo and CEo oppose or destroy each other, while C Oe and 6' Ee conspire, or strengthen each other, as in fig. 16.
Thus, then, the original polarized ray( 0, fig.14) has been resolved into four rays, two polarized in one plane, and the other two polarized in a plane rectangular to this. The two rays which interfere and destroy each other, differ by half an undulation. The colour produced by the interference of the conspiring rays, corresponds to the difference of the routes of the two polarized rays in the plate or film, while that which results from the interference of the opposing rays, is that which is due to the same difference augmented or diminished by half an undulation. In the case above noticed, in which COe and CEe (fig. 15) are opposed, the colour corresponds to the difference plus half an undulation. But it may be asked, What is the use of the polarizing plate? What is the reason that no colour is perceived if the light which is incident on the double refracting film be common or unpolarized? To explain this, let us suppose that a ray of common or unpolarized light consists of two rays rectangularly polarized. Each of these rays will suffer the same series of divisions, subdivisions, and interferences as the former; but the tints produced by the one ray will be complementary to those of the other; so that we shall thus obtain two pairs of complementary tints, and as the tints of each pair will emerge superposed, they will neutralize each other, and the resulting light will be of uniform whiteness.
Thus 1st PAIR OP 2(1 PAIR OP
Suppose the two complementary tints produced
by one ray to be Green and Red.
Those produced by the second ray will be Red "Green.
And the sum of each pair will be White. White.
For red and green are complementary tints, and produce by their union white light, as I have already demonstrated.
The office of the doubly refracting film, called the depolarizer, is to doubly refract the polarized light. It prepares the rays for the changes which they have ultimately to undergo and by which colour is to be produced. The thickness of the film or crystalline plate determines the tint; but the actual thickness required to produce a given tint depends on the nature of the crystal. By this plate or film two rectangularly polarized systems of waves are produced, which traverse the plate in different directions and with different velocities, and emerge in different phases of vibration. Now as they are superposed, and as the retardation amounts only to a few undulations and parts of an undulation, it might be supposed that colour would be produced by their interference. But I have already stated that two rectangularly polarized rays do not interfere, so as to produce colour. In order, therefore, to make them interfere, their planes of polarization must be made to coincide; and to do this is the function of the analyzer.
In order to assist us in comprehending how a polarized ray may be resolved into two others polarized in different planes, we may take, as an illustration, a stretched cord, fig. 17 A B, dividing at B into B C and B D, making a small angle with each other at B, and having either equal or unequal tension. Let us suppose the extremity A of the single cord to be made to vibrate regularly in either a horizontal or vertical plane; now, by means of two polished guiding-planes, E F and G H, inclined at different angles to the horizon, and making a right angle with each other, the horizontal vibrations of the cord A B, will give rise to two other vibrations, parallel respectively to E F
and OH. And if we assume the two branches B C and B D to be unequally tense, the waves produced by the vibration of A B will be propagated along them with unequal velocity. So that this illustration, which I have adopted from Sir John Herschel's able treatise on light, serves to explain not only how a vibration in one plane may be resolved into vibrations in two other planes, but also why the two resulting waves are propagated with unequal velocity.
Though a thin plate of Iceland-spar or of any other doubly refracting crystal serves, when placed in the polariscope, for the production of colour; yet certain crystals are preferable to others on account of the facility with which they may be split into thin laininee. Selenite and mica are especially convenient for this purpose; and the former of these is extensively employed by opticians in the preparation of a variety of beautiful and ingenious polariscope illustrations. On this account a brief notice of it is requisite.
Selenite, or sparry-gypsum, is the native crystallized hydrated sulphate of lime (CaO. S O3 + 2 Aq.) It occurs imbedded in London clay. It is found also at Shotover Hill, near Oxford, where the labourers call it quarry glass, and likewise at the Isle of Sheppy. Very large crystals of it are found at Montmartre, near Paris. The crystalline forms in which it occurs belong to the oblique rectangular prismatic system. Haiiy and the late Mr. William Phillips describe its primary form as a right obliqueangled prism; so that the lateral faces of the crystal are regarded by them as the terminal planes. But the optical characters of the crystal prove the incorrectness of the description of these celebrated mineralogists: and here, I would observe, is an excellent illustration of the great value of polarized light to the crystallographer. In this particular instance it enables him to distinguish a lateral face, from a terminal plane, of a prism.
The crystals of selenite which are most frequently met with, are oblique rectangular prisms, with ten rhomboidal faces, of which two are considerably larger than the others (fig. 18 A). They are very easily slit into thin laminae (a b, fig. 18 B), parallel to these larger lateral faces (terminal planes of Haiiy and W. Phillips).
Macles or hemitrope crystals of selenite are very common. By hemitrope, a word derived from the Greek (from q/u half, and rpeiro I turn), is meant a figure produced by cutting the primary crystal in two, causing one of the fragments to make half a revolution, and then uniting the sides actually in contact. The most singular and common hemitrope variety of selenite is that called arrow headed selenite (fig. 18 C), and which is so called because the crystal is formed like the barbed head of an arrow. Its nature may be easily explained. Cut a card or thin board in a rhomboidal form to represent one of the laminae taken from lateral faces of the prism (fig;. 18 D). Then divide it in the direction of its greater diagonal (a b), and transpose the separated parts in such a manner, that two of the alternate angles, produced by the diagonal division, shall make the point —the other two, the barbs—of the arrow-head.
The optical structure of films or thin plates of selenite, having a thickness of from -J^th to the ^th of an inch, is very curious. In two rectangular directions they allow perpendical rays of polarized light to traverse them unchanged: these directions are called the neutral axes. In two other directions, however, which form respectively angles of 45° with the neutral axes, these films have the property of double refraction. These directions are usually denominated depolarizing axes; but they might be more correctly termed doubly refracting axes.
In order to render these properties more intelligible, suppose the structure of the film to be that represented by fig. 19, in which the film is seen to be crossed by two series of light lines, or passages, the one perpendicular to the other. These are to represent the neutral axes. We may imagine, that in these directions only can the ethereal molecules vibrate. A ray of incident polarized light whose vibrations coincide with either of these lines, is transmitted through the film unchanged. But a ray of incident polarized light whose vibrations form an angle of 45° with these lines, or, in other words, which coincide with the diagonals of the square spaces, suffers double refraction; that is, it is resolved into two vibrations, one parallel with a b, the other parallel with c d, and, therefore, the directions of the diagonals of the squares are called the doubly refracting or depolarizing axes. But the two resulting vibrations are not propagated, in these two rectangular directions, with equal velocity, the one suffering greater retardation than the other, so that the waves, at their emergence, are in different phases of vibration, though they do not interfere
so as to produce colour, because their planes of vibration are rectangular. By the analyzer, however, iheir planes are made to coincide, and colour is produced; and on rotating the analyzer on its axis, the colour changes and becomes complementary.
To illustrate these statements, place a film of selenite, of uniform thickness, in the polariscope. On rotating the film (the analyzer and polarizer remaining still), a brilliant colour is perceived at every quadrant of a circle, but in intermediate positions it vanishes altogether. We observe, however, that the tint does not change, but only varies in intensity. If, now, the film be fixed and the analyzer rotated, we also observe colour at every quadrant of a revolution ; but the tint changes and becomes complementary at every quadrant—the same tint reappearing at every half revolution: so that when the film alone is revolved one colour only is seen, but when the analyzer alone is revolved, two colours are seen. Effect of revolving the film of Selenite. Effect of revolving the Analyzer.