Fig. 37.
In one of these two rectangular directions the ether within the gypsum is more sluggish than in the other; and, as a consequence, the waves that follow this direction are more retarded than the others. In both cases the undulations are shortened when they enter the gypsum, but in the one case they are more shortened than in the other. You can readily imagine that in this way the one system of waves may get half a wave-length, or indeed any number of half wavelengths, in advance of the other. The possibility of interference here at once flashes upon the mind. A little consideration, however, will render it evident that, as long as the vibrations are executed at right angles to each other, they cannot quench each other, no matter what the retardation may be. This brings us at once to the part played by the analyzer. Its sole function is to recompound the two vibrations emergent from the gypsum. It reduces them to a single plane, where, if one of them be retarded by the proper amount, extinction will occur.
But here, as in the case of thin films, the different lengths of the waves of light come into play. Red will require a greater thickness to produce the retardation necessary for extinction than blue; consequently when the longer waves have been withdrawn by interference, the shorter ones remain, the film of gypsum shining with the colours which the short waves confer. Conversely, when the shorter waves have been withdrawn, the thickness is such that the longer waves remain. An elementary consideration suffices to show, that when the directions of vibration of the prisms and the gypsum enclose an angle of forty-five degrees, the colours are at their maximum brilliancy. When the film is turned from this direction, the colours gradually fade, until, at the point where the directions of vibration in plate and prisms are parallel, they disappear altogether.
(The best way of obtaining a knowledge of these phenomena is to construct a model of thin wood or pasteboard, representing the plate of gypsum, its planes of vibration, and also those of the polarizer and analyzer. Two parallel pieces of the board are to be separated by an interval which shall represent the thickness of the film of gypsum. Between them two other pieces, intersecting each other at a right angle, are to represent the planes of vibration within the film; while attached to the two parallel surfaces outside are two other pieces of board, which represent the planes of vibration of the polarizer and analyzer. On the two intersecting planes the waves are to be drawn, showing the resolution of the first polarized beam into two others, and then the subsequent reduction of the two systems of vibrations to a common plane by the analyzer. Following out rigidly the interaction of the two systems of waves, we are taught by such a model that all the phenomena of colour obtained by the combination of the waves, when the planes of vibration of the two Nicols are parallel, are displaced by the complementary phenomena, when the planes of vibration are perpendicular to each other.)
In considering the next point, we will operate, for the sake of simplicity, with monochromatic light—with red light, for example, which is easily obtained pure by red glass. Supposing a certain thickness of the gypsum produces a retardation of half a wave-length, twice this thickness will produce a retardation of two half wave-lengths, three times this thickness a retardation of three half wave-lengths, and so on. Now, when the Nicols are parallel, the retardation of half a wave-length, or of any odd number of half wave-lengths, produces extinction; at all thicknesses, on the other hand, which correspond to a retardation of an even number of half wave-lengths, the two beams support each other, when they are brought to a common plane by the analyzer. Supposing, then, that we take a plate of a wedge form, which grows gradually thicker from edge to back, we ought to expect, in red light, a series of recurrent bands of light and darkness; the dark bands occurring at thicknesses which produce retardations of one, three, five, etc., half wave-lengths, while the bright bands occur between the dark ones. Experiment proves the wedge-shaped film to show these bands. They are also beautifully shown by a circular film, so worked as to be thinnest at the centre, and gradually increasing in thickness from the centre outwards. A splendid series of rings of light and darkness is thus produced.
When, instead of employing red light, we employ blue, the rings are also seen: but as they occur at thinner portions of the film, they are smaller than the rings obtained with the red light. The consequence of employing white light may be now inferred; inasmuch as the red and the blue fall in different places, we have iris-coloured rings produced by the white light.
Some of the chromatic effects of irregular crystallization are beautiful in the extreme. Could I introduce between our two Nicols a pane of glass covered by those frost-ferns which your cold weather renders now so frequent, rich colours would be the result. The beautiful effects of the irregular crystallization of tartaric acid and other substances on glass plates now presented to you, illustrate what you might expect from the frosted window-pane. And not only do crystalline bodies act thus upon light, but almost all bodies that possess a definite structure do the same. As a general rule, organic bodies act thus upon light; for their architecture implies an arrangement of the molecules, and of the ether associated with the molecules, which involves double refraction. A film of horn, or the section of a shell, for example, yields very beautiful colours in polarized light. In a tree, the ether certainly possesses different degrees of elasticity along and across the fibre; and, were wood transparent, this peculiarity of molecular structure would infallibly reveal itself by chromatic phenomena like those that you have seen.
§ 4. Colours produced by Strain and Pressure.
Not only do natural bodies behave in this way, but it is possible, as shown by Brewster, to confer, by artificial strain or pressure, a temporary double refracting structure upon non-crystalline bodies such as common glass. This is a point worthy of illustration. When I place a bar of wood across my knee and seek to break it, what is the mechanical condition of the bar? It bends, and its convex surface is strained longitudinally; its concave surface, that next my knee, is longitudinally pressed. Both in the strained portion and in the pressed portion of the wood the ether is thrown into a condition which would render the wood, were it transparent, double-refracting. For, in cases like the present, the drawing of the molecules asunder longitudinally is always accompanied by their approach to each other laterally; while the longitudinal squeezing is accompanied by lateral retreat. Each half of the bar of wood exhibits this antithesis, and is therefore double-refracting.