§ 3. Ordinary Refraction of Light explained by the Wave Theory.
We have now to exhibit the bearings of this act of crystallization upon optical phenomena. According to the undulatory theory, the velocity of light in water and glass is less than in air. Consider, then, a small portion of a wave issuing from a point of light so distant that the minute area may be regarded as practically plane. Moving vertically downwards, and impinging on a horizontal surface of glass or water, the wave would go through the medium without change of direction. As, however, the velocity in glass or water is less than the velocity in air, the wave would be retarded on passing into the denser medium.
Fig. 25.
But suppose the wave, before reaching the glass, to be oblique to the surface; that end of the wave which first reaches the medium will be the first retarded by it, the other portions as they enter the glass being retarded in succession. It is easy to see that this retardation of the one end of the wave must cause it to swing round and change its front, so that when the wave has fully entered the glass its course is oblique to its original direction. According to the undulatory theory, light is thus refracted.
With these considerations to guide us, let us follow the course of a beam of monochromatic light through our glass prism. The velocity in air is to its velocity in glass as 3: 2. Let A B C (fig. 25) be the section of our prism, and a b the section of a plane wave approaching it in the direction of the arrow. When it reaches c d, one end of the wave is on the point of entering the glass. Following it still further, it is obvious that while the portion of the wave still in the air passes over the distance c e, the wave in the glass will have passed over only two-thirds of this distance, or d f. The line e f now marks the front of the wave. Immersed wholly in the glass it pursues its way to g h, where the end g of the wave is on the point of escaping into the air. During the time required by the end h of the wave to pass over the distance h k to the surface of the prism, the other end g, moving more rapidly, will have reached the point i. The wave, therefore, has again changed its front, so that after its emergence from the prism it will pass on to l m, and subsequently in the direction of the arrow. The refraction of the beam is thus completely accounted for; and it is, moreover, based upon actual experiment, which proves that the ratio of the velocity of light in glass to its velocity in air is that here mentioned. It is plain that if the change of velocity on entering the glass were greater, the refraction also would be greater.
§ 4. Double Refraction of Light explained by the Wave Theory.
The two elements of rapidity of propagation, both of sound and light, in any substance whatever, are elasticity and density, the speed increasing with the former and diminishing with the latter. The enormous velocity of light in stellar space is attainable because the ether is at the same time of infinitesimal density and of enormous elasticity. Now the ether surrounds the atoms of all bodies, but it is not independent of them. In ponderable matter it acts as if its density were increased without a proportionate increase of elasticity; and this accounts for the diminished velocity of light in refracting bodies. We here reach a point of cardinal importance. In virtue of the crystalline architecture that we have been considering, the ether in many crystals possesses different densities, and different elasticities, in different directions; the consequence is, that in such crystals light is transmitted with different velocities. And as refraction depends wholly upon the change of velocity on entering the refracting medium, being greatest where the change of velocity is greatest, we have in many crystals two different refractions. By such crystals a beam of light is divided into two. This effect is called double refraction.
In ordinary water, for example, there is nothing in the grouping of the molecules to interfere with the perfect homogeneity of the ether; but, when water crystallizes to ice, the case is different. In a plate of ice the elasticity of the ether in a direction perpendicular to the surface of freezing is different from what it is parallel to the surface of freezing; ice is, therefore, a double refracting substance. Double refraction is displayed in a particularly impressive manner by Iceland spar, which is crystallized carbonate of lime. The difference of ethereal density in two directions in this crystal is very great, the separation of the beam into the two halves being, therefore, particularly striking.
I am unwilling to quit this subject before raising it to unmistakable clearness in your minds. The vibrations of light being transversal, the elasticity concerned in the propagation of any ray is the elasticity at right angles to the direction of propagation. In Iceland spar there is one direction round which the crystalline molecules are symmetrically built. This direction is called the axis of the crystal. In consequence of this symmetry the elasticity is the same in all directions perpendicular to the axis, and hence a ray transmitted along the axis suffers no double refraction. But the elasticity along the axis is greater than the elasticity at right angles to it. Consider, then, a system of waves crossing the crystal in a direction perpendicular to the axis. Two directions of vibration are open to such waves: the ether particles can vibrate parallel to the axis or perpendicular to it. They do both, and hence immediately divide themselves into two systems propagated with different velocities. Double refraction is the necessary consequence.