give us a very beautiful representation of the simultaneous propagation of undulations of different wave-length in the same medium.
Fig. 13.—Waves of diffusion refracted at a plane surface on passing from a less concentrated into a more concentrated solution. The refracted wave-front is flattened, the wave-length being less in the denser medium.
Like waves of light and sound, these waves of diffusion are refracted when they pass from one medium into another of a different density, where they have a different velocity. When, for instance, a diffusion wave passes from a 5 per cent. solution of gelatine into a 10 per cent. solution, the wave-front is retarded, the retardation being proportional to the length of the path through the denser medium. Hence the wave-front is flattened, the curvature of the refracted wave being less than that of the original wave of diffusion. The contrary is the case when the wave-front passes into a medium where its velocity is greater. The middle of the wave-front now travels faster than the flanks, and the curvature is increased.
These diffusion rings furnish us with most excellent diagrams of refraction at a "diopter," i.e. a spherical surface separating two media of different densities. Fig. 14 shows the refraction at a convergent diopter, i.e. a surface where the denser medium is convex. The diffusion waves in this case emanate from the principal focus of the diopter, and therefore become plane on passing through the convex surface of the denser gelatine.
These periodic diffusion rings also illustrate the phenomena of colour diffraction. Diffusion waves of different
wavelength are unequally refracted by a gelatine lens. Hence rings of different wave-length which, originating at the same spot, are at first concentric, are no longer parallel after passing through a gelatine lens. A convergent lens which will change the long spherical incident waves into shorter plane waves, will transform the short incident waves into concave waves whose curvature is opposite to that of the original waves, i.e. it will transform a divergent into a convergent beam. This is an illustration of what is called the aberration of refrangibility.
In the same way we may demonstrate the course of diffusion waves through a gelatine prism, showing the refraction on their incidence and again on emergence. The prism is made of a stronger gelatine solution, which is more refractive than the gelatine around it. The waves of diffusion whilst traversing the prism are retarded, and this retardation is greatest at the base where the passage is longer. Hence the wave-front is tilted towards the base of the prism, and this tilting is repeated when the wave-front leaves the prism.
If we examine diffusion waves of different wave-length on their emergence from the gelatine prism, we shall see that they cut one another. With a dense prism, the wave-front of the shorter waves is more tilted towards the base than the wave-front of the longer waves. For diffusion as for light the shorter waves are the most refracted. Both refraction and dispersion are due to the unequal resistances of the medium to undulatory movements of different periodicity.