The Atomic Theory of Refraction

THE ATOMIC THEORY OF REFRACTION We have so far treated refraction as an effect of matter in bulk without enquiry as to how it comes about. The gross effect must be a superposition of the effects of the separate atoms and mole cules, and we shall now consider how this superposition takes place. The light arising from an atom may have a great variety of characters, but whatever these are it must have one feature, that the wave is a spherical wave with the atom in its centre. We shall therefore first investigate what types of spherical wave are possible. In discussing diffraction we described a spherical wave emerging from a point source with amplitude inversely propor tional to the distance. Though that sufficed to give the outline of the theory, it took no account of polarization, and it must be further refined for our present purpose. We naturally build the complete theory by considering what types of electromagnetic waves can emerge from a point.

Types of Spherical Waves.

The transverse nature of light makes it impossible to have a wave going out uniformly in all directions. We give the mathematical form of the simplest possi ble wave. Let and A is a constant. Then the electric and magnetic forces are given by If these are worked out they lead to expressions which are rather complicated in general, but simpler for points at a great distance from the source, and it will suffice to discuss the latter case. Con sider a large globe, surrounding the source, marked with circles of latitude and longitude, the pole being the axis of x. The ob server is on this sphere at angular distance 0 from the pole. Then the wave that reaches him will have its electric force polarized so as to vibrate in the north and south direction, and the magnetic force will be east and west and equal in magnitude. The electric force is inversely proportional to the radius of the globe and to the square of the wave-length, but, most important of all, it varies as sine, vanishing at the pole and having its maximum at the equator. The actual value is In fig. 19 (a) the observer takes up various positions on the globe (marked by his co-latitude), and looks towards the centre; then the diagram shows the vibration of the electric force that will reach him.

In the classical electromagnetic theory this is the wave which would be emitted by an electron of charge e vibrating with fre quency c/ X and small amplitude a along the x-axis at the origin, provided that Area. If the observer were to watch this motion,

he would see it in perspective, and the electric force at the ob server is proportional to and in the same direction as the apparent motion of the electron. It is very convenient to have a name for this type of wave, including the complete distribution in all directions round the source, and in view of the motion of the emitting electron we shall call it a line-wave.

If the emitting electron de scribes a small circle instead of a line we have what we may call a circle-wave. This can be re garded as two superposed line waves with their poles at right angles and phases differing by a quarter wave-length. The pole of the circle is perpendicular to the poles of both lines. Fig. 19 (b) shows the electric force as seen by the observer for various positions on the globe. Its form again resembles the perspective view he would have of the elec tron. At either of the poles he receives circularly polarized light, and it is important to notice that they will be of opposite types, one right-handed and the other left-handed. For other directions the light is elliptically polarized and becomes plane polarized at the equator. The in tensity is twice as great at the poles as at the equator.

We must also consider a third type of wave which is not so simple. In the electromagnetic equations there is a mathematical symmetry between the electric and magnetic forces, so that we can obtain a solution by interchanging their roles. If we con struct a wave by adding to the ordinary line-wave a small "mag netic" line-wave with the same pole and same frequency, we ob tain a wave in which the light is everywhere of the same intensity as for a line-wave, but is elliptically polarized with axes in con stant ratio and lying in the directions of the circles of latitude and longitude. Such a wave is illustrated in fig. 19 (c). It is im portant to notice that in this case, unlike the circle-wave, the light-vector turns in the same direction in both hemispheres. Thus the whole wave has the same screw character and we shall call it a screw-wave. The screw-wave cannot be emitted by any motion of an electron. It would be emitted if there were a single magnetic pole moving with the electron, but such a thing does not exist and in fact the wave can only arise from a system itself having the screw character, such as a molecule with a chemically asymmetric atom in it.