In the course of his theoretical in vestigations Maxwell discovered the pressure of light. He derived this from the electromagnetic theory, but as a matter of fact it can be shown to follow from any wave-theory, and was foreseen in the 18th century by Euler. If plane waves fall perpendicularly on a surface it may be shown that they exert a pressure on it of a magnitude equal to the density of energy in the waves. This result is exceedingly difficult to observe, as the pressure is very small in practical cases. The first attempt led to the invention of the radiometer by Crookes. In this instrument freely moving vanes are coated with black on one side and are polished oh the other. The side which is black absorbs the radiation while the reflecting side sends it back; so there is more energy in the space in front of the reflecting side and therefore a greater pressure. When the radiometer is illuminated it does go round, but the wrong way ! This is due to a rather complicated effect depending on the heating of the residual gas in the vessel, and in order to observe the pressure of radiation much more delicate means are required. It was even tually measured by Lebedev by so improving the radiometer that the effect of the gas was eliminated. There are also indirect methods by which the pressure of light can be verified, chief among which is the thermodynamic law for the emission of radia tion (see HEAT). Light pressure plays scarcely any part in our common experience, but grows to enormous values in the hot interiors of stars and plays a dominating part in controlling their state, The Doppler Effect.—When monochromatic light passes through any fixed optical system there is one property that is al ways conserved, the frequency of the vibrations; but this fre quency can be changed if the light is reflected by a moving mir ror, or if there is a difference in the motions of source and ob server. This change of frequency is called the Doppler effect, after its discoverer, and is easily explained by the wave theory. Con sider a fixed source emitting light of frequency v, and sending it to an observer who is receding at velocity v. On account of his motion the successive crests of the light-waves will reach him at longer intervals than if he were at rest and a simple calculation shows that he will receive them with a frequency v (r—v/c) ; the light will appear to him redder than it really is. If he is approach ing, it will appear bluer, and if his motion is oblique to the direc tion of the source, the change of frequency will depend on the component of his velocity in the line of sight. In the case where light is reflected from a receding mirror it has to traverse the in creasing distance twice over, and so the effect is doubled, and the frequency of the reflected light is v (I-2v/c). It should be said that these values are not quite precise when v is large. The Dop pler effect plays a very important practical part in astronomy, for by its means it is possible to discover the velocity of stars in the line of sight, and thus for example to calculate the motion of the components of a double star which are so close together that they cannot be seen separate. It is also vital in the theoretical investi gation of the distribution of energy in the spectrum. A further consequence arises in practical spectroscopy. In a hot gas some of the atoms will be approaching the spectroscope and so will give light bluer than the average, while others will give a redder light in consequence of their recession, and thus the light will never be purely monochromatic. In some experiments it is necessary to minimise this effect by cooling the gas with liquid air.
Plates.—There is no essential difference
between the phenomena of diffraction and interference, but only a difference in emphasis. Thus the term diffraction is used for phenomena connected with the spreading of waves on passing through a slit, shadow formation, etc., while interference arises, as in Young's experiment, when two waves from separate but coherent sources are superposed. We shall now discuss some im portant cases of interference, including the explanation of Newton's rings.
We have already described Huygens' construction for reflection and refraction. When a beam of light falls on a surface part is directly reflected and part is refracted. Consider now a thin plate, say a soap-film, under the action of an incident beam of mono chromatic light (fig. 5). The beam refracted at the first surface comes to the second, and part emerges, while the rest is reflected back. This second part comes back to the first face and part of it emerges, while part is again reflected. Thus, if we want to know the total amount reflected, we have to consider the compounded effects of all the waves arising from direct reflection and any num ber of internal reflections. Now, in order to explain the process, fig. 5 has been drawn as though the rays AP, CQ, ER . . . were separate from one another, but they will not in fact be so, for the film is supposed thin, whereas the incident beam is fairly broad.
The reflected beams will there fore overlie one another and this is a case like Young's experiment in which we have to consider the phases of the various waves. If these phases agree we shall have a brilliant reflection, otherwise it will be feeble. We shall see that the phases only agree for one colour at a time, and so the film looks coloured though it is illum inated by white light. In order to see the detail of this we must examine the process of refraction somewhat more closely.
We first consider a single interface illuminated obliquely by a plane wave of light K (see fig. 6). This will be broken into a reflected wave L and a refracted wave M. The strengths of these can be calculated exactly in the detailed theory (they give Fres nel's sine and tangent formulae), but we do not require their values here. Let us say that, if K has unit amplitude, then L has amplitude r and M has amplitude t. We shall assume (from the more detailed theory) that there is no change of phase at the interface. We also require to consider the effect of a beam coming to the surface from the other side. Let us suppose that the reversed wave M would give a transmitted wave along K of amplitude t' and a reflected wave along N of amplitude r'. Now there is an important and very general mechanical principle, that, if all the parts of a system are simultaneously reversed in their motions, the system will retrace its course to the point from which it started. Thus, if we take a wave r along L reversed and simul taneously t along M reversed, they will give rise to unit ampli tude along K reversed and no wave along N. The wave r from L gives
along K and rt along N, while t from M gives tt' along K and tr' along N. We thus have the two equations
1, rt+tri=o. The last implies that r' must be equal to r, but that there is a change of phase of
at the interface; we can allow for it completely by simply writing —r for r'.
AP has amplitude r, the ray AB has t. Of this a fraction r' is reflected at B, so that tr' ar rives at C and CQ has amplitude tr't' , while CD has
Similarly ER will have
and so on. On the other side the waves emerging at B, D, F will have amplitudes tt',
, tr'ot', etc. We must now compare the various phases of the paths OAP,