CHAPTER VII

PRESSURE OF RADIATION

+Prediction of Pressure by Maxwell.+--Had the fact that light exerts a pressure been known in Newton's time there is no doubt that it would have been hailed as conclusive proof of the superiority of the corpuscular theory over the wave theory. Yet, ironically enough, it was reserved for James Clerk Maxwell to predict its existence and calculate its value on the assumption of his electromagnetic wave theory; and further, the measurement of its value has given decisive evidence in favour of the wave theory, for the value predicted by the latter is only one-half that predicted by the corpuscular theory, and the measurements by Nicholls and Hull agree to within 1 per cent. with the wave theory value.

Maxwell showed that all waves which come up to and are absorbed by a surface exert a pressure on every square centimetre of the surface equal to the amount of energy contained in one cubic centimetre of the beam.

If the surface is a perfect reflector, the reflected waves produce an equal back pressure, and therefore the pressure is doubled. As the waves are reflected back along their original direction, the energy in the beam will also be doubled, and so {65} the pressure will still be equal to the energy per cubic centimetre of the beam.

As the energy which is received in one second from the sun on any area can be measured by measuring the heat absorbed, and since the speed of light is known, we can calculate the energy contained in one cubic centimetre of full sunlight, and hence the pressure on one square centimetre of surface. For the energy received on one square centimetre of surface in one second must have been spread originally over a length of beam equal to the distance which the light has travelled in one second, _i.e._ over a length equal to the speed of light. If we divide that energy, therefore, by the speed of light, we shall get the energy in a one-centimetre length of the beam, and therefore in one cubic centimetre.

This turns out to be an extremely small pressure indeed, being only a little more than the weight of half a milligram, on a square metre of surface.

Maxwell suggested that a much greater energy of radiation might be obtained by means of the concentrated rays of an electric lamp. Such rays falling on a thin, metallic disc delicately suspended in a vacuum might perhaps produce an observable mechanical effect.

Nearly thirty years after Maxwell's suggestion it was successfully carried out by Prof. Lebedew of Moscow, who used precisely the arrangement which Maxwell had suggested.

+Measurement of the Pressure.+--A beam of light from an arc lamp was concentrated on to a disc suspended very delicately in an exhausted glass {66} globe about 8 inches across. Actually four discs were suspended, as in Fig. 24, and arrangements were made to concentrate the beam on to either side of any of the four discs.

The suspension was a very fine quartz fibre _q_. The discs _d_, _d_, _d_, _d_, were half a centimetre in diameter and were fixed on two light arms, so that their centres were one centimetre from the glass rod, _g_, which carried them. A mirror, _m_, served to measure the angle through which the whole system was twisted owing to the pressure of the beam on one of the discs. In order to measure the angle a telescope viewed the reflection of a scale in _m_, and as _m_ turned different divisions of the scale came into view.

The two discs on the left were polished and therefore the pressure on them should be about twice that on the blackened discs on the right.

Having measured the angle through which a beam of light has turned the system, it is a simple matter to measure the force which would cause this twist in the fibre q. In order to test whether the pressure agrees with the calculated value, we must find the energy in the beam of light. This was done by receiving the beam on a blackened block of copper and measuring the rate at which its temperature rose. From this rate and the weight of copper it is easy to calculate the amount of heat received per second, and therefore the amount of energy received per second on one square {67} centimetre of the area. Knowing the speed of the light we can, as suggested above, calculate the energy in one cubic centimetre of the beam.

Lebedew's result was in very fair accord with the calculated value. The chief difficulty in the experiment is to eliminate the effects due to the small amount of gas which remains in the globe. Each disc is heated by the beam of light, and the gas in contact with it becomes heated and causes convection currents in the gas. At very low pressures a slightly different action of the gas becomes a disturbing factor. This effect is due to the molecules which come up to the disc becoming heated and rebounding from the disc with a greater velocity than that with which they approached it. The rebound of each molecule causes a backward kick on to the disc, and the continual stream of molecules causes a steady pressure.

This would be the same on both sides of the disc if both sides were at the same temperature, but since the beam of light comes up to one side, that side becomes hotter than the other and there will be an excess of pressure on that side. This action is called "radiometer" action, because it was first made use of by Crookes in detecting radiation.

Between the Scylla of convection currents at higher pressures and the Charybdis of radiometer action at lower pressures, there seems to be a channel at a pressure of about two or three centimetres of mercury. For here the convection currents are small and the radiometer action has scarcely begun to be appreciable.

By working at this pressure and using one or two {68} other devices for eliminating and allowing for the gas action, Professors Nicholls and Hull also measured the pressure of light in an exceedingly careful and masterly way. Their results were extremely consistent among themselves, and agreed with the calculated value to within one per cent. Those who know the difficulty of measuring such minute forces, and the greatness of the disturbing factors, must recognise in this result one of the finest experimental achievements of our time.

+Effect of Light Pressure in Astronomy.+--Forces due to light pressure are so small that we should not expect to be able to detect their effects on astronomical bodies, and certainly we cannot hope to observe them in the large bodies of our system.

The pressure of the sunlight on the whole surface of the earth is about 75,000 tons weight. This does not sound small until we compare it with the pull of the sun for the earth, which is two hundred million million times as great.

When we consider very small bodies, however, we find that the pressure of the light may even exceed the gravitational pull, and therefore these small particles will be driven right away from our system.

In order to show that the light pressure becomes more and more important, let us imagine two spheres of the same material, one of which has four times the radius of the other.

Then the weight of the larger one, that is its gravitational pull, will be sixty-four times as great as that of the smaller one, while the area, and therefore the light pressure, will be sixteen times as great.

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The light pressure is therefore four times as important in the sphere of one-quarter the radius. For a sphere whose radius is one two hundred million millionth of the radius of the earth and of the same density, the pressure of the light would equal the pull of the sun, and therefore such a sphere would not be attracted to the sun at all.

This is an extremely small particle, much smaller than the finest visible dust, but even for much larger things the light pressure has an appreciable effect.

Thus for a sphere of one centimetre radius and of the same density as the earth, the pressure due to the sunlight is one seventy-four thousandth of the pull due to gravitation. It therefore need not move in its orbit with quite such a high speed in order that it may not fall into the sun, and its year is therefore lengthened by about three minutes. The lengthening out of comets' tails as they approach the sun, and the apparent repulsion of the tail by the sun, has sometimes been attributed to pressure of sunlight, but it is pretty certain that the forces called into play are very much greater than can be accounted for by the light.

+Doppler Effect.+--The Doppler effect also has some influence on the motion of astronomical bodies. When a body which is receiving waves moves towards the source of the waves, it receives the waves more rapidly than if it were still, and therefore the pressure is greater. When the body is moving away from the source it receives the waves less rapidly, and hence the pressure of light on it is less than for a stationary body. If a body is moving in an elliptical orbit, it is moving towards the sun in one part of its orbit and {70} away in another part; it will therefore be retarded in both parts, and the ultimate result will be that the orbit will be circular.

The Doppler effect can act in another way. A body which is receiving waves from the sun on one side is thereby heated and emits waves in all directions. As it is moving in its orbit it will crowd up the waves which it sends out in front of it and lengthen out those which it sends out behind it. But the energy per cubic centimetre will be greater where the waves are crowded up than where they are drawn out, and therefore the body will experience a retarding force in its orbit. As the body tends to move more slowly it falls in a little towards the sun, and so approaches the sun in a spiral path.

+Three Effects of Light Pressure.+--We thus have three effects of light pressure on bodies describing an orbit round the sun. The first effect is to lengthen their period of revolution, the second is to make their orbits more circular, and the third is to make them gradually approach the sun in a spiral path. These effects are quite inappreciable for bodies anything like the size of the earth, but for small bodies of the order of one centimetre diameter or less the effects would be quite large. Our system is full of such bodies, as is evidenced by the number of them which penetrate our atmosphere and form shooting stars. The existence of such bodies is somewhat of a problem, as whatever estimate of the sun's age we accept as correct, he is certainly of such an age that if these bodies had existed at his beginning they would all have been drawn in to him long ago. We must therefore {71} suppose that they are continually renewed in some way, and since we can see no sufficient source inside the Solar system, we must come to the conclusion that they are renewed from outside. There is every reason to believe that some of them originate in comets which have become disintegrated and spread out along their orbits. These form the meteoric showers.

Thus the very finest dust is driven by the sun right out of our system, and all the rest he is gradually drawing in to himself.

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