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.
[Illustration: FIG. 24.]
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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