THE LAWS OF RADIATION
+Absorbing Power.+--A perfectly dull black surface is simply one which
absorbs all the light which is falling on it and reflects or diffuses
none of it back. If the surface absorbs the heat as well as the light
completely, it is called a perfect or full absorber. Other surfaces
merely absorb a fraction of the heat and light falling on them, and
this fraction, expressed usually as a percentage, is called the
absorbing power of the surface. The absorbing powers of different
kinds of surfaces can be measured in a great many ways, but the
following may be taken as fairly typical. A perfectly steady beam of
heat and light is made to fall on a small metallic disc, and the amount
of heat which is absorbed per second is calculated from the mass of the
metal and the rate at which its temperature rises. The disc is first
coated with lamp-black, and the rate at which it then receives heat is
taken as the rate at which a full absorber absorbs heat under these
conditions. The disc is then coated with the surface whose absorbing
power is to be measured, and the experiment is repeated. Then the rate
at which heat is received in the second case divided by the rate at
which it is received in the first is the absorbing power of the second
surface. {38} Experiments with a large number of surfaces show that
the lighter in colour and the more polished is the surface, the smaller
is its absorbing power.
+Radiating Power.+--But the character of the surface affects not only
the rate at which heat and light are absorbed, but also the rate at
which they are emitted. For example, if we heat a fragment of a willow
pattern china plate in a blowpipe flame until it is bright red hot, we
shall notice that the dark pattern now stands out brighter than the
rest. Thus the dark pattern, which absorbs more of the light which
falls on it when it is cold, emits more light than the rest of the
plate when it is hot. This is one example of a general rule, for it is
found that the most perfect absorbers are the greatest radiators, and
_vice-versa_. The perfectly black surface is therefore taken as a
standard in measuring the heat and light emitted by surfaces, in
exactly the same way as for heat and light absorbed. Thus the emissive
or radiating power of a surface is defined as the quantity of heat
radiated per second by the surface divided by the amount radiated per
second by a perfectly black surface under the same conditions. As it
is somewhat paradoxical to call a surface a perfectly black surface
when it may even be white hot, the term "a full radiator" has been
suggested as an alternative and will be used in this book.
[Illustration: FIG. 19]
+Relation between Absorbing and Radiating Powers.+--The exact relation
between the absorbing and radiating powers of a surface was first
determined by Ritchie by means of an ingenious experiment. Two equal
air-tight metal chambers A and B were connected by a glass tube bent
twice at right angles as {39} in Fig. 19. A drop of mercury in the
horizontal part of this tube acted as an indicator. When one of the
vessels became hotter than the other, the air in it expanded and the
mercury index moved towards the colder side. Between the two metal
chambers a third equal one was mounted which could be heated up by
pouring boiling water into it and could thus act as a radiator to the
other two. One surface of this radiator was coated with lamp-black and
the opposite one with the surface under investigation, _e.g._ cinnabar.
The inner surfaces of the other two vessels were coated in the same
way, the one with lamp-black, the other with cinnabar. The middle
vessel was first placed so that the lamp-blacked surface was opposite
to a cinnabar one, and _vice-versa_. In this position, when hot water
was poured into it no movement of the mercury drop was detected, and
therefore the amounts of heat received by the two outer vessels must
have been exactly equal. On the one side the heat given out by the
cinnabar surface of the middle vessel is only a fraction, equal to its
radiating power, of the heat given out by the black surface. All the
heat given out by the cinnabar surface to the black surface opposite to
it is absorbed, however, while of the heat given out by the black
surface to the cinnabar surface opposite it only a fraction is absorbed
equal to the absorbing power of the cinnabar surface. Thus on the one
side only a fraction is sent out but all of it is absorbed, and on the
other side all is sent out and only a fraction absorbed. Since {40}
the quantities absorbed are exactly equal, it is obvious that the two
fractions must be exactly equal, or the absorbing and radiating powers
of any surface are exactly equal. This result is known as Kirchoff's
law, and it applies solely to radiation which is caused by temperature.
Later experiments have shown that it applies to each individual
wave-length, _i.e._ to any portion of the spectrum which we isolate, as
well as to the whole radiation. Thus at any particular temperature let
the dotted line in Fig. 20 represent the wave-length--energy curve for
a full radiator, and let the solid line represent it for the surface
under investigation. Then for any wave-length, ON, the radiating power
of the surface would be equal to QN divided by PN.
[Illustration: FIG. 20.]
Now a wave-length--energy curve may be as easily constructed for
absorbed as for emitted radiation by means of a Langley's bolometer.
The strip of the bolometer is first coated with lamp-black and the
spectrum of the incident radiation is explored in exactly the same way
as is described in Chapter III. {41} The strip is then coated with the
surface under investigation and the spectrum is again explored. Since
the incident radiation is exactly the same in the two experiments, the
differences in the quantities of heat absorbed must be due solely to
the difference in the absorbing powers of the two surfaces. In Fig. 21
the dotted line represents the wave-length--energy curve for the
radiation absorbed by the blackened bolometer strip, and the solid line
the curve for the strip coated with the surface under investigation.
[Illustration: FIG. 21.]
The actual form of the curves may and probably will be quite different
from the form in Fig. 20, but it will be found for the same wave-length
ON that PN/QN is exactly the same in the two figures.
It has already been mentioned that dull, dark-coloured surfaces radiate
the most heat, and that polished surfaces radiate the least. A
radiator for heating a room should therefore have a dull, dark surface,
while a vessel which is designed to keep its contents from losing heat
should have a highly polished exterior.
A perfectly transparent substance would radiate no energy, whatever the
temperature to which it is {42} raised, for its absorbing power is zero
and therefore its radiating power is also zero. No perfectly
transparent substances exist, but some substances are a very near
approach to it. A fused bead of microcosmic salt heated in a small
loop of platinum wire in a blowpipe flame may be raised to such a
temperature that it is quite painful to look at the platinum wire, yet
the bead itself is scarcely visible at all. Any speck of metallic dust
on the surface of the bead will at the same time shine out like a
bright star.
+Gases as Radiators.+--Most gases are an even nearer approach to the
perfectly transparent substance, and consequently, with one or two
exceptions, the simple heating of gases causes no appreciable radiation
from them. Of course, gases do radiate heat and light under some
circumstances, but the radiation seems to be produced either by
chemical action, as in the flames coloured by metallic vapours, or by
electric discharge, as in vacuum tubes, the arc or the electric spark.
The agitation of the electrons is thus produced in a different way in
gases, and we must not apply Kirchoff's law to them, although at first
sight they appear to conform to it. We have seen that the particular
waves which an incandescent gas radiates are also absorbed by it. This
we should expect, because the particular electron which has such a
period of vibration that it sends out a certain wave-length will
naturally be in tune to exactly similar waves which fall on it, and
will so resound to them, and absorb their energy. The quantitative
law, however, that the absorbing power is exactly equal to the
radiating power, is not true for gases.
{43}
+Emission of Polarised Light.+--One very interesting result of
Kirchoff's law is the emission of polarized light by glowing tourmaline
and by one or two other crystal when they are heated to incandescence.
In ordinary light the vibrations are in all directions perpendicular to
the line along winch the light travels, that is, the vibrations at any
point are in a plane perpendicular to this line. Now any vibration in
a plane may be expressed as the sum of two component vibrations, one
component in one direction and the other in a perpendicular direction.
If we divide up the vibrations all along the wave in this way we shall
have two waves, one of which has its vibrations all in one direction
and the other in a perpendicular direction. Such waves, in which the
vibrations all lie in one plane, are said to be plane polarised.
Tourmaline is possessed of the curious property of absorbing vibrations
in one direction of the crystal much more rapidly than it does those
vibrations perpendicular to this direction, and therefore light which
passes through it emerges partially, or in some cases wholly, plane
polarised.
Since the absorbing power of tourmaline is different for the two
components, the emissive power should also be different, and that
component which was most absorbed should be radiated most strongly.
This was found to be true by Kirchoff himself, who detected and roughly
measured the polarised light emitted. Subsequently in 1902, Pflüger
carried out exact experiments which gave a beautiful confirmation of
the law.
{44}