Absolute Temperature. Observed Energy. Energy calculated fromPlanck's Formula.85 -20.6 -21.9193 -11.8 -12293 0 0523 +31 +30.4773 64.6 63.81023 98.1 97.21273 132 1321523 164 1601773 196 200
We have therefore the means of calculating both the total quantity and the kind of radiation given out by any full radiator at any temperature, and a number of very interesting problems may be solved by means of the results.
Efficiency in Lighting.—One very simple problem is concerned with efficiency in lighting. We see by reference to Fig. 16, that in the radiation from the electric arc very little of the energy is in the visible part of the spectrum even though the temperature in the arc is the highest yet obtained on the earth, whereas the energy in the visible part of the spectrum from a gas flame is almost wholly negligible. The problem of efficient lighting is to get as big a proportion as possible of the energy into the visible part of the spectrum, and therefore the higher the temperature the greater the efficiency. This is the reason of the greater efficiency of the incandescent gas mantle over the ordinary gas burner, for the introduction of the air into the gas allows the combustion to be much more complete, and therefore the temperature of the mantle becomes very much higher than that of the carbon particles in the ordinary flame. The modern metallic filament electric lamps have filaments made of metals whose melting point is extremely high, and they may therefore be raised to a much higher temperature than the older carbon filaments. The arc is even more efficient than the metallic filament lamps, because its temperature is higher still; and we must assume that the temperature of the sun is very much higher even than the arc, since its maximum of energy lies in the visible spectrum.
Temperature of the Sun.—The actual temperature of the sun may be calculated approximately by means of Stefan's fourth power law. We will first assume that the earth and the sun are both full radiators, andthat the earth is a good conductor, so that its temperature is the same all over. The first assumption is very nearly true, and we will make a correction for the small error it introduces; and the second, although far from true, makes very little difference to the final result, for it is found that the values obtained on the opposite assumption that the earth is an absolute non-conductor differ by less than 2 per cent. from those calculated on the first assumption. We will further assume that the heat radiated out by the earth is exactly equal to the heat which it receives from the sun. This is scarcely an assumption, but rather an experimental fact, for experiment shows that heat is conducted from the interior of the earth to the exterior, and so is radiated, but at such a small rate that it is perfectly negligible compared with the rate at which the earth is receiving heat from the sun.
The sun occupies just about one 94,000th part of the hemisphere of the heavens or one 188,000th part of the whole sphere. If the whole sphere surrounding the earth were of sun brightness, the earth would be in an enclosure at the temperature of the sun, and would therefore be at that temperature itself. The sphere would be sending heat at 188,000 times the rate at which the sun is sending it, and the earth would be radiating it at 188,000 times its present rate. But the rate at which it radiates is proportional to the fourth power of its absolute temperature, and therefore its temperature would be the fourth root of 188,000 times its present temperature,i.e.20.8 times. If the radiating or absorbing power of the earth's surface be taken as 9/10, which is somewhere near the mark,the calculation gives the number 21.5 instead of 20.8. The average temperature of the earth's surface is probably about 17° C. or 290° absolute, and therefore the temperature of the sun is 290 x 21.5,i.e.about 6200° absolute.
It is easy to see that if we had known the temperature of the sun and not of the earth, we could have calculated that of the earth by reversing the process.
By this means we can estimate the temperatures of the other planets, at any rate of those for which we may make the same assumptions as for the earth. Probably those planets which are very much larger than the earth are still radiating a considerable amount of heat of their own, and therefore to them the calculation will not apply; but the smaller planets Mercury, Venus and Mars have probably already radiated nearly all their own heat and are now radiating only such heat as they receive from the sun. The temperatures calculated in this way are—
AverageAbsolute TemperatureMercury . . . . . . . . . 467°Venus . . . . . . . . . . 342°Earth . . . . . . . . . . 290°Mars . . . . . . . . . . 235°
Since the freezing point of water is 273° absolute, we see that the average temperature of Mars is 38° C. below freezing, and it is almost certain that no part of Mars ever gets above freezing point.
In a very similar way we may find the temperature to which a non-conducting surface reaches when it is exposed to full sunlight by equating the heat absorbed to the heat radiated, and the result comesto 412° absolute,i.e.139° C., or considerably above boiling point. This would be the upper limit to the temperature of the surface of the moon at a point where the sun is at its zenith.
On the surface of the earth the sunlight has had to pass through the atmosphere, and in perfectly bright sunshine it is estimated that only three-fifths of the heat is transmitted. Any surface is also radiating out into surroundings which are at about 300° absolute. Taking into account these two facts, we find that the upper limit to a non-conducting surface in full sunshine on the earth is about 365° absolute, or only a few degrees less than the boiling point of water.
Effective Temperature of Space.—The last problem we will attack by means of the fourth power law is the estimation of the effective temperature of space,i.e.the temperature of a full absorber shielded from the sun and far away from any planet.
It is estimated by experiment that zenith sun radiation is five million times the radiation from the stars. This estimate is only very rough, as the radiation from the stars is so minute. As the sun only occupies one 94,000th part of the heavens, the radiation from a sunbright hemisphere would be five million times 94,000 times starlight,i.e.470,000,000,000 times. The temperature of the sun is therefore the fourth root of this quantity times the effective temperature of space,i.e.about 700 times. Since the temperature of the sun is about 6200°, the temperature of space is a little under 10° absolute;i.e.lower than -263° C.
Note on Absolute Temperature.—It is found that, if a gas such as air has its temperature raised or lowered while its pressure is kept uniform, for every one degree centigrade rise or fall its volume is increased or decreased by one two hundred and seventy-third of its volume at freezing point,i.e.at 0° centigrade. If therefore it continued in the same way right down to -273° centigrade, its volume would be reduced to zero at this temperature. This temperature is therefore called the absolute zero of temperature, and temperatures reckoned from it are called absolute temperatures. To get absolute temperatures from centigrade temperatures we evidently need to add 273°.
No account of radiation would be complete without mentioning what becomes of the radiation which bodies absorb, but a good deal of the subject is in so uncertain a state that very little space will be devoted to it.
Absorbed Radiation converted into Heat.—The most common effect of absorbed radiation is to raise the temperature of the absorbing body, and so cause it to re-emit long heat-waves. As the usual arrangement is for the absorbing body to be at a lower temperature than the radiating one, the waves given out by the absorber are longer than those given out by the radiator, and so the net result is the transformation of shorter waves into longer ones. But we have seen by Prévost's theory of exchanges that radiator and absorber are interchangeable, and therefore we see that those waves which are emitted by the absorber and absorbed by the radiator are re-emitted by the latter as shorter waves.
The mechanism by means of which the waves are converted into heat in the body is still a mystery. That the waves should cause the electrons to vibrate is perfectly clear, but how the vibrations of the electrons are converted into those vibrations of the atomsand molecules which constitute heat is still unsolved, and the reverse process is, of course, equally puzzling.
The heating of the body and the consequent re-emission of heat-waves is not, however, the only process which goes on. In a large number of substances, waves are given out under the stimulus of other waves without any heating of the body at all. In most of these cases the emission stops as soon as the stimulating waves are withdrawn, and in these cases the phenomenon has been called fluorescence. The name has been derived from fluor spar, the substance which was first observed to exhibit this peculiar emission of waves.
A familiar example of fluorescence is provided by paraffin-oil, which glows with a blue light when it is illuminated with ordinary sunlight or daylight. Perhaps the easiest way to view it is to project a narrow beam of light through the paraffin-oil contained in a glass vessel and view the oil in a direction perpendicular to the beam. The latter will then show up a brilliant blue.
A water solution of sulphate of quinine, made acid by a few drops of sulphuric acid, also exhibits a blue fluorescence, while a water solution of æsculin (made by pouring hot water over some scraps of horse-chestnut bark) shines with a brilliant blue light.
Some lubricating oils fluoresce with a green light, as does also a solution in water of fluorescene, named thus because of its marked fluorescence.
A solution of chlorophyll in alcohol, which can be readily prepared by soaking green leaves in alcohol, shows a red fluorescence; uranium glass—the canary glass of which small vases are very frequentlymade—exhibits a brilliant green fluorescence, as does also crystal uranium nitrate.
It is found, on observing the spectrum of the fluorescent light, that a fairly small range of waves is emitted showing a well-marked maximum of intensity at a wave-length which is characteristic of the particular fluorescing substance.
There also seems to be a limited range of waves which can induce this fluorescence, and this range also depends upon the fluorescing substance. As a rule, the inducing waves are shorter in length than the induced fluorescence, but this rule has some very marked exceptions.
The fact that only a limited range of waves produces fluorescence explains a noticeable characteristic of the phenomenon. If the fluorescing solutions are at all strong the fluorescence is confined to the region close to where the light enters the solution, thus showing that the rays which are responsible for inducing the glow become rapidly absorbed, whereas the remainder of the light goes on practically unabsorbed.
Phosphorescence.—Sometimes the emission of the induced light continues for some time after the inducing waves are withdrawn, and then the phenomenon is termed phosphorescence, since phosphorus emits a continuous glow without rise of temperature.
Sometimes the glow will continue for several hours after the exciting rays have been cut off, a good example of this being provided by Balmain's luminous paint, which is a sulphide of calcium. With other substances the glow will only continue for a very small fraction of a second, so that it is impossible tosay where fluorescence ends and where phosphorescence begins.
In order to determine the duration of the glow in the case of these small times, an arrangement consisting of two rotating discs, each of which have slits in them, is set up. Through the slits in one of them the substance is illuminated, and through the slits in the other the substance is observed while the light is cut off. By adjusting the position of the discs with regard to each other the slits may be made to follow one another after greater or shorter intervals, and so the time of observation can be made greater or smaller after the illumination is cut off.
All the bodies which have been observed to exhibit phosphorescence are solid.
Theory of Fluorescence.—It is fairly simple to imagine a mechanism by which fluorescence might be brought about, as we might assume a relation between the periods of oscillation of certain types of electron in the substance and the period of the stimulating waves. Thus resonance might occur, and the consequent vibrations of the electrons would start a series of secondary waves.
If, however, we assume resonance, it is difficult to see why there is a range of wave-lengths produced and another range of wave-lengths which may produce them. We should have expected one definite wave-length or a few definite ones producing one or a few definite wave-lengths in the glow, while if a whole range of waves will produce the effect it is difficult to see why all bodies do not exhibit the phenomenon.
But the phenomenon of phosphorescence finallydisposes of any such description, for the two phenomena have no sharp distinction between them. Some substances are known in which the phosphorescence lasts for such an extremely small fraction of a second after the stimulating waves are withdrawn that it is difficult to know whether to call the effect fluorescence or phosphorescence. It is probable, therefore, that both are due to the same action. Now a wave of orange light completes about five hundred million million vibrations in one second, and therefore if an orange-coloured phosphoresence were to last for only one five-hundredth of a second it would mean that the electrons responsible for it vibrate one million million times after the stimulus is removed. This is hardly credible, and becomes more credible when we remember that in some phosphorescent substances the effect lasts for many hours.
Chemical Theory of Phosphoresence.—It is more probable that the stimulating rays produce an actual chemical change in the phosphorescent substance. For instance, it is possible that the vibrations of a certain type of electron in one kind of atom become so violent as to detach it from the atom and the temporarily free electron attaches itself immediately to another kind of atom.
The new arrangement may be quite stable; it is so in the action of light on a photographic plate, but it may only be stable when the electrons are being driven out of their original atoms, and in this case the electrons will begin to return to their old allegiance as soon as the stimulus is withdrawn. In the returnprocess the electrons will naturally be agitated, and will therefore emit waves having their characteristic period. The rate at which the return process takes place will evidently depend upon the stability of the new arrangement. If it is extremely unstable, the whole return may only occupy a fraction of a second, but if it is nearly as stable as the original arrangement the return may be extremely slow.
On this view, then, those substances will phosphoresce which have an electron which is fairly easily detached from its atom and which will attach itself to another atom, forming an arrangement which is less stable than the original.
Temperature and Phosphorescence.—A confirmation of this chemical view is provided by the effect of temperature on phosphorescence. The rate of a chemical change is usually very largely increased by rise of temperature, and further, at very low temperatures a large number of chemical changes which take place quite readily at ordinary temperatures do not take place at all.
Similarly at very low temperatures the action of the light may be more or less stable. For example, Dewar cooled a fragment of ammonium-platino-cyanide by means of liquid hydrogen, and exposed it to a strong light. After removing the light no phosphorescence was observed, though at ordinary temperatures a brilliant green phosphorescence is exhibited, but on allowing the fragment to warm up it presently glows very brightly.
A partial stability is shown by Balmain's luminous paint, for if it be kept in the dark until it becomes quite non-luminous it will begin to glow again for ashort time if warmed up in any way. By means of this property the infra-red region of the spectrum may be made visible. For this purpose a screen is coated with the paint, exposed to strong sunlight, and then placed so as to receive the spectrum. The first effect of the invisible heat rays is to make the portions of the screen on which they fall brighter than their surroundings; but this causes the phosphorescence to be emitted more rapidly, and soon it is all emitted, leaving a dark region where the heat has destroyed the phosphorescence.
On the whole, then, those substances which phosphoresce at ordinary temperatures do so more rapidly as the temperature rises.
But Dewar has found a number of substances which phosphoresce only at low temperatures,e.g.gelatine, celluloid, paraffin, ivory and horn. This is not a fatal objection to the idea of chemical change, as some chemical actions will only take place at low temperatures, but it is an objection as quite a large number of substances only phosphoresce at low temperatures, whereas there are not many chemical reactions which will only take place there.
As a matter of fact, even if the idea of a chemical change be the true one, it is not a very satisfactory one, as chemical changes are undoubtedly very complicated ones, and it would be too difficult to trace the change from the vibration of an electron to the chemical change, andvice-versa.
No satisfactory theory therefore exists to account for the absorption and the remission of the waves, whether accompanied or unaccompanied by a rise in temperature of the absorbing body.
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 sothe 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 glassglobe 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.
FIG. 24.FIG. 24.
The suspension was a very fine quartz fibreq. The discsd,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 inm, and asmturned 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 squarecentimetre 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 twoother 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.
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 andaway 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 thereforesuppose 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.
In this concluding chapter it is proposed to show how the wave-lengths of radiant heat have been determined and to state what range of wave-lengths has been experimentally observed. It is then proposed to show how electromagnetic waves have been produced by straightforward electrical means and how their wave-lengths have been measured. The similarity in properties of the radiant heat and of the electric waves will be noted, leading to the conclusion that the difference between the two sets of waves is merely one of wave-length.
Diffraction Grating.—The best method of measuring the wave-lengths of heat and light is by means of the "Diffraction Grating." This consists essentially of a large number of fine parallel equidistant slits placed very close to one another. For the measurement of the wave-lengths of light and of the shorter heat waves, it is usually produced by ruling a large number of very fine close equidistant lines on a piece of glass or on a polished mirror by means of a diamond point. The ruled lines are opaque on the glass and do not reflect on the mirror, and consequently the spaces in between act as slits.
Rowland's Gratings.—The ruling of these gratings is a very difficult and tedious business, but the difficulties have been surmounted in a very remarkable manner by Rowland, so that the gratings ruled on his machine have become standard instruments throughout the world. He succeeded in ruling gratings 6 inches in diameter with 14,000 lines to the inch, truly a remarkable performance when we remember that if the diamond point develops the slightest chip in the process, the whole grating is spoilt.
FIG. 25.FIG. 25.
The action of the grating can be made clear by means of Fig. 25. Let A, B, C, D represent theequidistant slits in a grating, and let the straight lines to the left of the grating represent at any instant the crests of some simple plane waves coming up to the grating. The small fractions of the original waves emerging from the slits A, B, C, D will spread out from the slits so that the crests of the small wavelets may at any instant be represented by a series of concentric circles, starting from each slit as centre. The series of crests from each slit are represented in the figure.
Now notice that a line PQ parallel to the original waves lies on one of the crests from each slit, and therefore the wavelets will make up a plane wave parallel to the original wave. This may therefore be brought to a focus by means of a convex lens just as if the grating were removed, except that the intensity of the wave is less. But a line, LM, also lies on a series of crests, the crest from A being one wave-length behind that from B, the one from B a wave-length behind that from C, and so on. The wavelets will therefore form a plane wave LM, which will move in the direction perpendicular to itself (i.e.the direction DK) and may be brought to a focus in that direction by means of a lens.
Draw CH and DK perpendicular to LM, and draw CE perpendicular to DK,i.e.parallel to LM. The difference between CH and DK is evidently one wave-length,i.e.DE is one wave-length. If α is the angle between the direction of PQ and LM, DE is evidently equal to CD sin α and therefore one wave-length=CD sin α.
From the ruling of the grating we know the valueof CD, and therefore by measuring α we can calculate the wave-length.
We find that a third line RS also lies on a series of crests, and therefore a plane wave sets out in the direction perpendicular to RS. We notice here that the crest from A is two wave-lengths behind that from B, and so on, and therefore if β is the angle between RS and PQ, CD sin β is equal to two wave-lengths.
Similarly we get another plane wave for a three wave-lengths difference, and so on. The intensity of the wavelets falls off fairly rapidly as they become more oblique to their original direction, and therefore the intensity of these plane waves also falls off rather rapidly as they become more oblique to the direction in which PQ goes.
We see that the essential condition for the plane wave to set out in any direction, is that the difference in the distances of the plane wave from two successive slits shall be exactly a whole number of wave-lengths. Should it depart ever so little from this condition we should see, on drawing the line, that there lie on the line an equal number of crests and troughs, and therefore, if a lens focus waves in this direction, the resulting effect is zero. The directions of the waves PQ, LM, RS, &c., will therefore be very sharply defined and will admit of very accurate determination.
Dispersion by Grating.—Evidently the deviations α, β will be greater the greater is DE,i.e.the greater the wave-length, and therefore the light or heat will be "dispersed" into its different wave-lengths as in the prism; but in this case the dispersionis opposite to that in the normal prism, the long waves being dispersed most and the short waves least.
Evidently, too, the smaller the distance CD the greater the angle, and therefore for the extremely short wave-lengths of light and of ultraviolet rays we require the distance between successive slits to be extremely small.
FIG. 26.FIG. 26.
The Spectrometer.—The grating is usually used with a spectrometer, as shown in plan diagrammatically in Fig. 26. The slit S from which the waves radiate is placed at the principal focus of the lens L, and therefore the waves emerge from L as plane waves which come up to the grating G. The telescope T is first turned until it views the slit directly,i.e.until the plane waves like PQ in Fig. 25 are brought to a focus at the principal focus F of the objective of the telescope. The eyepiece E views the image of the slit S which is formed at F. The telescope is then turned through an angle, α, until it views the second image of the slit which will be formed by the plane waves similar to LM in Fig. 25. The angle α is carefully measured by the graduated circle on the spectrometer,and hence the wave-length of a particular kind of light, or of a particular part of the spectrum, is measured.
This spectrometer method is exactly the method used for measuring the wave-lengths in the visible part of the spectrum.
For the ultraviolet rays, instead of viewing the image of the slit by means of the eyepiece of the telescope, a photographic plate is placed at the principal focus F of the objective of the telescope, and serves to detect the existence and position of these shorter waves. For the heat rays a Langley's bolometer strip is placed at F, in fact the bolometer strip might be used throughout, but it is not quite so sensitive for the visible and ultraviolet rays as the eye and the photographic plate.
Absorption by Glass and Quartz.—Two main difficulties arise in these experiments. The first one is that although glass, or better still quartz, is extremely transparent to ultraviolet, visible, and the shorter infra-red waves, yet it absorbs some of the longer heat waves almost completely.
For these waves, therefore, some arrangement must be devised in which they are not transmitted through a glass diffraction grating or through glass or quartz lenses. To effect this, the convex lenses are replaced by concave mirrors and the ruled grating is replaced by one which is made of very fine wires, which are stretched on a frame parallel to and equidistant from each other. The wire grating cannot be constructed with such fine or close slits as the ruled grating, but for the longer waves this is unnecessary.
Reflecting Spectrometer.—An arrangement used by Rubens is represented roughly in plan in Fig. 27. L represents the source of heat, the rays from which are reflected at the concave mirror M, and brought to a focus on the slit S. Emerging from S the rays are reflected at M2and are thereby rendered parallel before passing through the wire grating G. After passing through the grating, the rays are reflected at M3and are thereby focussed on to a bolometer strip placed at B. Turning the mirror M3in this arrangement is evidently equivalent to turning the telescope in the ordinary spectrometer arrangement.
FIG. 27.FIG. 27.
Absorption of Waves by Air.—By using a spectrometer in an exhausted vessel Schumann discovered that waves existed in the ultraviolet region of much smaller wave-length than any previously found, and that these waves were almost completely absorbed on passing through a few centimetres of air. To all longer waves, however, air seems to be extremely transparent.
The second difficulty arises from the fact, already explained, that a diffraction grating produces not one, but a number of spectra. If only a small range of waves exists, this will lead to no confusion, but if a large range is being investigated, we may get two or more of these spectra overlapping.
Suppose, for example, we have some waves of wave-length DE (in Fig. 25), some of wave-length one-halfDE and some of one-third DE. Then in the direction DK we shall get plane waves of each of these wave-lengths setting out and being brought to a focus in the same place. This difficulty can be fairly simply surmounted where the measurement of wave-length alone is required, by placing in the path of the rays from the source of light, suitable absorbing screens, which will only allow a very small range of wave-lengths to pass through them. There will then be no overlapping and no confusion.
Where the actual distribution of energy in the spectrum of any source of heat is to be determined the difficulty becomes more serious, and probably there is some error in the determinations, especially in the longest waves, which are masked almost completely by the overlapping shorter waves.
Rest-Strahlen or Residual Rays.—A very beautiful method of isolating very long heat waves, and so freeing them from the masking effect of the shorter waves, was devised by Rubens and Nichols.
It is found that when a substance very strongly absorbs any waves that pass through it, it also strongly reflects at its surface the same waves. For example, a sheet of glass used as a fire-screen will cut off most of the heat coming from the fire, although it is perfectly transparent to the light. If, now, it is placed so as to reflect the light and heat from the fire, it is found to reflect very little light but a very large proportion of the heat.
Some substances have a well-defined absorption band,i.e.they absorb a particular wave-length very strongly, and these substances will therefore reflectthis same wave-length strongly. If instead of a single reflection a number of successive reflections be arranged, at each reflection the proportion of the strongly reflected wave-length is increased until ultimately there is practically only this one wave-length present. It can therefore be very easily measured. These waves resulting from a number of successive reflections, rest-strahlen or residual rays as they have been named, have been very largely used for investigating long waves. Quartz gives rest-strahlen of length .00085 centimetres and very feeble ones of .0020 centimetres long. Sylvite gives the longest rays yet isolated, the wave-length being .006 centimetres.
Range of the Waves.—The lengths of the waves thus far measured are:—
Schumann waves . . . . . . . . .00001 to .00002 cms.Ultraviolet . . . . . . . . . .00002 to .00004 "Violet . . . . . . . . . . . . .00004 "Green . . . . . . . . . . . . .00005 "Red . . . . . . . . . . . . . .00006 to .000075 "Infra-red . . . . . . . . . . .000075 to about .0001 "Rest-strahlen from quartz . . .00085 and .0020 "Rest-strahlen from Sylvite . . .0060 "
Thus the longest waves are six hundred times the length of the shortest.
The corresponding range of wave-lengths of sound would be a little more than eight octaves, of which the visible part of the spectrum is less than one.
Electromagnetic Induction.—In the attempt to explain the nature of an electromagnetic wave (pp. 17-21) it was stated that an electric wave must always be accompanied by a magnetic wave. In order tounderstand the production of these waves, the relation between electric and magnetic lines of force must be stated in more detail. A large number of quite simple experiments show that whenever the electric field at any point is changing,i.e.whenever the lines of force are moving perpendicular to themselves, a magnetic field is produced at the point, and this magnetic field lasts while the change is taking place. An exactly similar result is observed when the magnetic field at a point is changing—an electric field is produced which lasts while the magnetic field is changing. When the electric field changes, therefore, there is both an action and a reaction—a magnetic field is produced and this change in magnetic field produces a corresponding electric field. This induced electric field is always of such a kind as to delay the change in the original electric field; if the original field is becoming weaker the induced field is in the same direction, thus delaying the weakening, and if the original field is becoming stronger the induced field is in the opposite direction, thus delaying the increase.
Momentum of Moving Electric Field.—Imagine now a small portion of an electric field moving at a steady speed; it will produce, owing to its motion, a steady magnetic field. If now the motion be stopped, the magnetic field will be destroyed, and the change in the magnetic field will produce an electric field so as to delay the change,i.e.so as to continue the original motion. The moving electric field thus has momentum in exactly the same way as a moving mass has. The parallel between the twois strictly accurate. The mass has energy due to its motion, and in order to stop the mass this energy must be converted into some other form of energy and work must therefore be done. The electric field has energy due to its motion—the energy of the magnetic field—and therefore to stop the motion of the electric field, the energy of the magnetic field must be converted into some other form, and work must therefore be done. One consequence of the momentum of a moving mass is well illustrated by the pendulum. The bob of the pendulum is in equilibrium when it is at its lowest point, but when it is displaced from that point and allowed to swing, it does not swing to its lowest point and stay there, but is carried beyond that point by its momentum. The work done in displacing the bob soon brings it to rest on the other side, and it swings back again only to overshoot the mark again. The friction in the support of the pendulum and the resistance ofthe air to the motion makes each swing a little smaller than the one before it, so that ultimately the swing will die down to zero and the pendulum will come to rest at its lowest point. The graph of the displacement of the bob at different times will therefore be something like Fig. 28. Should the pendulum be put to swing, not in air, but in some viscous medium like oil, its vibrations would be damped down very much more rapidly, and if the medium be viscous enough the vibrations may be suppressed, altogether, the pendulum merely sinking to its lowest position.
FIG. 28.FIG. 28.
Electric Oscillation.—These conditions have their exact counterpart in the electric field. To understand them, three properties of lines of force must be borne in mind: (i.) lines of force act as if in tension and therefore always tend to shorten as much as possible; (ii.) the ends of lines of force can move freely on a conductor; (iii.) lines of force in motion possess momentum. Now imagine two conducting plates A and B, Fig. 29, charged positively and negatively, and therefore connected by lines of force as indicated. Let the two plates be suddenly connected by the wirew, so that the ends of the lines of force may freely slide from A to B orvice-versa, and therefore all the lines will slide upwards along A and B, and then towards each other alongw, until they shrink to zerosomewhere inw. The condition of equilibrium will evidently be reached when all the lines have thus shrunk to zero, but the lines which are travelling from A towards B will have momentum and will therefore overshoot the equilibrium condition and pass right on to B. That is, the positive ends of the lines will travel on to B, and similarly the negative ends will pass on to A. The lines of force between A and B will therefore be reversed. The tension in the lines will soon bring them to rest, and they will slide back again, overshoot the mark again, reach a limit in the original direction and still again slide back. The field between A and B will therefore be continually reversed, but each time its value will be a little less, until ultimately the vibrations will die down to zero. Thus if we were to replace the displacement in Fig. 29 by the value of the field between A and B we should have an exactly similar graph.
FIG. 29.FIG. 29.
The amount by which the oscillations are damped down will depend upon the character of the wirew. If it is a very poor conductor it will offer a large resistance to the sliding of the lines along it, and the vibrations will be quickly damped down or, if the resistance is great enough, be suppressed altogether.
This rapid alternation of the electric field will send out electromagnetic waves which die down as the oscillations decrease.
The Spark Discharge.—In practice the wirewis not actually used, but the air itself suddenly becomes a conductor and makes the connection. When the electric field at a point in the air exceeds a certain limiting strength, the air seems to break down andsuddenly become a conductor and remains one for a short time. This breaking down is accompanied by light and heat, and is known as the spark discharge or electric spark.
Experiments of Hertz.—In the brilliant experiments carried out by Hertz at Karlsruhe between 1886 and 1891, he not only demonstrated the existence of the waves produced in this way, but he showed that they are reflected and refracted like ordinary light, he measured their wave-length and roughly measured their speed, this latter being equal to the speed of light within the errors of experiment.
FIG. 30.FIG. 30.
One arrangement used by Hertz is shown in plan in Fig. 30. A Ruhmkorff coil R serves to charge the two conductors A and B until the air breaks down at the gap G, and a spark passes. Before the spark isproduced, the lines of force on the lower side of AB will in form be something like the dotted lines in the figure, but as soon as the air becomes a conductor, the positive ends of the lines will surge from A towards B and on to B, and the negative ends will surge on to A. These to and fro surgings will continue for a little while, but will gradually die out. As the surgings are all up and down AB, the electric vibrations in the electromagnetic waves sent outwill all be parallel to AB, and therefore they will be polarised.
FIG. 31.FIG. 31.
This is characteristic of all electric waves, as no single sparking apparatus will produce anything but waves parallel to the spark gap. The electric vibrations coming up to a conductor placed in the position of the wire rectangle, M, will cause surging of the lines along it, and, if these surgings are powerful enough, will cause a spark to pass across the small gap S.
Such a rectangle was therefore used by Hertz as a detector of the waves, but since that time many detectors of very much greater sensitiveness have been devised.
Reflection.—In order to show that these waves are reflected in the same way as light waves, Hertz placed the sparking knobs, G, at the focus of a large parabolic metallic reflector, and his detector, D, at the focus of a similar reflector placed as in Fig. 31, but much farther away (cf. Fig. 1). In this position sparking at G produced strong sparking in the detector, although the distance was such that no sparking was produced without the reflectors.
Refraction.—The refraction of the waves wasshown by means of a large prism made of pitch. This had an angle of 30° and was about 1.5 metres high and 1.2 metres broad.
FIG. 32.FIG. 32.
Setting it up as shown in plan in Fig. 32, strong sparking was produced in the detector, thus showing that the rays of electric waves were deflected by 22° on passing through the prism.
Moving the mirror and detector in either direction from the line LM, made the sparks decrease rapidly in intensity, so that the exact position of LM can be determined with considerable definiteness.
Wave-length, by Stationary Waves.—The wave-lengths of the oscillations were found by means of what are known as stationary waves. When two exactly similar sets of waves are travelling in opposite directions over the same space, they produce no effects at certain points called nodes. These nodes are just half a wave-length apart. Their production can be understood by reference to Fig. 33. The dotted lines represent the two waves which are travelling in the direction indicated by the arrows. In A the time is chosen when the waves are exactly superposed, and the resultant displacement will be represented by the solid line. The points marked with a cross will be points at which the displacement is zero.
FIG. 33.FIG. 33.
In B each wave has travelled a distance equal to a quarter of a wave-length, and it will be seen that the two sets of waves cause equal and opposite displacements. The resulting displacement is therefore zero, as indicated by the solid line. In C the waves have travelled another quarter of a wave-length andare superposed again, but in this case the displacements will be in the opposite directions from those in A. In D, still another quarter wave-length has been traversed by each wave, and another quarter wave-length would bring back the position A.
In E, we have the successive positions of the wave drawn in one diagram, and we notice that the points indicated by a cross are always undisplaced and their distance apart is one-half a wave-length.
Hertz produced these conditions by setting up his coil and sparking knobs at some distance from a reflecting wall, Fig. 34. Then the waves which are coming up to the wall and those which are reflectedfrom the wall will be travelling in opposite directions over the same space. True, the reflected waves will be rather weaker than the original ones, so that there will be a little displacement even at the nodes, but there will be a well-marked minimum. Thus when the detector is placed at A, B, C or D no sparking or very feeble sparking occurs, while midway between these points the sparking is very vigorous, and the distance between two successive minima is one-half a wave-length.
FIG. 34.FIG. 34.
The wave-length will depend upon the size, form, &c., of the conductors between which the sparking occurs, for the time which the lines of force take to surge backwards and forwards in the conductors will depend upon these things. Other things being equal, the smaller the conductors the smaller the time and therefore the shorter the wave-length. The shortest wave which Hertz succeeded in producing was 24 centimetres long, but since then waves as little as 6 millimetres long have been produced.
The waves which are produced in a modern wireless telegraphy apparatus are miles in length.
We thus see that there is rather a large gap between the longest heat waves which have been isolated, .006 cms., and the shortest electric waves, .6 cms. The surprising fact, however, is that this gap is so small, for the heat waves are produced by vibrations within a molecule, or at most within a small group of molecules, whereas the electric surgings, even in the smallest conductors, take place over many many millions of molecules.
In conclusion, therefore, we see that from the Schumann waves up to the longest heat waves a little over eight octaves of electromagnetic waves have been detected, then after a gap of between five and six octaves the ordinary electrically produced electromagnetic waves begin and extend on through an almost indefinite number of octaves.
J. H. Poynting,The Pressure of Light.
E. Edser,Heat for Advanced Students: the chapters on Radiation.
E. Edser,Light for Advanced Students: the chapters on the Spectrum.
B. W. Wood,Physical Optics: the chapters on Fluorescence and Phosphorescence, Laws of Radiation, Nature of White Light, and Absorption of Light.