CHAPTER VIII

THE RELATION BETWEEN RADIANT HEAT AND ELECTRIC WAVES

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.

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+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.

The action of the grating can be made clear by means of Fig. 25. Let A, B, C, D represent the {74} equidistant 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 [Greek: alpha] is the angle between the direction of PQ and LM, DE is evidently equal to CD sin [Greek: alpha] and therefore one wave-length=CD sin [Greek: alpha].

From the ruling of the grating we know the value {75} of CD, and therefore by measuring [Greek: alpha] 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 [Greek: beta] is the angle between RS and PQ, CD sin [Greek: beta] 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 [Greek: alpha], [Greek: beta] 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 dispersion {76} is 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.

+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, [Greek: alpha], 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 [Greek: alpha] is carefully measured by the graduated circle on the spectrometer, {77} 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.

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+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 M(sub)2 and are thereby rendered parallel before passing through the wire grating G. After passing through the grating, the rays are reflected at M(sub)3 and are thereby focussed on to a bolometer strip placed at B. Turning the mirror M(sub)3 in this arrangement is evidently equivalent to turning the telescope in the ordinary spectrometer arrangement.

+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-half {79} DE 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 reflect {80} this 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 to {81} understand 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 two {82} is 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 of {83} the 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.

+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 wire _w_, so that the ends of the lines of force may freely slide from A to B or _vice-versa_, and therefore all the lines will slide upwards along A and B, and then towards each other along _w_, until they shrink to zero {84} somewhere in _w_. 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.

The amount by which the oscillations are damped down will depend upon the character of the wire _w_. 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 wire _w_ is 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 and {85} suddenly 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.

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 is {86} produced, 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 out {87} will all be parallel to AB, and therefore they will be polarised.

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 was {88} shown 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.

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.

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 and {89} are 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 reflected {90} from 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.

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.

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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.

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BOOKS FOR FURTHER READING

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.

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INDEX

ABSORBING power, 37 -- and radiating power, 38 Absorption, spectra, 34 -- by glass and quartz, 77 -- by air, 78 Addition of waves, 25 Amplitude, 23

BALMAIN, luminous paint, 59 Boltzmann, laws of radiation, 48

CONVECTION currents, 67 Corpuscular theory, 10 -- reflection and refraction by, 11 Crookes' radiometer, 67

DEWAR, temperature and phosphorescence, 62 Diffraction grating, 72 -- dispersion by, 75 -- wire grating, 77 Dispersion, 29, 75 Doppler effect, 69

EFFICIENCY in lighting, 52 Elastic solid theory, 17 Electric field, 18 Electric charges within the atom, 21 Electric oscillations, 19, 83 Electrification, positive and negative, 18 Electromagnetic induction, 80 Electromagnetic waves, 17, 84 Electrons, 30 Energy in simple wave, 25 Energy--wave-length curve, 27

FLUORESCENCE, 58 -- theory of, 60 Foucault, speed of light in different media, 17 Fourier's series of waves, 26, 30 Fraunhöfer lines, 35 Full radiator and absorber, 44, 45

GASES as radiators, 42

HUYGHENS' wave theory, 13 Hertz, experiments on electric waves, 85 -- reflection, 86 -- refraction, 87 -- wave-length by stationary waves, 88

INFRA-RED rays, 32 Interference, 13

KIRCHOFF'S law, 40

LANGLEY, Bolometer, 32, 48, 49, 77 Lebedew, pressure of light, 65 Lummer and Pringsheim, law of radiation, 48, 50

MAGNETIC oscillations, 20 Maxwell, electromagnetic theory, 17 -- pressure of light, 64 Momentum of moving electric field, 81

NEWTON, dispersion, 29 -- corpuscular theory, 12 -- law of cooling, 46 Nichols, Rubens and, Rest-strahlen, 79 Nicholls and Hull, pressure of light, 64, 68

PFLÜGER, emission from tourmaline, 43 Phase, 22 Phosphorescence, 59 -- chemical theory of, 61 -- temperature and phosphorescence, 62 Planck, energy and wave-length, 51 Polarised light, emission from tourmaline, 42 Pressure of light, prediction of by Maxwell, 64 -- measurement by Lebedew, 65 -- measurement by Nicholls and Hull, 64, 68 -- on the earth, 68 -- on fine dust, 69 -- on comets' tails, 69 -- three effects of in astronomy, 70 Prévost, Theory of Exchanges, 46

RADIATING power, 38 Radiometer action, 67 Reflection, corpuscular theory, 11 -- of electric waves, 87 Refraction, corpuscular theory, 11 -- of electric waves, 87 Resonance, 30 Rest-strahlen or residual rays, 79 Ripples on mercury, 13 Ritchie, radiating and absorbing powers, 38 Rowland, gratings, 73 Rubens and Kurlbaum, proof of Planck's law, 51 Rubens and Nichols, Rest-strahlen, 79

SCHUMANN waves, 78 Simple harmonic motion, simple periodic motion, 24 Spark discharge, 84 Spectrometer, 76 -- reflecting, 78 Spectrum, 29 -- the whole, 32 -- incandescent solid or liquid, 33 -- incandescent gas, 33 -- analysis, 34 -- emission and absorption, 34 -- sun, 35 -- stars and nebulæ, 36 -- and temperature, 48 Stationary waves, 88 Stefan, law of radiation, 47

TEMPERATURE, absolute, 56 -- of planets, 54 -- of space, 55 -- of sun, 53

ULTRAVIOLET rays, 32, 77

WAVE form, 24 Wave-length, 22 -- range of, 80 -- of electric waves, 90 Wave theory, rectilinear propagation, 13 Wien, Law of Radiation, 50

YOUNG, interference, 16

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