Light waves and their uses/Lecture VI

by Albert Abraham Michelson

 

LECTURE VI

 

ANALYSIS OF THE ACTION OF MAGNETISM ON LIGHT WAVES BY THE INTERFEROMETER AND THE ECHELON

 

A little over a year ago the scientific world was startled by the announcement that Professor Zeeman had discovered a new effect of magnetism on light. The experiment that he tried may be briefly described in the following way: If we place a sodium flame in front of the slit of a spectroscope, we get in the field of view a bright double line. If the flame is placed between the poles of a powerful electro-magnet, it is found that the lines are very much broadened; at least this was the way in which the announcement of the discovery was first made. It may be mentioned that a somewhat similar observation was made by M. Fievez a long time before. He found that the sodium lines in the spectrum were modified by the magnetic field, but not quite in the way that Zeeman announced; instead of the lines being broadened, he thought that each separate sodium line was doubled or quadrupled. It seems that, long before this, the experiment had actually been tried by Faraday, who, guided by theoretical reasons, conjectured that there should be some effect produced by a powerful magnetic field upon radiations.

The only reason why Faraday did not succeed in observing what Fievez and Zeeman observed afterward was that the spectroscopic means at his disposal at the time were far from being sufficiently powerful. The effect is very small at best. The distance between the sodium lines being taken as a kind of unit for reference, the separate sodium lines, as was shown in a preceding lecture, have a width of about one-hundredth of the distance between the two. The broadening, or doubling, or other modification which is produced in the spectrum by the magnetic field, is of the order of one-fortieth, or perhaps one-thirtieth, of the distance between the sodium lines. Hence, in order to see this effect at all, the highest spectroscopic power at our disposal must be employed. Subsequent investigation has shown, indeed, that still other modifications ensue, which are very much smaller even than this, and which cover a space of perhaps only one-hundredth to one hundred-and-fiftieth of the distance between the sodium lines. They are, therefore, beyond reach of the most powerful spectroscope.

It occurred to me at once to try this experiment by the interference method, which is particularly adapted to the examination of just such cases as this, in which the effect to be observed is beyond the range of the spectroscopic method. The investigation was repeated in very much the same way as described by Zeeman, namely: A little blow-pipe flame was placed between the poles of a powerful electro-magnet; a piece of glass was placed in the flame to color it with sodium light. The light, instead of passing into the spectroscope, was sent into an interferometer and analyzed by the method described in Lecture IV. The visibility curves which were thus obtained showed that, instead of a broadening, as was first announced by Zeeman, each of the sodium lines appeared to be double. The visibility curves which were observed are shown in Fig. 78, and in Fig. 79, the curves which give the corresponding distribution of the light in the source. In the former figure the vertical distances of the different curves represent the clearness of the fringes, and the horizontal distances the differences in path. In curve A, as the difference in the paths increases, the fringes become less and less distinct, until at forty millimeters the fringes have almost entirely disappeared. This curve represents the visibility of the sodium flame without any magnetic field. The corresponding intensity curve A (Fig. 79) shows that the center of the line has the greatestFIG. 78 intensity and that the intensity falls off rapidly on either side, the width of the line corresponding to something like one-hundredth of the distance between the two sodium lines. When the field was created by simply closing the current through the magnet, the visibility curve assumed the form indicated in curve B. The corresponding distribution of light is shown in the second of the intensity curves, B (Fig. 79) and we see that the line shows simply a broadening, with a possible indication of doubling. TheFIG. 79 field was then increased considerably; curve C (Fig. 78) represents the visibility. The corresponding intensity curve shows clearly that the line is double. The other curves were obtained by increasing the field gradually, and it will be noted that the result is an increasing separation of the line and, at the same time, a considerable broadening out of the two separate elements.

This same experiment was tried with other substances, especially with cadmium, and it was found that almost identical results were obtained with cadmium light as with sodium. It was therefore inferred that the observations announced by Zeeman were, at any rate, incomplete, and it was thought that possibly the instruments at his command were not sufficiently powerful to show the phenomena of the doubling. Shortly after this experiment was published another announcement was made by Zeeman. In this he states that there is not simply a broadening of the lines, but a separation of them into three components, and, what was very much more interesting, that these three components are polarized in directions at right angles with each other: the middle line polarized in one plane and the two outer lines in another.

To make the meaning of this clear, we shall have to make a brief digression into the subject of the polarization of light. It will be remembered that in one of the first illustrations of wave motion light waves were compared with the waves along a cord, and it was stated that the vibrations which caused the phenomena of light are known to be vibrations of this character rather than of the character of sound waves. The sound waves consist of vibrations in the direction of the propagation of the sound itself. The motion of the particles in the light waves are at right angles to their direction of propagation. These transverse vibrations, as they are called, may be vertical or horizontal, or they may be diagonal, or they may move in a curved path, for instance in circles or ellipses.

In the case of ordinary light the vibrations are so mixed up together in all possible planes that it is impossible to separate any one particular vibration from the rest without special devices, and such devices are termed "polarizers." They may be likened very roughly to a grating the apertures of which determine the plane of vibration. Through such a grating we can transmit vibrations along a cord only in the plane of the apertures. A vibration at right angles to this plane will not travel along the cord beyond the grating. The corresponding light phenomena may be illustrated by attempting to pass a beam of light which has been polarized through a medium which acts toward the light waves as does the grating toward the waves on the cord. It is found that crystals act as such media. Thus a plate of tourmaline possesses this property. For, as is well known, if two plates of tourmaline be placed so that their optical axes are parallel with each other, almost as much light will pass through the two as through either one alone. But if the axes are set at right angles to each other by turning one of them through 90°, the light is entirely cut off. Turning again through 90°, the light again appears, etc. In the case of the tourmaline the vibrations which have passed through one plate are all in one plane.

There is another important case in which the light is said to be polarized, namely, when the motion of the particles is circular. We may have two such circular vibrations—one in which the motion is in the direction of the hands of a watch, called right-handed, and the other in which the motion is in the direction opposite to that of the hands of a watch, and which is therefore called left-handed. We may consider that each one of these vibrations is compounded of two plane vibrations of equal intensity, in one of which the motion is horizontal and in the other vertical, and which differ from one another in phase, this difference being one-fourth of a period for the left-handed and three-fourths of a period for the right-handed. If we add together two such circular vibrations of equal intensity, their horizontal components would exactly neutralize each other, so that there would be no horizontal motion at all. The vertical components, however, being inFIG. 80 the same direction, will add to each other, so that the resultant of two beams of light polarized circularly in opposite directions and of equal intensity is a plane polarized ray.

To return, now, to Zeeman's phenomenon. Fig. 80 represents one of the sodium lines when examined in a direction at right angles to the magnetic field. The upper line represents the appearance when the light is polarized so that only horizontal vibrations reach the spectroscope. If, however, the polarizer is rotated through 90°, so that only vertical vibrations pass, the appearance is that of the lower half of the diagram, the two side lines appearing and the central line disappearing. Finally, if the light is examined in the direction of the magnetic field, which can be accomplished by boring a hole through the pole of the magnet, it is found that only two are visible—the two outside ones; and one of these is composed of light which vibrates circularly in the direction of the hands of a watch, and the other is circularly polarized in the oppositeFIG. 81 direction.

An extremely beautiful and simple explanation of this phenomenon has been given by Lorentz, Larmor, Fitzgerald, and a number of others. At the risk of introducing a few technicalities, I will venture to repeat this explanation in a simple form. For this purpose it is necessary to know that the particles or atoms of matter are each supposed to be associated with an electric charge, and that such a charged particle is termed an "electron." This hypothesis, made long before Zeeman made his discovery, was found necessary to account for the facts of electrolysis. For the decomposition of an electrolyte by an electric current is most simply explained upon the hypothesis that it contains positively and negatively charged particles, and that the positively charged atoms go toward the negative pole, and the negatively charged toward the positive pole. They then give up their electricity, and this giving up of electricity constitutes an electric current. Hence this assumption, which is useful in explaining the Zeeman effect, is nothing new. It is known, also, that the vibrations of these particles, or of their electric charges, produce the disturbance in the ether which is propagated in the form of light waves; and that the period of any light wave corresponds to the period of vibration of the electric charge which produces it.

The most general form of path of such a vibrating electric charge would be an ellipse. Now, an elliptical vibration can always be resolved into a circular vibration and a plane one, so that any polarized ray may be resolved into a plane polarized ray and a circularly polarized ray. So all we need to consider are plane and circularly polarized rays. But we may suppose that a plane vibration is due to two oscillations in a circle, one going in a direction opposite to that of the hands of a watch, and the other in their direction. Hence, we need consider only circular vibrations. Now, if the electric charge is moving in a circle, it can be shown that when the plane of the circle is at right angles to the direction between the two poles of the magnet, the effect of the field would be to accelerate the motion when the rotation is, say, counter-clockwise, but to retard it when it is clockwise.

It was shown above that the position of a spectral line in the spectrum depends on the period of the light which produces it. Hence the position of the line will be altered when any current is passing about the electro-magnet. When the current is passing in a certain direction, the velocity of rotation of the particles moving, say counter-clockwise, is increased. Hence the period of vibration is smaller; i. e., the number of vibrations, or the frequency, is greater. In this case there will be a shifting toward the blue end of the spectrum by an amount corresponding to the amount of the acceleration. Those particles which are rotating in an opposite direction, i. e., clockwise, will be retarded, the frequency will be less, and the spectral lines will be shifted toward the red. These two shiftings would account, then, for the double line. It is further clear that those vibrations which occurred in planes parallel to the lines of force of the magnetic field would be unaltered. These vibrations would then produce the middle line, which is not shifted from its position by the magnetic field.

Again, if we are viewing the light in a direction at right angles to the lines of force of the field, the vibrations of those particles which are affected by the field would have no components parallel to the field. If the particles are revolving in a plane perpendicular to the field, then, when viewed in this direction, they would appear to be moving only up and down; i. e., they would send out plane polarized light whose vibrations are vertical. These two vertical vibrations form the two outer lines of the triplet, and it can be shown that the light is plane polarized by passing it through a polarizer. Those particles which are vibrating horizontally do not have their period of vibration altered by the field. Consequently we get a single line whose position in the spectrum is not changed, and which is plane polarized in a plane at right angles to that of the other two.

When this second announcement of Zeeman appeared, it seemed worth while to repeat the experiments with the interferometer, especially as it was pointed out that probably the reason why a single or a double line appeared, instead of a triple line, was because part of the light corresponding to the middle line was cut off by the reflection from the separating plate of the interferometer. The light thus reflected is polarized, and most of the light which should have formed the central image is thus cut off. It was therefore determined to repeat these experiments underFIG. 82 such conditions that we could be perfectly sure that light which reached the interferometer vibrated in only one plane. To accomplish this it is necessary merely to introduce a polarizer into the path of the light.

Fig. 82 represents the arrangement of the experiment with the interferometer. The source of light, instead of being sodium in a Bunsen flame, is vapor in a vacuum tube, illuminated by an electric discharge. The capillary part of the tube is placed between the poles of the magnet.

The light is first passed through an ordinary spectroscope, so that there is formed at s a spectrum, any part of which we may examine. The slit at s allows only one radiation to pass into the interferometer. Thus, if we examine cadmium light, we may allow the red to pass through, or the green, or the blue. The light is made parallel by a lens and then passes into the interferometer. The arrangement for examining separately the vertical vibrations alone and the horizontal vibrations alone is represented at N, and consists merely of a Nicol prism which can be rotated about a horizontal axis.

With this arrangement a different set of visibility curves was obtained.FIG. 83 These are shown in Figs. 83, 84, 85.

The upper curve of Fig. 83 represents the visibility curve produced by the horizontal vibrations of the red cadmium light in a strong magnetic field. For the vertical vibrations the visibility curve is something totally different, and is shown in the lower half of the figure. The effect of the field is readily appreciated by comparing this figure with Fig. 66, which corresponds to the red cadmium line without any magnetic field.

The upper curve of Fig. 84 represents the visibility curve of the blue cadmium vapor when the horizontal vibrations only are allowed to pass through. When vertical vibrations only are allowed to pass through, the curve has the form shown in the lower half of the figure.

The case of the green radiation, when there is no field, is shown in Fig. 67 above. When the magnetic field is on, and when the horizontal vibrations only are allowed to pass through, the visibility curve has the form of the upper curve in Fig. 85. When vertical vibrations are allowed to pass through, it has the form of the lower curve.

The intensity curves corresponding to Figs. 83, 84, and 85 are shown in Fig. 86. The upper three correspond to the horizontal vibrations, while the lower three correspond to the vertical vibrations. In the case of the red radiations it will be noted that, whether there is a magnetic field or not, there is no particular change for red cadmium light when the horizontal vibrations alone are considered. When the field is on,FIG. 84 the vertical vibrations give a double line, or possibly one of more complex form.

In the case of the blue radiations, however, when there is a magnetic field and only horizontal vibrations are allowed to pass through, the line is double. The doubling is very distinct, and the separation is so wide that it should be easily seen by means of the spectroscope. When the vertical vibrations alone are allowed to pass through, there is a very much more complicated effect. In all cases we can see that the line is double, as in the case of red cadmium light, but in this case each component of the double lines is at least quadruple, or even more complex.

In the case of the green radiation, when horizontal vibrations only are considered, we have a triple line for the central line of the Zeeman triplet. When horizontal vibrations alone are allowed to pass through without a magnetic field, it resembles in general character the red line (cf. Fig. 67). When vertical vibrations are examined in the magnetic field, the line is highly complex; and in this case it is absolutely certain that each of the components of the double consists of at least three separate lines. The phenomenon is perfectly symmetrical about the central line.

It appears from these results that the Zeeman effect is a much more complex phenomenon than was at first supposed, and therefore the simple explanation that was given above no longer applies. At any rate, it must be very seriously modified in order to account for the much more highly complex characterFIG. 85 of the phenomena, as here described. The complete theory has not yet been worked out, and meanwhile we must gather whatever information we can concerning the behavior of as many different radiations as possible. Every attempt to deduce some general law which will cover all cases at present known has thus far proved unsuccessful. There are a number of anomalies which seem even more difficult to account for than the doubling of this middle line and the multiplication of the side lines. For example, in one of the radiations examined, the line without any magnetic field appeared as quadruple, but when the magnetic field was on, it appeared as a single line.

There are quite a number of other interesting cases, which we have not time to consider now. The explanation of these anomalies will probably not be given until long after the explanation of the doubling and tripling and multiplication of separate lines.

The examination of spectral lines by means of the interferometer, while in some respects ideally perfect, is still objectionable for several reasons. In particular, it requires a very long time to make a set of observations, and we can examine only one line at a time. The method of observation requires us to stop at each turn of the screw, and note the visibility of the fringes at each stopping-place. During the comparatively long time which it takes to do this the character of the radiations themselves may change. Besides, we have the trouble of translating our visibility curves into distribution curves. Hence it is rather easy for errors to creep in.

On account of these limitations of the interferometer method, attention was directed to something which shouldFIG. 96 be more expeditious, and the most promising method of attack seemed to be to try to improve the ordinary diffraction grating. The grating, as briefly explained in one of the preceding lectures, consists of a series of bars very close together, which permit light to pass through the intervals between them. The first gratings ever made were of this nature, for they consisted of a series of wires wound around two screws, one above and one below. This first form of grating answered very well for the preliminary work, but is objectionable because the interval between the wires is necessarily rather large, i. e., the grating is rather coarse. If we allow light to pass through these intervals, each interval may be considered to act as a source of light. From each of these sources it is spread out in circular waves. If the incident wave is plane and falls normally upon the grating, all these waves start from the separate openings in the same phase of vibration. Hence, in a plane parallel to the grating we should have, as the resultant of all these waves, a plane wave traveling in the direction of the normal to the grating. When this wave is concentrated in the focus of a lens, it produces a single bright line, which is the image of the slit and is just as though the grating were not present.

FIG. 87

 

Suppose we consider another direction, say AC (Fig. 87). We have a spherical wave, starting from the point B, another in the same phase from the point a, etc. Now, if the direction AC is such that the distance ab from the opening a to the line through B perpendicular to AC is just one wave, then along the line BC the light from the openings B and a differ in phase by one whole wave. When ab is equal to one wave, cd will be equal to two waves; hence, along BC the light from the opening c will be one wave behind the light from a, etc.; and if these waves are brought to a focus, they will produce a bright image of the source. Since the wave lengths are different for different colors, the direction AC in which this condition is fulfilled will be different for different colors. A grating will therefore sort out the colors from a source of light and bend them at different angles, forming a spectrum. Since the blue waves are shorter than the red, the blue will be bent least and the red most, the intervening colors coming in their proper order between. Again, we may also have an image formed when the direction AC is such that this difference in phase of the light from successive openings, instead of one wave, is two. The spectrum thus formed is said to be of the second order. When this difference in phase is three waves, the spectrum is said to be of the third order, etc.

Plate I, Fig. 2, represents the spectrum produced by a coarse grating. The source of light was a narrow slit illuminated by sunlight. The central image appears just as though no grating were present, and on either side are diffuse spectral images colored as on Plate I. Three such images, which are the spectra of the first, second, and third orders, may be counted on the right, and the same on the left. The grating used in producing this picture had about six hundred openings to the inch. Now, a finer grating produces a much greater separation of the colors. The large concave gratings used for the best grade of spectroscopic work produce spectra of the first order which are four feet long. Those of higher order are correspondingly longer.

The efficiency of such gratings depends on the total difference of path in wave lengths between the first wave and the last. Thus in the grating shown in Fig. 87 there will be, in the case of the first spectrum, as many waves along AC as there are openings between A and B. If we call the total number of openings in the grating n, then there will be n waves along AC. In the second spectrum, then, since each one of the intervals corresponds to two waves, the total difference in the path is twice as great, so that the number of waves in AC will be 2n. For the third spectrum the number would be 3n, and for the mth spectrum mn.

The efficiency of the grating depends on the order m of the spectrum and the number n of lines in the grating, i. e., on the product of the two. Hitherto the efforts of makers of gratings have been directed toward increasing n as much as possible by making the total number of lines in the grating as great as possible. It has been found that as many as 100,000 lines can be ruled side by side on a metallic surface; but in ruling 100,000 lines it is extremely difficultFIG. 88 to get them in their proper position. Very little attention has as yet been directed toward producing a spectrum of a very high order. The chief reason for this is that the intensity of the light in the spectra of higher orders diminishes very rapidly as the order increases. The first spectrum is by far the brightest; the second has an intensity of something like one-third of the first, and the succeeding spectra are still fainter. There have been, occasionally, gratings in which the diamond point happened to rule in such a way as to throw an abnormal proportion of light in one spectrum. Such are exceedingly rare and exceedingly valuable. It seems to be a matter of chance whether the diamond rules such gratings or not. It was with the double purpose of multiplying the order of the spectrum, and at the same time of throwing all the light in one spectrum, that the instrument shown in Fig. 88 was devised.

The method of reasoning which led to the invention of this instrument may be of interest. We will suppose that, in order to throw the light in one spectrum, the diamond point could be made to rule a grating with a section like that shown in Fig. 89, the distance between the steps being exactly equal and theFIG. 89 surfaces of the grooves perfectly polished. Suppose that the light came in the direction indicated nearly normal to the surface of the groove. The light would be reflected back in the opposite direction, and that which came from each successive groove would differ in phase from that from the adjacent grooves by a number of waves corresponding to double the difference in path. The retardation, instead of being one wave, would be twice the number of waves in this distance. If the distance between the grooves were very large, the number of waves in this distance would also be very large, so that the order of the resulting spectrum would be correspondingly high. Further, almost all the light returns in one direction, so that the spectrum we are using will be as bright as possible.

We have thus shown, at least theoretically, the possibility of producing a very high order of spectrum, and at the same time of getting almost all the light in one spectrum. However, the necessary condition is that the distances between the grooves be equal within a very small fraction of a light wave. This is a difficult, but not a hopeless, problem. In fact, we may obtain the desired retardation by piling up plates of glass of the same thickness. These plates of glass can be made originally of a single piece, as nearly uniform in thickness as possible. It has been possible to obtain plates, plane parallel, so accurate that the thickness was the same all over to within one-hundredth of a light wave; that is, less than one five-millionth of an inch. If we could place a number of such plates in contact with each other, we should have the means of producing any desired retardation of light reflected from one surface over the light reflected from the next nearest surface, and should be able to make this retardation exactly the same number of waves for all the intervals. The difficulty lies in the fact that we cannot place the plates in contact even by applying a pressure large enough to distort the glasses, because of dust particles. The thickness of such particles is of the order of a light wave. It is therefore difficult to get the plates much closer together than about three waves. If this distance were constant, no harm would be done, but it varies in different cases; so the extreme accuracy of the thickness of the glass is practically valueless.

Fortunately there is a way of getting around the difficulty, and this way has, at the same time, other advantages. Suppose that, instead of reflecting the light from such a pile of glass plates, we allow it to go through. The light travels more slowly in glass than in air—in the ratio of one and one-half to one—and the retardations produced by the successive plates in the light which has passed through are now exactly the same. In this way it has been found possible to utilize as many as twenty or thirty of such plates, and the retardation produced by each plate would correspond to the difference in the optical path between a layer of air and an equally thick layer of glass. Some of these plates have been made as thick as one inch. Roughly speaking, there are 50,000 waves in an inch of air; the number in an equal thickness of glass would be one and one-half times as great, so that the difference in path would be 25,000 waves. But the resolving power is the order of spectrum multiplied by the number of plates. If we are observing, therefore, in the 25,000th spectrum, and there are thirty such plates, the resolving power would be 750,000; whereas the resolving power of the best gratings is about 100,000.

There are, however, disadvantages in the use of this instrument. One of these may be illustrated as follows: Suppose we take the case of the ordinary grating; the first spectral image is rather widely separated from the central image of the slit, the second spectral image is twice as far away as the first, and the third spectral image will start three times as far away as the first, and will also be three times as long. The result is that parts of the second and third overlap. The overlapping becomes greater and greater as the order of the spectrum increases, so that when the 25,000th spectrum is reached the spectra are inextricably confused. Where we have to deal with a few simple radiations, however, as in cadmium or sodium, this overlapping is not so serious as might be supposed. We have a very simple means of getting rid of the worst of it by analyzing the light by means of a prism before it enters the pile of plates.

The construction of the instrument is not very different from that of the ordinary spectroscope. The light passes through a slit and then through a lens, by which it is made parallel. It then passes through the pile of plates—the echelon, as it has been named—and into the observing telescope. With this instrument the results obtained by the method of visibility curves have been confirmed. Thus Fig. 81 shows the appearance of the green mercury line in the field of view of the echelon when the source is in a strong magnetic field. In the three central components the vibrations are horizontal, while in the outer three on both sides the vibrations are vertical. An idea of the power of this instrument can be obtained by comparing Fig. 81 with Fig. 80, which gives the appearance of the line as seen in the best grating spectroscope.

 

SUMMARY

 

1. The investigation of the changes produced in the radiations of substances by placing them in the magnetic field is in general a phenomenon barely within the range of the best spectroscopes, and there are some features of it which it would be entirely hopeless to attack by this method.

2. Such investigations, however, are precisely the kind for which the interference method is particularly adapted. In fact, the results of the investigation by the method of visibility curves have furnished a number of new and interesting developments which could only with difficulty have been obtained by the ordinary spectrometer methods.

3. Fertile as this method has shown itself to be, there are, nevertheless, a number of serious drawbacks. In order to obviate these a new instrument was devised, the echelon spectroscope, which has all the advantages of the grating spectroscope, together with a resolving power many times as great. With the aid of this instrument all the preceding deductions have been amply verified and a number of new and interesting facts added to the store of our knowledge of the Zeeman effect.