16 December 2005 | Vol. 5, No. 4
The Wave Theory of Light
It is indeed my humble part to bring before you only some mathematical and dynamical details of this great theory. I cannot have the pleasure of illustrating them to you by anything comparable with the splendid and instructive experiments which many of you have already seen. ... I must say, in the first place, without further preface, as time is short and the subject is long, simply that sound and light are both due to vibrations propagated in the manner of waves; and I shall endeavor in the first place to define the manner of propagation and the mode of motion that constitute those two subjects of our senses.
Each is due to vibrations, but the vibrations of light differ widely from the vibrations of sound. Something that I can tell you more easily than anything in the way of dynamics or mathematics respecting the two classes of vibrations is, that there is a great difference in the frequency of the vibrations of light when compared with the frequency of the vibrations of sound. ... Consider, then, in respect to sound. ... The notes of the modern scale correspond to different frequencies of vibrations. A certain note and the octave above it, correspond to a certain number of vibrations per second, and double that number.
I may conveniently explain in the first place the note called 'C'; I mean the middle 'C'; I believe it is the C of the tenor voice that most nearly approaches the tones used in speaking. That note corresponds to 256 full vibrations per second—256 times to and fro per second of time.
Think of one vibration per second of time. ... Take a ten-inch pendulum of a drawingroom clock, which vibrates twice as fast as the pendulum of an ordinary eight-day clock, and it gives a vibration of one per second, a full period of one per second to and fro. Now think of three vibrations per second. I can move my hand three times per second easily, and by a violent effort I can move it to and fro five times per second. ... If a person were nine times as strong as the most muscular arm can be, he could vibrate his hand to and fro thirty times per second, and without any other musical instrument could make a musical note by the movement of his hand which would correspond to one of the pedal notes of an organ.
If you want to know the length of a pedal pipe, you can calculate it in this way. There are some numbers you must remember, and one of them is this. You, in this country, are subjected to the British insularity in weights and measures; you use the foot and inch and yard. I am obliged to use that system, but I apologize to you for doing so, because it is so inconvenient, and I hope all Americans will do everything in their power to introduce the French metrical system. ... I say this seriously: I do not think any one knows how seriously I speak of it. I look upon our English system as a wickedly brain-destroying piece of bondage under which we suffer. The reason why we continue to use it is the imaginary difficulty of making a change, and nothing else. ...
I know the velocity of sound in feet per second. If I remember rightly, it is 1,089 feet per second in dry air at the freezing temperature, and 1,115 feet per second in air of what we would call moderate temperature, 59 or 60 degrees—(I do not know whether that temperature is ever attained in Philadelphia or not; I have had no experience of it, but people tell me it is sometimes 59 or 60 degrees in Philadelphia, and I believe them)—in round numbers let us call the speed 1,000 feet per second. Sometimes we call it a thousand musical feet per second, it saves trouble in calculating the length of organ pipes; the time of vibration in an organ pipe is the time it takes a vibration to run from one end to the other and back. In an organ pipe 500 feet long the period would be one per second; in an organ pipe ten feet long the period would be 50 per second.... [G]oing up to 256 periods per second, the vibrations correspond to those of a pipe two feet long. Let us take 512 periods per second; that corresponds to a pipe about a foot long. In a flute, open at both ends, the holes are so arranged that the length of the sound-wave is about one foot, for one of the chief "open notes." Higher musical notes correspond to greater and greater frequency of vibration....; 4,000 vibrations per second correspond to a piccolo flute of exceedingly small length; it would be but one and a half inches long. Think of a note from a little dog-call, or other whistle, one and a half inches long, open at both ends, or from a little key having a tube three quarters of an inch long, closed at one end; you will then have 4,000 vibrations per second.
A wavelength of sound is the distance traversed in the period of vibration. ... Alternate condensations and rarefactions of the air are made continuously by a sounding body. When I pass my hand vigorously in one direction, the air before it becomes dense, and the air on the other side becomes rarefied. ... Each condensation is succeeded by a rarefaction. Rarefaction succeeds condensation at an interval of one-half what we call "wavelengths." Condensation succeeds condensation at the full interval of a wavelength.
I shall show the distinction between these vibrations and the vibrations of light. Here is the fixed appearance of the particles when displaced but not in motion. You can imagine particles of something, the thing whose motion constitutes light. This thing we call the luminiferous ether. That is the only substance we are confident of in dynamics. One thing we are sure of, and that is the reality and substantiality of the luminiferous ether. ... You must first imagine a line of particles in a straight line, and then you must imagine them disturbed into a wave-curve, the shape of the curve corresponding to the disturbance. ... The wavelength of light is the distance from crest to crest of the wave, or from hollow to hollow.
[The] wavelength of violet light...is but one-half the length of the upper wave of red light; the period of vibration is but half as long. The variation in wavelength between the most extreme rays is in the proportion of four and a half of red to eight of the violet; the red waves are nearly as one to two of the violet.
To make a comparison between the number of vibrations for each wave of sound and the number of vibrations constituting light waves, I may say that 30 vibrations per second is about the smallest number which will produce a musical sound; 50 per second gives one of the grave pedal notes of an organ, 100 or 200 per second give the low notes of the bass voice, higher notes with 250 per second, 300 per second, 1,000, 4,000 up to 8,000 per second give about the shrillest notes audible to the human ear.
Instead of the numbers, which we have, say in the most commonly used part of the musical scale, i.e., from 200 or 300 to 600 or 700 per second, we have millions of millions of vibrations per second in light waves; that is to say, 400 per second, instead of 400 million million per second, which is the number of vibrations performed when we have red light produced.
An exhibition of red light traveling through space from the remotest star is due to propagation by waves or vibrations, in which each individual particle of the transmitting medium vibrates to and fro 400 million million times in a second.
Some people say they cannot understand a million million. Those people cannot understand that twice two makes four. That is the way I put it to people who talk to me about the incomprehensibility of such large numbers. I say finitude is incomprehensible, the infinite in the universe is comprehensible. Now apply a little logic to this. Is the negation of infinitude incomprehensible? What would you think of a universe in which you could travel one, ten, or a thousand miles, or even to California, and then find it come to an end? Can you suppose an end of matter or an end of space? The idea is incomprehensible. Even if you were to go millions and millions of miles the idea of coming to an end is incomprehensible. You can understand one thousand per second as easily as you can understand one per second. You can go from one to ten, and ten times ten and then to a thousand without taxing your understanding and then you can go on to a thousand million and a million million. You can all understand it.
Now 400 million million vibrations per second is the kind of thing that exists as a factor in the illumination by red light. Violet light...I need not tell you corresponds to vibrations of about 800 million million per second. There are recognizable qualities of light caused by vibrations of much greater frequency and much less frequency than this. You may imagine vibrations having about twice the frequency of violet light, and others having about one-fifteenth the frequency of red light, and still you do not pass the limit of the range of continuous phenomena, only a part of which constitutes visible light.
When we go below visible red light what have we? We have something we do not see with the eye, something that the ordinary photographer does not bring out on his photographically sensitive plates. ... It is commonly called radiant heat. ... The heat effect you experience when you go near a bright hot coal fire, or a hot steam boiler; or when you go near, but not over, a set of hot water pipes used for heating a house; the thing we perceive in our faces and hands when we go near a boiling pot and hold the hand on a level with it, is radiant heat; the heat of the hands and face caused by a hot fire, or by a hot kettle when held under the kettle, is also radiant heat.
You might readily make the experiment with an earthen teapot; it radiates heat better than polished silver. Hold your hands below the teapot and you perceive a sense of heat; above it you get more heat; either way you perceive heat. If held over the teapot you readily understand that there is a little current of hot air rising; if you put your hand under the teapot you find cold air rising, and the upper side of your hand is heated by radiation while the lower side is fanned and is actually cooled by virtue of the heated kettle above it.
That perception by the sense of heat, is the perception of something actually continuous with light. We have knowledge of rays of radiant heat perceptible down to (in round numbers) about four times the wavelength, or one-fourth the period, of visible or red light. Let us take red light at 400 million million vibrations per second, then the lowest radiant heat, as yet investigated, is about 100 million million per second of frequency of vibration.
Everybody knows the "photographer's light," and has heard of invisible light producing visible effects upon the chemically prepared plate in the camera. Speaking in round numbers, I may say that, in going up to about twice the frequency I have mentioned for violet light, you have gone to the extreme end of the range of known light of the highest rates of vibration; I mean to say that you have reached the greatest frequency that has yet been observed. Photographic, or actinic light, as far as our knowledge extends at present, takes us to a little less than one-half the wavelength of violet light.
One thing common to the whole is the heat effect. It is extremely small in moonlight, so small that until recently nobody knew there was any heat in the moon's rays. Herschel thought it was perceptible in our atmosphere by noticing that it dissolved away very light clouds, an effect which seemed to show in full moonlight more than when we have less than full moon. Herschel, however, pointed this out as doubtful; but now, instead of its being a doubtful question, we have Professor Langley giving as a fact that the light from the moon drives the indicator of his sensitive instrument clear across the scale, showing a comparatively prodigious heating effect!
Now what force is concerned in those vibrations as compared with sound at the rate of 400 vibrations per second? Suppose for a moment the same matter was to move to and fro through the same range but 400 million million times per second. The force required is as the square of the number expressing the frequency. Double frequency would require quadruple force for the vibration of the same body. Suppose I vibrate my hand again, as I did before. If I move it once per second a moderate force is required; for it to vibrate ten times per second 100 times as much force is required; for 400 vibrations per second 160,000 times as much force. If I move my hand once per second through a space of a quarter of an inch a very small force is required; it would require very considerable force to move it ten times a second, even through so small a range; but think of the force required to move a tuning fork 400 times a second, and compare that with the force required for a motion of 400 million million times a second. If the mass moved is the same, and the range of motion is the same, then the force would be one million million million million times as great as the force required to move the prongs of the tuning fork—it is as easy to understand that number as any number like 2, 3, or 4. Consider now what that number means and what we are to infer from it. What force is there in the space between my eye and that light? What forces are there in the space between our eyes and the sun, and our eyes and the remotest visible star? There is matter and there is motion, but what magnitude of force may there be?
I move through this "luminiferous ether" as if it were nothing. But were there vibrations with such frequency in a medium of steel or brass, they would be measured by millions and millions and millions of tons' action on a square inch of matter. There are no such forces in our air. Comets make a disturbance in the air, and perhaps the luminiferous ether is split up by the motion of a comet through it. So when we explain the nature of electricity, we explain it by a motion of the luminiferous ether. We cannot say that it is electricity. What can this luminiferous ether be? It is something that the planets move through with the greatest ease. It permeates our air; it is nearly in the same condition, so far as our means of judging are concerned, in our air and in the inter-planetary space. The air disturbs it but little; you may reduce air by air-pumps to the hundred thousandth of its density, and you make little effect in the transmission of light through it. The luminiferous ether is an elastic solid, for which the nearest analogy I can give you is this jelly which you see, and the nearest analogy to the waves of light is the motion, which you can imagine, of this elastic jelly, with a ball of wood floating in the middle of it. Look there, when with my hand I vibrate the little red ball up and down, or when I turn it quickly round the vertical diameter, alternately in opposite directions;—that is the nearest representation I can give you of the vibrations of luminiferous ether.
Another illustration is Scottish shoemakers' wax or Burgundy pitch, but I know Scottish shoemakers' wax better. It is heavier than water, and absolutely answers my purpose. I take a large slab of the wax, place it in a glass jar filled with water, place a number of corks on the lower side and bullets on the upper side. It is brittle like the Trinidad pitch or Burgundy pitch which I have in my hand—you can see how hard it is—but when left to itself it flows like a fluid. The shoemakers' wax breaks with a brittle fracture, but it is viscous and gradually yields.
What we know of the luminiferous ether is that it has the rigidity of a solid and gradually yields. Whether or not it is brittle and cracks we cannot yet tell, but I believe the discoveries in electricity and the motions of comets and the marvelous spurts of light from them, tend to show cracks in the luminiferous ether—show a correspondence between the electric flash and the aurora borealis and cracks in the luminiferous ether. Do not take this as an assertion, it is hardly more than a vague scientific dream: but you may regard the existence of the luminiferous ether as a reality of science; that is, we have an all-pervading medium, an elastic solid, with a great degree of rigidity—a rigidity so prodigious in proportion to its density that the vibrations of light in it have the frequencies I have mentioned, with the wavelengths I have mentioned. The fundamental question as to whether or not luminiferous ether has gravity has not been answered. We have no knowledge that the luminiferous ether is attracted by gravity; it is sometimes called imponderable because some people vainly imagine that it has no weight; I call it matter with the same kind of rigidity that this elastic jelly has.
...I cannot speak to you about qualities of light without speaking of the polarization of light. I want to show you a most beautiful effect of polarizing light, before illustrating a little further by means of this large mechanical illustration which you have in the bowl of jelly. ... Now I put in the lantern an instrument called a "Nicol prism...." A Nicol prism is a piece of Iceland spar, cut in two and turned one part relatively to the other in a very ingenious way, and put together again and cemented into one by Canada balsam. The Nicol prism takes advantage of the property which the spar has of double refraction, and produces the phenomenon which I now show you. I turn one prism round in a certain direction and you get light—a maximum of light. I turn it through a right angle and you get blackness. I turn it one quarter round again, and get maximum light; one quarter more, maximum blackness; one quarter more, and bright light. We rarely have a grand specimen of a Nicol prism as this. ... Look at this diagram, the light goes from left to right; we have vibrations perpendicular to the line of transmission. There is a line up and down which is the line of vibration. Imagine here a source of light, violet light, and here in front of it is the line of propagation. Sound-vibrations are to and fro in, this is transverse to, the line of propagation. Here is another, perpendicular to the diagram, still following the law of transverse vibration; here is another, circular vibration. Imagine a long rope, you whirl one end of it and you see a screw-like motion running along, and you can get this circular motion in one direction or in the opposite.
Plane-polarized light is light with the vibrations all in a single plane, perpendicular to the plane through the ray which is technically called the "plane of polarization." Circularly polarized light consists of undulations of luminiferous ether having a circular motion. Elliptically polarized light is something between the two, not in a straight line, and not in a circular line; the course of vibration is an ellipse. Polarized light is light that performs its motions continually in one mode or direction. If in a straight line it is plane-polarized; if in a circular direction it is circularly polarized light; when elliptical it is elliptically polarized light.
With Iceland spar, one unpolarized ray of light divides on entering it into two rays of polarized light, by reason of its power of double refraction, and the vibrations are perpendicular to one another in the two emerging rays. Light is always polarized when it is reflected from a plate of unsilvered glass, or from water, at a certain definite angle of fifty-six degrees for glass, fifty-two degrees for water, the angle being reckoned in each case from a perpendicular to the surface. The angle for water is the angle whose tangent is 1.4. I wish you to look at the polarization with your own eyes. Light from glass at fifty-six degrees and from water at fifty-two degrees goes away vibrating perpendicularly to the plane of incidence and plane of reflection.
We can distinguish it without the aid of an instrument. There is a phenomenon well known in physical optics as "Haidinger's Brushes." ... Look at the sky in a direction of ninety degrees from the sun, and you will see a yellow and blue cross, with the yellow toward the sun, and from the sun, spreading out like two foxes' tails with blue between, and then two red brushes in the space at right angles to the blue. If you do not see it, it is because your eyes are not sensitive enough, but a little training will give them the needed sensitiveness. If you cannot see it in this way try another method. Look into a pail of water with a black bottom; or take a clear glass dish of water, rest it on a black cloth, and look down at the surface of the water on a day with a white cloudy sky (if there is such a thing ever to be seen in Philadelphia). You will see the white sky reflected in the basin of water at an angle of about fifty degrees. Look at it with the head tipped on one side and then again with the head tipped to the other side, keeping your eyes on the water, and you will see Haidinger's brushes. Do not do it fast or you will make yourself giddy. The explanation of this is the refreshing of the sensibility of the retina. The Haidinger's brush is always there, but you do not see it because your eye is not sensitive enough. After once seeing it you always see it; it does not thrust itself inconveniently before you when you do not want to see it. You can also readily see it in a piece of glass with a dark cloth below it, or in a basin of water.
I am going to conclude by telling you how we know the wavelengths of light, and how we know the frequency of the vibrations, and we shall actually make a measurement of the wavelength of yellow light. ...
I can show you an instrument which will measure the wavelengths of light. Without proving the formula, let me tell it to you. A spirit-lamp with salt sprinkled on the wick gives very nearly homogeneous light, that is to say, light of one wavelength, or all of the same period. I have here a little grating which I take in my hand. I look through this grating and see that candle before me. Close behind it you see a blackened slip of wood with two white marks on it ten inches asunder. The line on which they are marked is placed perpendicular to the line at which I shall go from it. When I look at this salted spirit-lamp I see a series of spectrums of yellow light. As I am somewhat short-sighted I am making my eye see with this eye-glass and the natural lenses of the eye what a long-sighted person would make out without an eye-glass. On that screen you saw a succession of spectrums. I now look direct at the candle and what do I see? I see a succession of five or six brilliantly colored spectrums on each side of the candle. But when I look at the salted spirit-lamp, now I see ten spectrums on one side and ten on the other, each of which is a monochromatic band of light.
I will measure the wavelength of the light thus. I walk away to a considerable distance and look at the spirit-lamp and marks. I see a set of spectrums, The first white line is exactly behind the flame. I want the first spectrum to the right of that white line to fall exactly on the other white line, which is ten inches from the first. As I walk away from it I see it is now very near it; it is now on it. Now the distance from my eye is to be measured, and the problem is again to reduce feet to inches. The distance from the spectrum of the flame to my eye is thirty-four feet nine inches. Mr. President, how many inches is that? 417 inches, in round numbers 420 inches. Then we have the proportion, as 420 is to 10 so is the length from bar to bar of the grating to the wavelength of sodium light. That is to say as forty-two is to one. The distance from bar to bar is the four hundredth of a centimeter: therefore the forty-second part of the four hundredth of a centimeter is the wavelength according to our simple, and easy and hasty experiment. The true wavelength of sodium light, according to the most accurate measurement, is about a 17,000th of a centimeter, which differs by scarcely more than one percent from our result!
The only apparatus you see is this little grating—a piece of glass having a space four-tenths of an inch wide ruled with 400 fine lines. Any of you who will take the trouble to buy one may measure the wavelength of a candle flame himself. I hope some of you will be induced to make the experiment for yourselves.
If I put salt on the flame of a spirit-lamp, what do I see through this grating? I see merely a sharply defined yellow light, constituting the spectrum of vaporized sodium, while from the candle flame I see an exquisitely colored spectrum, far more beautiful than that I showed you on the screen. I see in fact a series of spectrums on the two sides with the blue toward the candle flame and the red further out. I cannot get one definite thing to measure from in the spectrum from the candle flame, as I can with the flame of a spirit-lamp with the salt thrown on it, which gives as I have said a simple yellow light. The highest blue light I see in the candle flame is now exactly on the line. Now measure to my eye, it is forty-four feet four inches, or 532 inches. The length of this wave then is the 532d part of the four hundredth of a centimeter which would be the 21,280th of a centimeter, say the 21,000th of a centimeter. Then measure for the red and you will find something like the 11,000th for the lowest of the red light.
Lastly, how do we know the frequency of vibration?
Why, by the velocity of light. How do we know that? We know it in a number of different ways, which I cannot explain now because time forbids, and I can now only tell you shortly that the frequency of vibration for any particular ray is equal to the velocity of light divided by the wavelength for that ray. The velocity of light is about...300,000 kilometers, or 30,000,000,000 centimeters, per second. Take now the wavelength of sodium light, as we have just measured it by means of the salted spirit-lamp, to be one 17,000th of a centimeter, and we find the frequency of vibration of the sodium light to be 510 million million per second. There, then, you have a calculation of the frequency from a simple observation which you all can make for yourselves.
Lastly, I must tell you about the color of the blue sky which is illustrated by this spherule imbedded in an elastic solid. I want to explain to you in two minutes the mode of vibration. Take the simplest plane-polarized light. Here is a spherule which is producing it in an elastic solid. Imagine the solid to extend miles horizontally and miles up and down, and imagine this spherule to vibrate up and down. It is quite clear that it will make transverse vibrations similarly in all horizontal directions. The plane of polarization is defined as a plane perpendicular to the line of vibration. Thus, light produced by a molecule vibrating up and down, as this red glove in the jelly before you, is polarized in a horizontal plane because the vibrations are vertical.
Here is another mode of vibration. Let me twist this spherule in the jelly as I am now doing, and that will produce vibrations, also spreading out equally in all horizontal directions. When I twist this glove round it draws the jelly round with it; twist it rapidly back and the jelly flies back. By the inertia of the jelly the vibrations spread in all directions and the lines of vibration are horizontal all through the jelly. Everywhere, miles away that solid is placed in vibration. You do not see the vibrations, but you must understand that they are there. If it flies back it makes vibration, and we have waves of horizontal vibrations traveling out in all directions from the exciting molecule.
I am now causing the red glove to vibrate to and fro horizontally. That will cause vibrations to be produced which will be parallel to the line of motion at all places of the plane perpendicular to the range of the exciting molecule. What makes the blue sky? These are exactly the motions that make the blue light of the sky, which is due to spherules in the luminiferous ether, but little modified by the air. Think of the sun near the horizon, think of the light of the sun streaming through and giving you the azure blue and violet overhead. Think first of any one particle and think of it moving in such a way as to give horizontal and vertical vibrations and circular and elliptic vibrations.
You see the blue sky in high pressure steam blown into the air; you see it in the experiment of Tyndall's blue sky in which a delicate condensation of vapor gives rise to exactly the azure blue of the sky.
Now the motion of the luminiferous ether relatively to the spherule gives rise to the same effect as would an opposite motion impressed upon the spherule quite independently by an independent force. So you may think of the blue color coming from the sky as being produced by to and fro vibrations of matter in the air, which vibrates much as this little glove vibrates imbedded in the jelly.
The result in a general way is this: The light coming from the blue sky is polarized in a plane through the sun, but the blue light of the sky is complicated by a great number of circumstances and one of them is this, that the air is illuminated not only by the sun but by the earth. If we could get the earth covered by a black cloth then we could study the polarized light of the sky with a simplicity which we cannot do now. There are, in nature, reflections from the seas and rocks and hills and waters in an infinitely complicated manner.
Let observers observe the blue sky not only in winter when the earth is covered with snow, but in summer when it is covered with dark green foliage. This will help to unravel the complicated phenomena in question. But the azure blue of the sky is light produced by the reaction on the vibrating ether of little spherules of water, of perhaps a fifty thousandth or a hundred thousandth of a centimeter diameter, or perhaps little motes, or lumps, or crystals of common salt, or particles of dust, or germs of vegetable or animal species wafted about in the air. Now what is the luminiferous ether? It is matter prodigiously less dense than air—millions and millions and millions of times less dense than air. We can form some sort of idea of its limitations. We believe it is a real thing, with great rigidity in comparison with its density: it may be made to vibrate 400 million million times per second; and yet be of such density as not to produce the slightest resistance to any body going through it.
Going back to the illustration of the shoemakers' wax; if a cork will, in the course of a year, push its way up through a plate of that wax when placed under water, and if a lead bullet will penetrate downwards to the bottom, what is the law of the resistance? It clearly depends on time. The cork slowly in the course of a year works its way up through two inches of that substance; give it one or two thousand years to do it and the resistance will be enormously less; thus the motion of a cork or bullet, at the rate of one inch in 2,000 years, may be compared with that of the earth, moving at the rate of six times ninety-three million miles a year, or nineteen miles per second, through the luminiferous ether; but when we can have actually before us a thing elastic like jelly and yielding like pitch, surely we have a large and solid ground for our faith in the speculative hypothesis of an elastic luminiferous ether, which constitutes the wave theory of light.
About the author:
1824-1907. William Thomson, Baron Kelvin of Largs, was born in Belfast, Ireland to the professor of mathematics at Glasgow University. Thomson himself attended Glasgow University. After graduating from Cambridge at twenty-one, and after further studying in Paris, he returned to Glasgow as a professor of natural philosophy. His contributions to the sciences are vast and varied, recognized by fame and by numerous awards across his lifetime. His efforts in physics greatly aided its unification into its modern form. His contributions to the Atlantic Cable led to his knighthood in 1866. In 1892 he was raised to the peerage. He held his professorship at Glasgow for fifty-three years, eventually chosen its Chancellor. He is buried in Westminster Abbey.
Learn more about Sir William Thomson at Wikipedia.