Six Lectures on Light Part 2

LECTURE II.

ORIGIN OF PHYSICAL THEORIES SCOPE OF THE IMAGINATION NEWTON AND THE EMISSION THEORY VERIFICATION OF PHYSICAL THEORIES THE LUMINIFEROUS ETHER WAVE THEORY OF LIGHT THOMAS YOUNG FRESNEL AND ARAGO CONCEPTION OF WAVE-MOTION INTERFERENCE OF WAVES CONSt.i.tUTION OF SOUND-WAVES a.n.a.lOGIES OF SOUND AND LIGHT ILl.u.s.tRATIONS OF WAVE-MOTION INTERFERENCE OF SOUND-WAVES OPTICAL ILl.u.s.tRATIONS PITCH AND COLOUR LENGTHS OF THE WAVES OF LIGHT AND RATES OF VIBRATION OF THE ETHER-PARTICLES INTERFERENCE OF LIGHT PHENOMENA WHICH FIRST SUGGESTED THE UNDULATORY THEORY BOYLE AND HOOKE THE COLOURS OF THIN PLATES THE SOAP-BUBBLE NEWTON'S RINGS THEORY OF 'FITS'

ITS EXPLANATION OF THE RINGS OVER-THROW OF THE THEORY DIFFRACTION OF LIGHT COLOURS PRODUCED BY DIFFRACTION COLOURS OF MOTHER-OF-PEARL.

-- 1. _Origin and Scope of Physical Theories_.

We might vary and extend our experiments on Light indefinitely, and they certainly would prove us to possess a wonderful mastery over the phenomena. But the vesture of the agent only would thus be revealed, not the agent itself. The human mind, however, is so const.i.tuted that it can never rest satisfied with this outward view of natural things.

Brightness and freshness take possession of the mind when it is crossed by the light of principles, showing the facts of Nature to be organically connected.

Let us, then, inquire what this thing is that we have been generating, reflecting, refracting and a.n.a.lyzing.

In doing this, we shall learn that the life of the experimental philosopher is twofold. He lives, in his vocation, a life of the senses, using his hands, eyes, and ears in his experiments: but such a question as that now before us carries him beyond the margin of the senses. He cannot consider, much less answer, the question, 'What is light?' without transporting himself to a world which underlies the sensible one, and out of which all optical phenomena spring. To realise this subsensible world the mind must possess a certain pictorial power. It must be able to form definite images of the things which that world contains; and to say that, if such or such a state of things exist in the subsensible world, then the phenomena of the sensible one must, of necessity, grow out of this state of things.

Physical theories are thus formed, the truth of which is inferred from their power to explain the known and to predict the unknown.

This conception of physical theory implies, as you perceive, the exercise of the imagination--a word which seems to render many respectable people, both in the ranks of science and out of them, uncomfortable. That men in the ranks of science should feel thus is, I think, a proof that they have suffered themselves to be misled by the popular definition of a great faculty, instead of observing its operation in their own minds. Without imagination we cannot take a step beyond the bourne of the mere animal world, perhaps not even to the edge of this one. But, in speaking thus of imagination, I do not mean a riotous power which deals capriciously with facts, but a well-ordered and disciplined power, whose sole function is to form such conceptions as the intellect imperatively demands. Imagination, thus exercised, never really severs itself from the world of fact.

This is the storehouse from which its materials are derived; and the magic of its art consists, not in creating things anew, but in so changing the magnitude, position, grouping, and other relations of sensible things, as to render them fit for the requirements of the intellect in the subsensible world.[9]

Descartes imagined s.p.a.ce to be filled with something that transmitted light _instantaneously_. Firstly, because, in his experience, no measurable interval was known to exist between the appearance of a flash of light, however distant, and its effect upon consciousness; and secondly, because, as far as his experience went, no physical power is conveyed from place to place without a vehicle. But his imagination helped itself farther by ill.u.s.trations drawn from the world of fact. 'When,' he says,' one walks in darkness with staff in hand, the moment the distant end of the staff strikes an obstacle the hand feels it. This explains what might otherwise be thought strange, that the light reaches us instantaneously from the sun. I wish thee to believe that light in the bodies that we call luminous is nothing more than a very brisk and violent motion, which, by means of the air and other transparent media, is conveyed to the eye, exactly as the shock through the walking-stick reaches the hand of a blind man. This is instantaneous, and would be so even if the intervening distance were greater than that between earth and heaven. It is therefore no more necessary that anything material should reach the eye from the luminous object, than that something should be sent from the ground to the hand of the blind man when he is conscious of the shock of his staff.' The celebrated Robert Hooke at first threw doubt upon this notion of Descartes, but he afterwards substantially espoused it. The belief in instantaneous transmission was destroyed by the discovery of Roemer referred to in our last lecture.

-- 2. _The Emission Theory of Light_.

The case of Newton still more forcibly ill.u.s.trates the position, that in forming physical theories we draw for our materials upon the world of fact. Before he began to deal with light, he was intimately acquainted with the laws of elastic collision, which all of you have seen more or less perfectly ill.u.s.trated on a billiard-table. As regards the collision of sensible elastic ma.s.ses, Newton knew the angle of incidence to be equal to the angle of reflection, and he also knew that experiment, as shown in our last lecture (fig. 3), had established the same law with regard to light. He thus found in his previous knowledge the material for theoretic images. He had only to change the magnitude of conceptions already in his mind to arrive at the Emission Theory of Light. Newton supposed light to consist of elastic particles of inconceivable minuteness, shot out with inconceivable rapidity by luminous bodies. Optical reflection certainly occurred _as if_ light consisted of such particles, and this was Newton's justification for introducing them.

But this is not all. In another important particular, also, Newton's conceptions regarding the nature of light were influenced by his previous knowledge. He had been pondering over the phenomena of gravitation, and had made himself at home amid the operations of this universal power. Perhaps his mind at this time was too freshly and too deeply imbued with these notions to permit of his forming an unfettered judgment regarding the nature of light. Be that as it may, Newton saw in Refraction the result of an attractive force exerted on the light-particles. He carried his conception out with the most severe consistency. Dropping vertically downwards towards the earth's surface, the motion of a body is accelerated as it approaches the earth. Dropping downwards towards a horizontal surface--say from air on to gla.s.s or water--the velocity of the light-particles, when they came close to the surface, is, according to Newton, also accelerated.

Approaching such a surface obliquely, he supposed the particles, when close to it, to be drawn down upon it, as a projectile is deflected by gravity to the surface of the earth. This deflection was, according to Newton, the refraction seen in our last lecture (fig. 4). Finally, it was supposed that differences of colour might be due to differences in the 'bigness' of the particles. This was the physical theory of light enunciated and defended by Newton; and you will observe that it simply consists in the transference of conceptions, born in the world of the senses, to a subsensible world.

But, though the region of physical theory lies thus behind the world of senses, the verifications of theory occur in that world. Laying the theoretic conception at the root of matters, we determine by deduction what are the phenomena which must of necessity grow out of this root.

If the phenomena thus deduced agree with those of the actual world, it is a presumption in favour of the theory. If, as new cla.s.ses of phenomena arise, they also are found to harmonise with theoretic deduction, the presumption becomes still stronger. If, finally, the theory confers prophetic vision upon the investigator, enabling him to predict the occurrence of phenomena which have never yet been seen, and if those predictions be found on trial to be rigidly correct, the persuasion of the truth of the theory becomes overpowering.

Thus working backwards from a limited number of phenomena, the human mind, by its own expansive force, reaches a conception which covers them all. There is no more wonderful performance of the intellect than this; but we can render no account of it. Like the scriptural gift of the Spirit, no man can tell whence it cometh. The pa.s.sage from fact to principle is sometimes slow, sometimes rapid, and at all times a source of intellectual joy. When rapid, the pleasure is concentrated, and becomes a kind of ecstasy or intoxication. To any one who has experienced this pleasure, even in a moderate degree, the action of Archimedes when he quitted the bath, and ran naked, crying 'Eureka!'

through the streets of Syracuse, becomes intelligible.

How, then, did it fare with the Emission Theory when the deductions from it were brought face to face with natural phenomena? Tested by experiment, it was found competent to explain many facts, and with transcendent ingenuity its author sought to make it account for all.

He so far succeeded, that men so celebrated as Laplace and Malus, who lived till 1812, and Biot and Brewster, who lived till our own time, were found among his disciples.

-- 3. _The Undulatory Theory of Light_.

Still, even at an early period of the existence of the Emission Theory, one or two great men were found espousing a different one.

They furnish another ill.u.s.tration of the law that, in forming theories, the scientific imagination must draw its materials from the world of fact and experience. It was known long ago that sound is conveyed in waves or pulses through the air; and no sooner was this truth well housed in the mind than it became the basis of a theoretic conception. It was supposed that light, like sound, might also be the product of wave-motion. But what, in this case, could be the material forming the waves? For the waves of sound we have the air of our atmosphere; but the stretch of imagination which filled all s.p.a.ce with a _luminiferous ether_ trembling with the waves of light was so bold as to shock cautious minds. In one of my latest conversations with Sir David Brewster, he said to me that his chief objection to the undulatory theory of light was, that he could not think the Creator capable of so clumsy a contrivance as the filling of s.p.a.ce with ether to produce light. This, I may say, is very dangerous ground, and the quarrel of science with Sir David, on this point as with many estimable persons on other points, is, that they profess to know too much about the mind of the Creator.

This conception of an ether was advocated, and successfully applied to various phenomena of optics, by the ill.u.s.trious astronomer, Huyghens.

He deduced from it the laws of reflection and refraction, and applied it to explain the double refraction of Iceland spar. The theory was espoused and defended by the celebrated mathematician, Euler. They were, however, opposed by Newton, whose authority at the time bore them down. Or shall we say it was authority merely? Not quite so.

Newton's preponderance was in some degree due to the fact that, though Huyghens and Euler were right in the main, they did not possess sufficient data to _prove_ themselves right. No human authority, however high, can maintain itself against the voice of Nature speaking through experiment. But the voice of Nature may be an uncertain voice, through the scantiness of data. This was the case at the period now referred to, and at such a period, by the authority of Newton, all antagonists were naturally overborne.

The march of mind is rhythmic, not uniform, and this great Emission Theory, which held its ground so long, resembled one of those circles which, according to your countryman Emerson, the intermittent force of genius periodically draws round the operations of the intellect, but which are eventually broken through by pressure from behind. In the year 1773 was born, at Milverton, in Somersetshire, a circle-breaker of this kind. He was educated for the profession of a physician, but was too strong to be tied down to professional routine. He devoted himself to the study of natural philosophy, and became in all its departments a master. He was also a master of letters. Languages, ancient and modern, were housed within his brain, and, to use the words of his epitaph, 'he first penetrated the obscurity which had veiled for ages the hieroglyphics of Egypt.' It fell to the lot of this man to discover facts in optics which Newton's theory was incompetent to explain, and his mind roamed in search of a sufficient theory. He had made himself acquainted with all the phenomena of wave-motion; with all the phenomena of sound; working successfully in this domain as an original discoverer. Thus informed and disciplined, he was prepared to detect any resemblance which might reveal itself between the phenomena of light and those of wave-motion. Such resemblances he did detect; and, spurred on by the discovery, he pursued his speculations and experiments, until he finally succeeded in placing on an immovable basis the Undulatory Theory of Light.

The founder of this great theory was Thomas Young, a name, perhaps, unfamiliar to many of you, but which ought to be familiar to you all.

Permit me, therefore, by a kind of geometrical construction which I once ventured to employ in London, to give you a notion of the magnitude of this man. Let Newton stand erect in his age, and Young in his. Draw a straight line from Newton to Young, tangent to the heads of both. This line would slope downwards from Newton to Young, because Newton was certainly the taller man of the two. But the slope would not be steep, for the difference of stature was not excessive.

The line would form what engineers call a gentle gradient from Newton to Young. Place underneath this line the biggest man born in the interval between both. It may be doubted whether he would reach the line; for if he did he would be taller intellectually than Young, and there was probably none taller. But I do not want you to rest on English estimates of Young; the German, Helmholtz, a kindred genius, thus speaks of him: "His was one of the most profound minds that the world has ever seen; but he had the misfortune to be too much in advance of his age. He excited the wonder of his contemporaries, who, however, were unable to follow him to the heights at which his daring intellect was accustomed to soar. His most important ideas lay, therefore, buried and forgotten in the folios of the Royal Society, until a new generation gradually and painfully made the same discoveries, and proved the exactness of his a.s.sertions and the truth of his demonstrations."

It is quite true, as Helmholtz says, that Young was in advance of his age; but something is to be added which ill.u.s.trates the responsibility of our public writers. For twenty years this man of genius was quenched--hidden from the appreciative intellect of his country-men--deemed in fact a dreamer, through the vigorous sarcasm of a writer who had then possession of the public ear, and who in the _Edinburgh Review_ poured ridicule upon Young and his speculations. To the celebrated Frenchmen Fresnel and Arago he was first indebted for the rest.i.tution of his rights; for they, especially Fresnel, independently remade and vastly extended his discoveries. To the students of his works Young has long since appeared in his true light, but these twenty blank years pushed him from the public mind, which became in time filled with the fame of Young's colleague at the Royal Inst.i.tution, Davy, and afterwards with the fame of Faraday. Carlyle refers to a remark of Novalis, that a man's self-trust is enormously increased the moment he finds that others believe in him. If the opposite remark be true--if it be a fact that public disbelief weakens a man's force--there is no calculating the amount of damage these twenty years of neglect may have done to Young's productiveness as an investigator. It remains to be stated that his a.s.sailant was Mr. Henry Brougham, afterwards Lord Chancellor of England.

-- 4. _Wave-Motion, Interference of Waves, 'Whirlpool Rapids' of Niagara_.

Our hardest work is now before us. But the capacity for hard work depends in a great measure on the antecedent winding up of the will; I would call upon you, therefore, to gird up your loins for coming labours.

In the earliest writings of the ancients we find the notion that sound is conveyed by the air. Aristotle gives expression to this notion, and the great architect Vitruvius compares the waves of sound to waves of water. But the real mechanism of wave-motion was hidden from the ancients, and indeed was not made clear until the time of Newton. The central difficulty of the subject was, to distinguish between the motion of the wave itself, and the motion of the particles which at any moment const.i.tute the wave.

Stand upon the seash.o.r.e and observe the advancing rollers before they are distorted by the friction of the bottom. Every wave has a back and a front, and, if you clearly seize the image of the moving wave, you will see that every particle of water along the front of the wave is in the act of rising, while every particle along its back is in the act of sinking. The particles in front reach in succession the crest of the wave, and as soon as the crest is past they begin to fall. They then reach the furrow or _sinus_ of the wave, and can sink no farther.

Immediately afterwards they become the front of the succeeding wave, rise again until they reach the crest, and then sink as before. Thus, while the waves pa.s.s onwards horizontally, the individual particles are simply lifted up and down vertically. Observe a sea-fowl, or, if you are a swimmer, abandon yourself to the action of the waves; you are not carried forward, but simply rocked up and down. The propagation of a wave is the propagation of a _form_, and not the transference of the substance which const.i.tutes the wave.

The _length_ of the wave is the distance from crest to crest, while the distance through which the individual particles oscillate is called the _amplitude_ of the oscillation. You will notice that in this description the particles of water are made to vibrate _across_ the line of propagation.[10]

And now we have to take a step forwards, and it is the most important step of all. You can picture two series of waves proceeding from different origins through the same water. When, for example, you throw two stones into still water, the ring-waves proceeding from the two centres of disturbance intersect each other. Now, no matter how numerous these waves may be, the law holds good that the motion of every particle of the water is the algebraic sum of all the motions imparted to it. If crest coincide with crest and furrow with furrow, the wave is lifted to a double height above its sinus; if furrow coincide with crest, the motions are in opposition and their sum is zero. We have then _still_ water. This action of wave upon wave is technically called _interference_, a term, to be remembered.

To the eye of a person conversant with these principles, nothing can be more interesting than the crossing of water ripples. Through their interference the water-surface is sometimes shivered into the most beautiful mosaic, trembling rhythmically as if with a kind of visible music. When waves are skilfully generated in a dish of mercury, a strong light thrown upon the shining surface, and reflected on to a screen, reveals the motions of the liquid metal. The shape of the vessel determines the forms of the figures produced. In a circular dish, for example, a disturbance at the centre propagates itself as a series of circular waves, which, after reflection, again meet at the centre. If the point of disturbance be a little way removed from the centre, the interference of the direct and reflected waves produces the magnificent chasing shown in the annexed figure.[11] The light reflected from such a surface yields a pattern of extraordinary beauty. When the mercury is slightly struck by a needle-point in a direction concentric with the surface of the vessel, the lines of light run round in mazy coils, interlacing and unravelling themselves in a wonderful manner. When the vessel is square, a splendid chequer-work is produced by the crossing of the direct and reflected waves. Thus, in the case of wave-motion, the most ordinary causes give rise to most exquisite effects. The words of Emerson are perfectly applicable here:--

[Ill.u.s.tration: Fig. 10.]

'Thou can'st not wave thy staff in the air, Or dip thy paddle in the lake, But it carves the brow of beauty there.

And the ripples in rhymes the oars forsake.'

The most impressive ill.u.s.tration of the action of waves on waves that I have ever seen occurs near Niagara. For a distance of two miles, or thereabouts, below the Falls, the river Niagara flows unruffled through its excavated gorge. The bed subsequently narrows, and the water quickens its motion. At the place called the 'Whirlpool Rapids,'

I estimated the width of the river at 300 feet, an estimate confirmed by the dwellers on the spot. When it is remembered that the drainage of nearly half a continent is compressed into this s.p.a.ce, the impetuosity of the river's escape through this gorge may be imagined.

Two kinds of motion are here obviously active, a motion of translation and a motion of undulation--the race of the river through its gorge, and the great waves generated by its collision with the obstacles in its way. In the middle of the stream, the rush and tossing are most violent; at all events, the impetuous force of the individual waves is here most strikingly displayed. Vast pyramidal heaps leap incessantly from the river, some of them with such energy as to jerk their summits into the air, where they hang suspended as bundles of liquid pearls, which, when shone upon by the sun, are of indescribable beauty.

The first impression, and, indeed, the current explanation of these Rapids is, that the central bed of the river is c.u.mbered with large boulders, and that the jostling, tossing, and wild leaping of the waters there are due to its impact against these obstacles. A very different explanation occurred to me upon the spot. Boulders derived from the adjacent cliffs visibly c.u.mber the _sides_ of the river.

Against these the water rises and sinks rhythmically but violently, large waves being thus produced. On the generation of each wave there is an immediate compounding of the wave-motion with the river-motion.

The ridges, which in still water would proceed in circular curves round the centre of disturbance, cross the river obliquely, and the result is, that at the centre waves commingle which have really been generated at the sides. This crossing of waves may be seen on a small scale in any gutter after rain; it may also be seen on simply pouring water from a wide-lipped jug. Where crest and furrow cross each other, the wave is annulled; where furrow and furrow cross, the river is ploughed to a greater depth; and where crest and crest aid each other, we have that astonishing leap of the water which breaks the cohesion of the crests, and tosses them shattered into the air. The phenomena observed at the Whirlpool Rapids const.i.tute, in fact, one of the grandest ill.u.s.trations of the principle of interference.

-- 5. _a.n.a.logies of Sound and Light._

Thomas Young's fundamental discovery in optics was that the principle of Interference was applicable to light. Long prior to his time an Italian philosopher, Grimaldi, had stated that under certain circ.u.mstances two thin beams of light, each of which, acting singly, produced a luminous spot upon a white wall, when caused to act together, partially quenched each other and darkened the spot. This was a statement of fundamental significance, but it required the discoveries and the genius of Young to give it meaning. How he did so will gradually become clear to you. You know that air is compressible: that by pressure it can be rendered more dense, and that by dilatation it can be rendered more rare. Properly agitated, a tuning-fork now sounds in a manner audible to you all, and most of you know that the air through which the sound is pa.s.sing is parcelled out into s.p.a.ces in which the air is condensed, followed by other s.p.a.ces in which the air is rarefied. These condensations and rarefactions const.i.tute what we call _waves_ of sound. You can imagine the air of a room traversed by a series of such waves, and you can imagine a second series sent through the same air, and so related to the first that condensation coincides with condensation and rarefaction with rarefaction. The consequence of this coincidence would be a louder sound than that produced by either system of waves taken singly. But you can also imagine a state of things where the condensations of the one system fall upon the rarefactions of the other system. In this case (other things being equal) the two systems would completely neutralize each other. Each of them taken singly produces sound; both of them taken together produce no sound. Thus by adding sound to sound we produce silence, as Grimaldi, in his experiment, produced darkness by adding light to light.

Through his investigations on sound, which were fruitful and profound, Young approached the study of light. He put meaning into the observation of Grimaldi, and immensely extended it. With splendid success he applied the undulatory theory to the explanation of the colours of thin plates, and to those of striated surfaces. He discovered and explained cla.s.ses of colour which had been previously unnoticed or unknown. On the a.s.sumption that light was wave-motion, all his experiments on interference were accounted for; on the a.s.sumption that light was flying particles, nothing was explained. In the time of Huyghens and Euler a medium had been a.s.sumed for the transmission of the waves of light; but Newton raised the objection that, if light consisted of the waves of such a medium, shadows could not exist. The waves, he contended, would bend round opaque bodies and produce the motion of light behind them, as sound turns a corner, or as waves of water wash round a rock. It was proved that the bending round referred to by Newton actually occurs, but that the inflected waves abolish each other by their mutual interference. Young also discerned a fundamental difference between the waves of light and those of sound. Could you see the air through which sound-waves are pa.s.sing, you would observe every individual particle of air oscillating to and fro, _in the direction of propagation_. Could you see the luminiferous ether, you would also find every individual particle making a small excursion to and fro; but here the motion, like that a.s.signed to the water-particles above referred to, would be _across_ the line of propagation. The vibrations of the air are _longitudinal_, those of the ether _transversal_.

The most familiar ill.u.s.tration of the interference of sound-waves is furnished by the _beats_ produced by two musical sounds slightly out of unison. When two tuning-forks in perfect unison are agitated together the two sounds flow without roughness, as if they were but one. But, by attaching with wax to one of the forks a little weight, we cause it to vibrate more slowly than its neighbour. Suppose that one of them performs 101 vibrations in the time required by the other to perform 100, and suppose that at starting the condensations and rarefactions of both forks coincide. At the 101st vibration of the quicker fork they will again coincide, that fork at this point having gained one whole vibration, or one whole wavelength, upon the other.

But a little reflection will make it clear that, at the 50th vibration, the two forks condensation where the other tends to produce a rarefaction; by the united action of the two forks, therefore, the sound is quenched, and we have a pause of silence. This occurs where one fork has gained _half a wavelength_ upon the other. At the 101st vibration, as already stated, we have coincidence, and, therefore, augmented sound; at the 150th vibration we have again a quenching of the sound. Here the one fork is _three half-waves_ in advance of the other. In general terms, the waves conspire when the one series is an _even_ number of half-wave lengths, and they destroy each other when the one series is an _odd_ number of half-wave lengths in advance of the other. With two forks so circ.u.mstanced, we obtain those intermittent shocks of sound separated by pauses of silence, to which we give the name of beats. By a suitable arrangement, moreover, it is possible to make one sound wholly extinguish another. Along four distinct lines, for example, the vibrations of the two p.r.o.ngs of a tuning-fork completely blot each other out.[12]

The _pitch_ of sound is wholly determined by the rapidity of the vibration, as the _intensity_ is by the amplitude. What pitch is to the ear in acoustics, colour is to the eye in the undulatory theory of light. Though never seen, the lengths of the waves of light have been determined. Their existence is proved _by their effects_, and from their effects also their lengths may be accurately deduced. This may, moreover, be done in many ways, and, when the different determinations are compared, the strictest harmony is found to exist between them.