<193>

CHAPTER IX.

NEWTON'S DISCOVERIES ON THE INFLEXION OF LIGHT — PREVIOUS RESEARCHES OF HOOKE — NEWTON'S ANIMADVERSIONS ON THEM OFFENSIVE TO HOOKE — NEWTON'S THEORY OF INFLEXION AS DESCRIBED BY GRIMALDI, HAVING MADE NO EXPERIMENTS OF HIS OWN — DISCOVERIES OF GRIMALDI, WHICH ANTICIPATE THOSE OF HOOKE — HOOKE SUGGESTS THE DOCTRINE OF INTERFERENCE — NEWTON'S EXPERIMENTS ON INFLEXION — HIS VIEWS UPON THE SUBJECT UNSETTLED — MODERN RESEARCHES — DR. YOUNG DISCOVERS THE LAW OF INTERFERENCE — DISCOVERIES OF FRESNEL AND ARAGO — FRAUNHOFER'S EXPERIMENTS — DIFFRACTION BY GROOVED SURFACES — DIFFRACTION BY TRANSPARENT LINES — PHENOMENA OF NEGATIVE DIFFRACTION — EXPERIMENTS AND DISCOVERIES OF LORD BROUGHAM — EXPLANATION OF DIFFRACTION BY THE UNDULATORY THEORY.

Among the optical discoveries of Newton, those which he made on the inflexion of light hold a high place. They were first published in his Treatise on Optics in 1704, but we have not been able to ascertain at what period they were made. In the preface to this work, Sir Isaac informs us, that the third book, which contains his experiments on inflexion,"was put together out of scattered papers;" and he adds, at the end of his observations, that "he designed to repeat most of them with more care and exactness, and to make some new ones for determining the manner how the rays of light are bent in their passage by bodies for making the fringes of colours with the dark lines between them. But we were then interrupted, and cannot now think of taking these things into consideration."

The earliest notice of the inflexion of light by English <194> philosophers was taken by Dr. Hooke in a discourse read to the Royal Society on the 27th November 1672, "containing diverse optical trials made by himself, which seemed to discover some new properties of light, and to exhibit several phenomena in his opinion not ascribable to reflexion or refraction, or any other till then known properties of light." The Society desired him to pursue these experiments, and to register some account of them, in order "to preserve his discoveries from being usurped."

After an interval of more than two years, he communicated to the Society a second discourse "on the nature and properties of light, in which were contained several new properties of light, not observed that he knew of by optical writers." These properties were, —

"1. That there is an inflexion of light differing both from refraction and reflexion, and seeming to depend upon the unequal density of the constituent parts of the ray, whereby the light is dispersed from the place of condensation, and rarefied, or gradually diverged into a quadrant.

"2. That this deflexion is made towards the superficies of the opaque body perpendicularly.

"3. That in this deflexion of the rays, those parts of diverged radiation that are deflected by the greatest angle from the strait or direct radiations are faintest; those that are deflected by the least are the strongest.

"4. That rays cutting each other in one common foramen, do not make the angles ad verticem equal.

5. That colours may be made without refraction.

6. That the true bigness of the sun's diameter cannot be taken with common sights.

"7. That the same rays of light falling upon the same point of the object will turn into all sorts of colours, only by the various inclination of the object.

<195>

"8. That colours begin to appear when two pulses of light are blended so very well and near together, that the sense takes them for one."[1]

These observations of Hooke on the Inflexion of Light, were referred to, not very courteously, by Sir Isaac Newton, at the close of the celebrated Discourse on Colours, of which we have already given an account. After treating of the colours of natural bodies, he says, "that there is another strange phenomenon of colours which may deserve to be taken notice of Mr. Hooke," he adds, "you may remember, was speaking of an odd straying of light, caused in its passage near the edge of a razor, knife, or other opaque body, in a dark room; the rays which pass very near the edge being thereby made to stray at all angles into the shadow of the knife. To this Sir William Petty, then President, returned a very pertinent query, Whether that straying was in curve lines? and that made me (having heard Mr. Hooke, some days before, compare it to the straying of sound into the quiescent medium) say, that I took it to be only a new kind of refraction, caused perhaps by the external ether's beginning to grow rarer a little before it came at the opaque body, than it was in free spaces, the denser ether without the body, and the rarer within it, being terminated not in a mathematical superficies, but passing into one another through all intermediate degrees of density; whence the rays that pass so near the body, as to come within that compass where the outward ether begins to grow rarer, must be refracted by the uneven denseness thereof, and bended inwards towards the rarer medium of the body. To this Mr. Hooke was then pleased to answer, <196> that though it should be but a new kind of refraction, yet it was a new one. What to make of this unexpected reply I knew not, — having no other thoughts but that a new kind of refraction might be as noble an invention as any thing else about light; but it made me afterwards, I know not upon what occasion, happen to say, among some who were present to what passed before, that I thought I had seen the experiment before in some Italian author. And the author is Honoratus Faber, in his dialogue De Lumine, who had it from Grimaldi, whom I mention because I am to describe something further out of him."

This passage, which must have been very offensive to Hooke, may be fairly adduced as affording an additional apology for his statement that Newton had, in his Discourse, only carried farther, in some particulars, what was contained in his Micrographia. We have no doubt that Hooke discovered the inflexion of light, without knowing any thing of the previous experiments of Grimaldi. Hooke was right in calling his discovery a new property of light, and Newton was wrong in calling it "only a new kind of refraction," — thus stripping it of much of its value, and placing it ill the same category with his own discoveries. Hooke felt the bitterness of the remark, and with more temper than might have been expected, replied, "that though it should be but a new kind of refraction, yet it was a new one;" thus taking to himself the credit of making a new discovery even when reduced in importance by its new designation. Newton confesses that he knew not what to make of this unexpected reply. The reply was a proper one, and might have been expected; but though Newton felt its full significance, he had not the readiness to make the explanation which it required, <197> and which he subsequently gave. He had no thoughts, he afterwards said, of undervaluing the discovery of a property of light by calling it "a new kind of refraction;" yet he did not give this explanation till he had ascertained that the new property had been previously discovered by Grimaldi; and though he now gave its true value to the new discovery, he but embittered the admission when he announced to the Society, that the discovery belonged to an Italian philosopher. On a former occasion Newton had unnecessarily claimed for Descartes some of Hooke's theoretical opinions; and when a similar claim was made for Grimaldi, Hooke could not but feel the unkindness of his rival. Nearly two centuries have elapsed since these controversies raged; and it is not without its moral in intellectual strife, nor yet without its consolation to the humbler cultivators of science, that while Newton's Theory of the Inflexion of Light is maintained by nobody, the theory of Hooke, imperfect as it is, is adopted by the greater number of modern philosophers.

It is obvious from these details, that Newton had at this time made no important experiments on the Inflexion of Light. "He propounded his theory with diffidence," is he had "not made sufficient observation about it." It is equally obvious that he had not seen the work of Grimaldi,[2] which he quoted from Honoratus Faber, although a copy of the work had been three years in the possession of the Royal Society, or at least of their secretary, Mr. Oldenburg, who published an analysis of it in the Philosophical Transactions for January 22, 1671-72. The analysis, indeed, is a very imperfect one, in so far as it refers to the diffraction of light, and could scarcely have <198> led Hooke to his discovery, even if he had perused it with attention. "The author," says the reviewer, "explains how many ways light is propagated or diffused, viz., not only directly, and by refraction and reflexion, but also by diffraction; which last, according to him, is done when the parts of light, separated by a manifold dissection, do in the same medium proceed in different ways," — a definition of diffraction which Newton could scarcely have comprehended, and which, if he had, he would not have accepted.

That Newton had not seen Grimaldi's work in 1675, is avowed by himself; and there is every reason to believe that he had not even seen it in 1704, when he published his Optics. If he had seen it, and was aware of the discoveries which it contains, he has not only done great injustice to the Italian philosopher, but neglected the opportunity which it afforded him of anticipating the discoveries of his successors. In the third book of his Optics, he gives to Grimaldi the credit merely of having observed that the shadows of all bodies, placed in light let into a dark room through a small hole, were larger than they ought to be, and that these shadows had three parallel fringes of coloured light adjacent to them, whereas the Italian philosopher had penetrated more deeply into the subject, and achieved, as we shall now see, very important results.

Having admitted a ray of light through a small hole into a dark room, Grimaldi observed that it was diffused in the form of a cone, and that all bodies placed in this light had their shadows larger than they should have been had the light passed by their edges in straight lines. Upon a closer examination of these shadows, he discovered that they were surrounded by three coloured <199> fringes, growing narrower as they receded from the shadow. When the sun's light was strong, he perceived similar coloured fringes within the shadow of narrow bodies like a needle. These fringes were sometimes only two in number, and sometimes four, their number increasing and their size diminishing with the thickness of the body, and also, in the same shadow, when it was received on a sheet of paper at a greater distance from the body. From these new and valuable facts Grimaldi concluded that light is bent from its rectilineal direction in passing by the edges of bodies. By admitting the sun's rays through two small holes, so near each other that the two cones of light which they produced did not penetrate each other till they had reached to a considerable distance from the two holes, Grimaldi discovered the remarkable fact, that in consequence of the mutual interference of the two cones of light, the spot which was illuminated by both the pencils of light was more obscure than when it was illuminated by either of them singly, or, what is the same thing, "that a body actually illuminated may become more obscure by adding a light to that which it already receives." Grimaldi discovered also the beautiful phenomenon of the crested, or curved fringes exhibited within the shadow of the rectangular termination of bodies.

Although Hooke was anticipated by Grimaldi in the greater number of his observations, yet he is clearly entitled to share with the Italian philosopher in the discovery of the doctrine of the interference of light, though it was left to Dr. Thomas Young to complete the discovery.

Such was the state of the subject of Inflexion when Newton directed to it his powers of acute and accurate observation. His attention, however, was turned only to <200> the enlargement of the shadow of inflecting bodies, and to the three fringes adjacent to it. He was therefore led to take exact measures of the shadow of a human hair, and of the breadth of the fringes at different distances behind it, and to repeat these observations with light of different colours. In this way he was led to two new and remarkable results.

1. That these breadths were not proportional to the distances at which they were measured; and,

2. That the fringes made in homogeneous red light were red, and the largest; that those made in violet light were violet, and the smallest; and that those made in green light were green, and of an intermediate size, the rays which formed the red fringe passing by the hair at a greater distance than those which formed the violet.

When Newton made the preceding observations, he intended to repeat most of them with more care, and to make "some new ones, to determine the manner how the rays of light are bent in their passage by bodies;" but having been then interrupted, he could not think of resuming the inquiry.

It is very difficult to ascertain his real views on the subject of inflexion. In his Discourse, read in 1675, he ascribes it to the variable density of the ether within and without the inflecting body, thus regarding it as a new species of refraction; and in his letter to Robert Boyle in 1679, he takes the same view of the subject, and considers the several colours of the fringes as produced "by that refraction." Pursuing the same idea, he asserts in the Scholium to the 96th Prop. of the first book of the Principia, that the rays of light, in passing near bodies, are bent round them as if by attraction; that the rays which pass nearest them are most bent, as if they <201> were most attracted; that those which pass at a greater distance are less bent; and that those which pass at still greater distances, are bent in an opposite direction.

In this remarkable passage, Newton introduces, for the first time, the idea of a force bending the rays outwards; or of an inflecting force bending the rays inwards, accompanied with a deflecting force bending them outwards. This opinion, however, he subsequently abandoned; for, in the third book of his Optics, he refers all the phenomena to a force which "bends the rays not towards, but from the shadow ;" and he distinctly asserts, "that light is never known to follow crooked passages, nor to bend into the shadow."

These erroneous opinions, now wholly exploded, arose from Newton's having never observed the internal fringes, or those seen within the shadow. Grimaldi had described them minutely in his work, and, as they have been seen by almost every philosopher, it is not easy to explain how they should have escaped the notice of two such careful observers as Hooke and Newton. Without this cardinal fact our author stumbled in his path, and was misled into the erroneous propositions that bodies act upon light at a distance; that this action bends its rays with a force diminishing with the distance; and that rays which differ in refrangibility differ also in flexibility. Nor was he nearer the truth, when he conjectured in his third query that the rays of light, in passing by the edges of bodies, may be bent several times backwards and forwards with a motion like that of an eel, and that the three fringes of coloured light may arise from three such bendings.

A subject which had thus baffled the sagacity of Newton, was not likely to unfold its mysteries to ordinary observers. The experiments of Grimaldi and Newton <202> were repeated by various philosophers in various lands. Observations better made, and measures more accurately taken, were continually accumulating. A Pelion of inferences was heaped upon an Ossa of facts, but no Baconian conjurer could elicit from them the vital spark. The cardinal facts were still wanting, and a century passed away before a single experiment dissipated the inflexion theories of a graduated ether, of refracting atmospheres, and molecular actions. This humble experiment, which neither merits nor claims any particular notice, was, we believe, first made by ourselves in l798, and afterwards extended in 1812 and 1813. We found that ice, cork, metals, and diamond, the lightest and the heaviest bodies, the least refractive and the most refractive substances, produced exactly the same fringes; and that no change in the phenomena of inflexion was produced when a fibre of an opaque body was placed in fluids of precisely the same or of greater refractive power. Hence it followed, that the light which passed by the edges of bodies was not inflected by any refracting agent, or by any action whatever of the bodies themselves.

It is to Dr. Thomas Young, however, that we owe the master fact which enabled philosophers to unveil the mysteries of diffraction, and to account for a great variety of hitherto unexplained phenomena. In studying the internal fringes, and the crested ones discovered by Grimaldi, he found that, by intercepting the rays which passed by one side of the diffracting body, the internal and the crested fringes completely disappeared; and hence he concluded that the fringes were produced by the joint action, or by the interference, of the two portions of light which passed on each side of the diffracting body.

Having thus discovered the cause of internal fringes, <203> Dr. Young directed his attention to the external ones. He considered them as produced by the interference of the direct rays, or "those which have pursued their course without interruption," with those which are reflected from the margin of the diffracting body ; and as the fringes are on this supposition formed by light turned away from the substance near which it passes," he has characterized the phenomenon as one of deflected light.

M. Fresnel, to whose fine researches we owe the best experiments on diffraction, and the most perfect theory of it, followed Dr. Young in ascribing the external fringes to the influence of light reflected from the edge of the diffracting body, — an opinion which we never could reconcile with the palpable fact, that the fringes had always the same character, whatever was the reflecting power, or the shape of the edge of the body. Fresnel, influenced no doubt by the same consideration, suggested a different origin for the rays which interfere with the direct ones, namely, that the rays which pass at a sensible distance from the diffracting body deviate from their primitive direction towards the shadow, and thus interfere with the direct rays that pass near the body. In comparing these two hypotheses, and assuming with Dr. Young that half an undulation was lost by the reflected rays, he found that the real place of the fringe, on the hypothesis of a reflection, would be 17100ths of a millimètre different from what it really was.

In conducting his experiments on diffraction, Fresnel adopted a new and accurate method of observing and measuring the fringes. In place of using a small hole, he employed a convex lens of short focal length, which collected the solar rays into a focus, from which they again diverged, as if they had proceeded from a small <204> aperture.[3] When bodies were placed in this divergent light, he examined the fringes adjacent to their shadows by means of an eye-glass furnished with a micrometer, instead of receiving them upon a white surface; and he was thus able to measure their breadths even to the one hundred or two hundredth part of a millimètre. In this way he traced the external fringes to their origin, and with a lens of short focus he perceived the third fringe at a distance of less than the one-hundredth part of a millimètre from the edge of the inflecting body.

By measuring the angular inflexion of homogeneous red light, when the radiant point was placed at different distances in front of the diffracting body, and also when the radiant point remained fixed at different distances of the fringes behind the inflecting body, he was led to two important discoveries —

1. That the angular inflexion diminishes with the distance of the inflecting body from the radiant point; and,

2. That when the radiant point remains fixed, the successive positions of the same fringe are not in a straight line, but form a curve whose concavity is turned towards the diffracting body,[4] the curves being hyperbolas, having for their common foci the radiant point and the edge of the diffracting body.[5]

The discovery of Dr. Young, that an opaque screen, on one side of the inflecting body, extinguished the interior fringes, was extended by M. Arago, who found that the same effect is produced by a transparent screen of sufficient thickness, and that thin screens merely displace the <205> fringes, and transfer them from the side where they were formed. When such a screen is placed on each side of the diffracting body, the effect is equal to the difference of the transferences which each screen would have produced separately. As the amount of this transference may be computed theoretically from the thickness and refractive power of the screen, MM. Arago and Fresnel employed this method for measuring, with great exactness, the refractive power of gases.

The late M. Fraunhofer of Munich made a series of experiments on the diffraction of light on a large scale, and obtained many interesting results. The experiments were made with a telescope, which enabled him to obtain accurate measures of the fringes or rings produced by apertures of various forms; and he has published beautiful drawings of the spectra, and groups of spectra produced by a great number of diffracted rays, — by small apertures variously arranged, and by wire-gratings either acting singly, or crossed at right angles.

We have had occasion to study some of the same phenomena, when produced by lines cut upon polished steel with a diamond. The grooved surfaces which we employed were executed for us by the late Sir John Barton, and contained groups of lines varying from 500 to 10,000 in an inch. When divergent light was reflected from these surfaces, the central image formed by ordinary reflexion from the original surface of the steel plate was, in general, white, as observed in every case by Fraunhofer and others, and the other spectra had their usual character. But when the bright spaces in the plate, or those between the grooves had a certain relation to the width of the groove, or the part of the steel that was excavated by the diamond point, a series of new and remarkable phenomena were <206> produced. The light reflected from the original surface of the steel forming the central image was no longer white, but coloured, the colour varying with the angle of incidence at which the steel plate received the divergent beam. In some of the groups of lines, the colour varied slightly from 0° to 90° of incidence. In others it passed through the first order of colours, and in others, where the original steel surface was nearly removed, it passed through three or more orders of tints. The light which is obliterated from the central image, at any angle of incidence, or the complementary colour of the tint at that angle, is obliterated also from all the coloured spectra at less angles of incidence, the angle diminishing with the distance of the spectrum from the central one, and being less in each spectrum for the less refrangible rays.

If we cover the surface of the grooved steel with a fluid so as to reduce the refractive power of its surface, we develop more orders of colours on the white or central image, and consequently on all the spectra, higher tints being produced at a given incidence. But what is very remarkable, when the central image is perfectly white, and when the spectra are complete without any obliteration of their tints, the application of fluids to the grooved surface develops colours on the central or white image, and a corresponding obliteration of tints in the coloured spectra.[6]

In the experiments hitherto made on diffraction, the lines employed have been opaque, such as wires, hairs, or fibres of glass, which act upon light as if they were opaque. A series of beautiful phenomena are produced when we employ transparent lines drawn upon glass with <207> solutions of gums of different kinds, and different degrees of strength. A section of these transparent lines varies with the nature and density of the solution, though it is generally thicker at its edges. The consequence of this is, that the light which passes through the transparent line not only interferes with that which passes on each side of it, but also with part of the light which has its direction changed by the refraction of its curvilineal edges. Hence it follows, that a series of new interferences takes place, and we accordingly have a splendid display of coloured fringes infinitely surpassing in variety and brilliancy of colour the ordinary phenomena of diffraction.[7]

In all the experiments on inflexion and diffraction made by Newton and Fresnel, the fringes were viewed either on paper, or in the focus of a lens when the rays had actually interfered and produced the coloured fringes. The fringes thus seen may be called positive , because they are formed in space and out of the eye, on the retina of which they are afterwards delineated; but there is another form of these fringes, which I have examined, and which may be called negative, because they are not brought to a positive focus in space, or do not interfere till they reach the retina. In order to see these fringes, place the lens behind the diffracting body, so as to see the positive fringes, and then move it forward till these fringes disappear. The diffracting edge will now be in the anterior focus of the lens. If we advance the lens towards the diffracting body, the negative fringes will appear, and will increase in size till the lens touches the body, when they <208> will have the same magnitude as the positive fringes have when the lens is placed behind the body, at the distance of twice its focal length.

If we wish to see the fringes larger, we must use a lens with a longer focus; and when it is placed in contact with the diffracting body, the fringes will in every case be the same as the positive ones seen by the same lens placed behind the body twice its focal length. If the diffracting body is included in a fluid lens, or even placed in front of the lens, the negative fringes will be seen. In producing the negative fringes, the interfering rays are those which virtually radiate from the anterior focus of the lens, and which being refracted into parallel directions, enter the eye, and interfere on the retina; and in consequence of their not interfering till they enter the eye, they are much more distinct than the positive fringes.[8]

The most recent experiments on the inflexion of light have been made by Lord Brougham, who had investigated the subject so early as 1796, and given an account of his experiments in two interesting papers printed in the Philosophical Transactions.[9] These investigations were published before Dr. Young discovered the key to this class of phenomena, and before Fresnel had explained them on the principles of the undulatory theory. In his early papers, Lord Brougham considered the phenomena as produced by inflecting and deflecting forces emanating from the diffracting body, and acting, as Newton supposed, upon the passing rays; but in his recent researches he has used these terms merely for the purpose of making the narrative shorter and more distinct, and has avoided <209> all arguments and suggestions relating to the two rival theories.

The recent investigations of Lord Brougham were carried on under the clear sky of Provence, and with an excellent set of instruments constructed by M. Soleil of Paris. It would be impossible, without diagrams, to make them intelligible to the general reader, but some idea may be formed of the originality and importance of his discoveries from the two following propositions, which relate to a new property of the inflected and deflected rays : —

1. "The rays of light, when inflected by bodies near which they pass, are thrown into a condition or state which disposes them to be on one of their sides more easily deflected than before their first flexion, and disposes them on the other side to be less easily deflected; and when deflected by bodies, they are thrown into a condition or state which disposes them on one side to be more easily inflected, and on the other side to be less easily inflected than they were before the first flexion.

2. "The rays disposed on one side by the first flexion are polarized[10] on that side by the second flexion; and the rays polarized on the other side by the first flexion, are depolarized and disposed on that side by the second flexion."[11]

Whatever opinion we may form of the undulatory theory in its physical aspect, the explanation which it affords of a vast variety of optical phenomena, entitles it <210> to the, highest consideration. With the exception of Lord Brougham's discoveries, and the peculiar colours on the central image formed by grooved surfaces, to which we have already referred, the undulatory theory gives a satisfactory explanation of the leading phenomena of diffraction, while the Newtonian or atomical hypothesis has not even ventured to suggest a probable explanation.

[1] See Birch's Hist. Royal Society, vol. iii. pp. 63, 194, and Hooke's Posthumous works, pp. 186-190.

[2] Physico-Mathesis de Lumine, Coloribus, et Iride, aliisque annexis. Bononiæ, 1665. 4to.

[3] A concave lens is preferable to a convex one, for reasons which will presently be seen; and we recommend that it should be achromatic.

[4] This result had been previously obtained by Sir Isaac Newton.

[5] The hyperbolic form of the fringes had been previously discovered by Dr. Young. — Lect., vol. i. p. 287.

[6] See the Phil. Trans., 1829, pp. 301-317.

[7] These effects are so beautiful, that we have recommended the use of a diffracting apparatus for suggesting patterns for ribands. — See Reports of British Association, 1838, vol. vii. p. 12; Treatise on Optics, Edit. 1853, p. 117.

[8] See Reports of British Association, vol. vii. p. 12, 1838.

[9] Phil. Trans. 1796, p. 227; and 1797, p. 352.

[10] Lord Brougham uses the term polarisation "merely because the effect of the first edge resembles polarisation, and without giving any opinion as to its identity."

[11] Phil. Trans., 1850, pp. 235-260.

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