The Life of Isaac Newton
NEW THEORY OF INFLECTION
ALTHOUGH the discoveries of Newton respecting the Inflection of Light were first published in his Optics in 1704, yet there is reason to think that they were made at a much earlier period. Sir Isaac, indeed, informs us, in his preface to that great work, that the third book, which contains these discoveries, "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 I was then interrupted, and cannot now think of taking these things into consideration." On the 18th March, 1674, Dr. Hooke had read a valuable memoir on the phenomena of diffraction; and, as Sir Isaac makes no allusion whatever to this work, it is the more probable that his "scattered papers" had been written previous to the communication of Dr. Hooke's experiments.
The phenomena of the inflection of light were first discovered by Francis Maria Grimaldi, a learned Jesuit, who has described them in a posthumous work published in 1665, two years after his death.
Having admitted abeam of the sun's light through a small pin-hole in a piece of lead or card into a dark chamber, he found that the light diverged from this aperture in the form of a cone, and that the shadows of all bodies placed in this light were not only larger than might have been expected, but were surrounded with three coloured fringes, the nearest being the widest, and the most remote the narrowest. In strong light he discovered analogous fringes within the shadows of bodies, which increased in number with the breadth of the body, and became more distinct when the shadow was received obliquely and at a greater distance. When two small apertures or pin-holes were placed so near each other that the cones of light formed by each of them intersected one another, Grimaldi observed, that a spot common to the circumference of each, or, which is the same thing, illuminated by rays from each cone, was darker than the same spot when illuminated by either of the cones separately; and he announces this remarkable fact in the following paradoxical proposition, "that a body actually illuminated may become more dark by adding a light to that which it already receives."
Without knowing what had been done by the Italian philosopher, our countryman, Dr. Robert Hooke, had been diligently occupied with the same subject. In 1672, he communicated his first observations to the Royal Society, and he then spoke of his paper as "containing the discovery of a new property of light not mentioned by any optical writers before him." In his paper of 1674, already mentioned, and which is no doubt the one to which he alludes, he has not only described the leading phenomena of the inflection, or the deflection of light, as he calls it, but he has distinctly announced the doctrine of interference, which has performed so great a part in the subsequent history of optics.
Such was the state of the subject when Newton directed to it his powers of acute and accurate ob-servation. His attention was turned only to the enlargement of the shadow, and to the three fringes which surrounded it; and he begins his observations by ascribing the discovery of these facts to Grimaldi. After taking exact measures of the diameter of the shadow of a human hair, and of the breadth of the fringes at different distances behind it, he discovered the remarkable fact that these diameters and breadths were not proportional to the distances from the hair at which they were measured. In order to explain these phenomena, Newton supposed that the rays which passed by the edge of the hair are deflected or turned aside from it, as if by a repulsive force, the nearest rays suffering the greatest, and those more remote a less degree of deflection.
by the various inclination of the object 2. That colours begin to appear when two pulses of light are blended so well and so near together that the sense takes them for one.
Thus, if X, represents a section of the hair, and AB, CD, EF, GH, &c. rays passing at different distances from X, the ray AB will be more deflected than CD, and will cross it at m, the ray CD will for the same reason cross EF at n, and EF will cross GH at o. Hence the curve or caustic formed by the intersections m, n, 0, &c. will be convex outward, its curvature diminishing as it recedes from the vertex. As none of the passing light can possibly enter within this curve, it will form the boundary of the shadow of X.
The explanation given by Sir Isaac of the coloured fringes is less precise, and can be inferred only from the two following queries.
1. "Do not the rays which differ in refrangibility differ also in flexibility, and are they not, by these different inflections separated from one another, so as after separation to make the colours in the three fringes above described? And after what manner are they inflected to make those fringes ?
2. "Are not the rays of light in passing by the edges and sides of bodies bent several times backwards and forwards with a motion tike that of an eel? And do not the three fringes of light above mentioned arise from three such bendings?"
The idea thus indistinctly thrown out in the preceding queries has been ingeniously interpreted by Mr. Herschel in the manner represented in fig. 11, where SS are two rays passing by the edge of the body MN. These rays are supposed to undergo several bendings, as at a, b, c, and the particles of light are thrown off at one or other of the points of contrary flexure, according to the state of their fits or other circumstances. Those that are thrown outwards in the direction aA, bB, cC, dD, will produce as many caustics by their intersections as there are deflected rays; and each caustic, when received on a screen at a distance, will depict on it the brightest part or maximum of a fringe.
In this unsatisfactory state was the subject of the inflection of light left by Sir Isaac. His inquiries were interrupted, and never again renewed; and though he himself found that the phenomena were the same, "whether the hair was encompassed with air or with any other pellucid substance," yet this important result does not seem to have shaken his conviction, that the phenomena had their origin in the action of bodies upon light.
During two sets of experiments which I made on the inflection of light, the first in 1798, and the second in 1812 and 1813, I was desirous of examining the influence of density and refractive power over the fringes produced by inflection. I compared the fringes formed by gold-leaf with those formed by masses of gold, and those produced by films which gave the colours of thin plates with those formed by masses of the same substance. I examined the influence of platinum, diamond, and cork in inflecting light, the effect of non-reflecting grooves and spaces in polished metals, and of cylinders of glass immersed in a mixture of oil of cassia and oil of olives of the same refractive power; and, as the fringes had the same magnitude and character under all these circumstances, I concluded that they were not produced by any force inherent in the bodies themselves, but arose from a property of the light itself, which always showed itself when light was stopped in its progress.
Dr. Thomas Young, who had supported with great ingenuity and force of argument the undulatory theory of light, as maintained by Hooke and Huygens, was the first who gave a plausible explanation of the inflection of light. By interposing a small screen at B, fig. 10, and intercepting the rays that passed near the hair X, he was surprised to find that all the fringes within the shadow disappeared. The same effect took place when the screen intercepted the rays on the other side; and hence he concluded, that the rays on each side of the hair were necessary to the production of the inner fringes, and that the fringes were produced by the interference of the rays that passed on one side of the hair with those that passed on the other side. In order to account for the coloured fringes without the shadow, Dr. Young conceived that the rays which pass near the edge of the hair interfere with others, which he supposes may be reflected after falling very obliquely upon its edge, a supposition which, if correct, would certainly produce fringes very similar to those actually observed.
In pursuing these researches so successfully begun by Dr. Young, M. Fresnel had the good fortune to explain all the phenomena of inflection by means of the undulatory doctrine combined with the principle of interference. In place of transmitting the light through a small aperture, he caused it to diverge from the focus of a deep convex lens, and instead of receiving the shadow and its fringes upon a smooth white surface, as was done by Newton, he viewed them directly with his eye through a lens placed behind the shadow; and by means of a microscope he was able to measure the dimensions of the fringes with the greatest exactness. By this mode of observation he made the remarkable discovery, that the inflection of the light depended on the distance of the inflecting body from the aperture or from the focus of divergence; the fringes being observed to dilate as the body approached that focus, and to contract as it receded from it, their relative distances from each other, and from the margin of the shadow continuing invariable. In attempting to account for the formation of the exterior fringes, M. Fresnel found it necessary to reject the supposition of Dr. Young, that they were owing to light reflected from the edge of the body. He not only ascertained that the real place of the fringe was the 17/100 of a millimetre different from what it should be on that supposition, but he found that the fringes preserved the same intensity of light, whether the inflecting body had a round or a sharp edge, and even when the edge was such as not to afford sufficient light for their production. From this difficulty the undulatory theory speedily released him, and he was led by its indications to consider the exterior fringes, as produced by an infinite number of elementary waves of light emanating from a primitive wave when partly interrupted by an opaque body.
The various phenomena of inflection, which had so long resisted every effort to generalize them, having thus received so beautiful and satisfactory an explanation from the undulatory doctrine, they must of course be regarded as affording to that doctrine the most powerful support, while the Newtonian hypothesis of the materiality of light is proportionally thrown into the shade. It is impossible, indeed, even for national partiality to consider the views of Newton as furnishing any explanation of the facts discovered by Fresnel; and, as no attempt has been made by the small though able phalanx of his disciples to stay the decision with which, on this count at least, the doctrine of emission has been threatened, we shall venture to suggest some principles by which the refractory phenomena may perhaps be yet brought within the pale of the Newtonian theory.
That the particles of light, like those of heat, are endowed with a repulsive force which prevents them from accumulating when in a state of condensation, or when they are detained by the absorptive action of opaque bodies, will be readily admitted. By this power a beam of light radiating from a luminous point has, in every azimuth, the same degree of intensity at the same distance from its centre of divergence; but if we intercept a portion of such a beam by an opaque body, the repulsive force of the light which formerly occupied its shadow is withdrawn, and consequently the rays which pass near the body will be repelled into the shadow, and will form, by their interference with those similarly repelled on the other side, the interior fringes, which are parallel to the edges of the body. The rays which pass at a greater distance will in like manner be bent towards the body, but with less force, and, interfering with those rays which retain their primitive direction, from the state of their fits or the position of their poles, they will form the exterior fringes. When the inflecting body is placed near the point of divergence, the greater proximity of the rays will produce a greater repulsive force, and consequently a greater inflection of the passing light; while the removal of the body from the point of divergence will be accompanied with an increased distance of the particles, an inferior repulsive force, and a feebler inflection. As the phenomena of inflection, considered under this aspect, arise from a property of the light itself, it follows that they will remain invariable, whatever be the nature or density of the body, or the form of the edge which acts upon the passing rays.