Interference of Light—Undulatory Theory of Light—Propagation of Light—Newton’s Rings—Measurement of the Length of the Waves of Light, and of the Frequency of the Vibrations of Ether for each Colour—Newton’s Scale of Colours—Diffraction of Light—Sir John Herschel’s Theory of the Absorption of Light—Refraction and Reflection of Light.

Newton and most of his immediate successors imagined light to be a material substance, emitted by all self-luminous bodies in extremely minute particles, moving in straight lines with prodigious velocity, which, by impinging upon the optic nerves, produce the sensation of light. Many of the observed phenomena have been explained by this theory; it is, however, totally inadequate to account for the following circumstances.

When two equal rays of red light, proceeding from two luminous points, fall upon a sheet of white paper in a dark room, they produce a red spot on it which will be twice as bright as either ray would produce singly, provided the difference in the lengths of the two beams, from the luminous points to the red spot on the paper, be exactly the 0·0000258th part of an inch. The same effect will take place if the difference in the lengths be twice, three times, four times, &c., that quantity. But if the difference in the lengths of the two rays be equal to one-half of the 0·0000258th part of an inch, or to its 1¹/₂, 2¹/₂, 3¹/₂, &c., part, the one light will entirely extinguish the other, and will produce absolute darkness on the paper where the united beams fall. If the difference in the lengths of their paths be equal to the 1¹/₄, 2¹/₄, 3¹/₄, &c., of the 0·0000258th part of an inch, the red spot arising from the combined beams will be of the same intensity which one alone would produce. If violet light be employed, the difference in the lengths of the two beams must be equal to the 0·0000157th part of an inch, in order to produce the same phenomena; and for the other colours, the difference must be intermediate between the 0·0000258th and the 0·0000157th part of an inch. Similar phenomena may be seen by viewing the flame of a candle through two very fine slits in a card extremely near to one another (N.198); or by admitting the sun’s light into a dark room through a pin-hole about the fortieth of an inch in diameter, receiving the image on a sheet of white paper, and holding a slender wire in the light. Its shadow will be found to consist of a bright white bar or stripe in the middle, with a series of alternate black and brightly-coloured stripes on each side. The rays which bend round the wire in two streams are of equal lengths in the middle stripe; it is consequently doubly bright from their combined effect; but the rays which fall on the paper on each side of the bright stripe, being of such unequal lengths as to destroy one another, form black lines. On each side of these black lines the rays are again of such lengths as to combine to form bright stripes, and so on alternately till the light is too faint to be visible. When any homogeneous light is used, such as red, the alternations are only black and red; but on account of the heterogeneous nature of white light, the black lines alternate with vivid stripes or fringes of prismatic colours, arising from the superposition of systems of alternate black lines and lines of each homogeneous colour. That the alternation of black lines and coloured fringes actually does arise from the mixture of the two streams of light which flow round the wire, is proved by their vanishing the instant one of the streams is interrupted. It may therefore be concluded, as often as these stripes of light and darkness occur, that they are owing to the rays combining at certain intervals to produce a joint effect, and at others to extinguish one another. Now it is contrary to all our ideas of matter to suppose that two particles of it should annihilate one another under any circumstances whatever; while, on the contrary, two opposing motions may; and it is impossible not to be struck with the perfect similarity between the interferences of small undulations of air or of water and the preceding phenomena. The analogy is indeed so perfect, that philosophers of the highest authority concur in the belief that the celestial regions are filled with an extremely rare and highly elastic medium or ether, whose particles are capable of receiving the vibrations communicated to them by self-luminous bodies, and of transmitting them to the optic nerves, so as to produce the sensation of light. The acceleration in the mean motion of Encke’s comet, as well as of the comet discovered by M. Biela, renders the existence of such a medium certain. It is clear that, in this hypothesis, the alternate stripes of light and darkness are entirely the effect of the interference of the undulations; for, by actual measurement, the length of a wave of the mean red rays of the solar spectrum is equal to the 0·0000258th part of an inch; consequently, when the elevations of the waves combine, they produce double the intensity of light that each would do singly; and when half a wave combines with a whole—that is, when the hollow of one wave is filled up by the elevation of another—darkness is the result. At intermediate points between these extremes, the intensity of the light corresponds to intermediate differences in the lengths of the rays.

The theory of interferences is a particular case of the general mechanical law of the superposition of small motions; whence it appears that the disturbance of a particle of an elastic medium, produced by two co-existent undulations, is the sum of the disturbances which each undulation would produce separately; consequently, the particle will move in the diagonal of a parallelogram, whose sides are the two undulations. If, therefore, the two undulations agree in direction, or nearly so, the resulting motion will be very nearly equal to their sum, and in the same direction; if they nearly oppose one another, the resulting motion will be nearly equal to their difference; and, if the undulations be equal and opposite, the resultant will be zero, and the particle will remain at rest.

The preceding experiments, and the inferences deduced from them, which have led to the establishment of the doctrine of the undulations of light, are the most splendid memorials of our illustrious countryman Dr. Thomas Young, though Huygens was the first to originate the idea.

It is supposed that the particles of luminous bodies are in a state of perpetual agitation, and that they possess the property of exciting regular vibrations in the molecules of the ethereal medium, corresponding to the vibrations of their own molecules; and that, on account of its elastic nature, one particle of the ether when set in motion communicates its vibrations to those adjacent, which in succession transmit them to those farther off; so that the primitive impulse is transferred from particle to particle, and the undulating motion darts through ether like a wave in water; so that light is motion, and therefore subject to the laws of dynamics and mathematical analysis. Although the progressive motion of light is known by experience to be uniform and in a straight line, the vibrations of the particles are always at right angles to the direction of the ray. The propagation of light is like the spreading of waves in water; but, if one ray alone be considered, its motion may be conceived by supposing a rope of indefinite length stretched horizontally, one end of which is held in the hand. If it be agitated to and fro at regular intervals, with a motion perpendicular to its length, a series of similar and equal tremors or waves will be propagated along it; and if the regular impulses be given in a variety of planes, as up and down, from right to left, and also in oblique directions, the successive undulations will take place in every possible plane. An analogous motion in the ether, when communicated to the optic nerves, would produce the sensation of common light. It is evident that the waves which flow from end to end of the cord in a serpentine form are altogether different from the perpendicular vibratory motion of each particle of the rope, which never deviates far from a state of rest. So, in ether, each particle vibrates perpendicularly to the direction of the ray; but these vibrations are totally different from and independent of the undulations which are transmitted through it, in the same manner as the vibrations of each particular ear of corn are independent of the waves that rush from end to end of a harvest-field when agitated by the wind.

The intensity of light depends upon the amplitude or extent of the vibrations of the particles of ether, while its colour depends upon their frequency. The time of the vibration of a particle of ether is, by theory, as the length of a wave directly, and inversely as its velocity. Now, as the velocity of light is known to be 190,000 miles in a second, if the lengths of the waves of the different coloured rays could be measured, the number of vibrations in a second corresponding to each could be computed. That has been accomplished as follows:—All transparent substances of a certain thickness, with parallel surfaces, reflect and transmit white light; but, if they be extremely thin, both the reflected and transmitted light is coloured. The vivid hues on soap-bubbles, the iridescent colours produced by heat on polished steel and copper, the fringes of colour between the laminÆ of Iceland spar and sulphate of lime, all consist of a succession of hues disposed in the same order, totally independent of the colour of the substance, and determined solely by its greater or less thickness—a circumstance which affords the means of ascertaining the length of the waves of each coloured ray, and the frequency of the vibrations of the particles producing them. If a plate of glass be laid upon a lens of almost imperceptible curvature, before an open window, when they are pressed together a black spot will be seen in the point of contact, surrounded by seven rings of vivid colours, all differing from one another (N.199). In the first ring, estimated from the black spot, the colours succeed each other in the following order:—black, very faint blue, brilliant white, yellow, orange, and red. They are quite different in the other rings, and in the seventh the only colours are pale bluish green and very pale pink. That these rings are formed between the two surfaces in apparent contact may be proved by laying a prism on the lens instead of the plate of glass, and viewing the rings through the inclined side of it that is next to the eye, which arrangement prevents the light reflected from the upper surface mixing with that from the surfaces in contact, so that the intervals between the rings appear perfectly black—one of the strongest circumstances in favour of the undulatory theory; for, although the phenomena of the rings can be explained by either hypothesis, there is this material difference, that, according to the undulatory theory, the intervals between the rings ought to be absolutely black, which is confirmed by experiment; whereas, by the doctrine of emanation, they ought to be half illuminated, which is not found to be the case. M. Fresnel, whose opinion is of the first authority, thought this test conclusive. It may therefore be concluded that the rings arise entirely from the interference of the rays: the light reflected from each of the surfaces in apparent contact reaches the eye by paths of different lengths, and produces coloured and dark rings alternately, according as the reflected waves coincide or destroy one another. The breadths of the rings are unequal; they decrease in width, and the colours become more crowded, as they recede from the centre. Coloured rings are also produced by transmitting light through the same apparatus; but the colours are less vivid, and are complementary to those reflected, consequently the central spot is white.

The size of the rings increases with the obliquity of the incident light, the same colour requiring a greater thickness or space between the glasses to produce it than when the light falls perpendicularly upon them. Now, if the apparatus be placed in homogeneous instead of white light, the rings will all be of the same colour with that of the light employed, that is to say, if the light be red, the rings will be red, divided by black intervals. The size of the rings varies with the colour of the light. They are largest in red, and decrease in magnitude with the succeeding prismatic colours, being smallest in violet light.

Since one of the glasses is plane and the other spherical, it is evident that from the point of contact the space between them gradually increases in thickness all round, so that a certain thickness of air corresponds to each colour, which in the undulatory system measures the length of the wave producing it (N.200). By actual measurement Sir Isaac Newton found that the squares of the diameters of the brightest part of each ring are as the odd numbers, 1, 3, 5, 7, &c.; and that the squares of the diameters of the darkest parts are as the even numbers, 0, 2, 4, 6, &c. Consequently, the intervals between the glasses at these points are in the same proportion. If, then, the thickness of the air corresponding to any one colour could be found, its thickness for all the others would be known. Now, as Sir Isaac Newton knew the radius of curvature of the lens, and the actual breadth of the rings in parts of an inch, it was easy to compute that the thickness of air at the darkest part of the first ring is the ¹/₈₉₀₀₀ part of an inch, whence all the others have been deduced. As these intervals determine the length of the waves on the undulatory hypothesis, it appears that the length of a wave of the extreme red of the solar spectrum is equal to the 0·0000266th part of an inch; that the length of a wave of the extreme violet is equal to the 0·0000167th part of an inch; and, as the time of a vibration of a particle of ether producing any particular colour is directly as the length of a wave of that colour, and inversely as the velocity of light, it follows that the molecules of ether producing the extreme red of the solar spectrum perform 458 millions of millions of vibrations in a second; and that those producing the extreme violet accomplish 727 millions of millions of vibrations in the same time. The lengths of the waves of the intermediate colours, and the number of their vibrations, being intermediate between these two, white light, which consists of all the colours, is consequently a mixture of waves of all lengths between the limits of the extreme red and violet. The determination of these minute portions of time and space, both of which have a real existence, being the actual results of measurement, do as much honour to the genius of Newton as that of the law of gravitation.

The number of advancing waves of light in an inch is known to be from 37,600 to 59,880, and the number of lateral vibrations is from 458 to 727 billions in a second, but the extent of these lateral vibrations of the particles of the ethereal medium is not known, though both their extent and velocity are probably very small compared with the length of the advancing waves and the velocity of propagation. Colour is identified with the number of vibrations; but whether reflection, refraction, absorption, &c., have any relations to the lateral vibrations, or whether they are dependent in part upon some physical action of the ethereal medium unknown and unsuspected, are points as yet undetermined. To ascertain these circumstances, Dr. Faraday instituted a series of the most refined experiments upon the relation of the minute particles of metals to the vibrations of light.

Gold acts powerfully on light, and possesses a real transparency, transmitting green rays when very thin; and being capable of extreme division by solvents without losing its metallic character, its particles transmit rays of various colours according to their size; those that transmit the rose-colour in Bohemian glass are of inconceivable minuteness. The progressive waves of the ether are so long compared with the dimensions of the molecules to which gold can be reduced, that it seemed probable to Dr. Faraday when the latter were placed in a sunbeam that some effective relation might be discovered between them and the smaller vibrations of the ethereal medium; in which case, if reflection, refraction, &c., depended upon such relations, there was reason to expect that these functions would change sensibly by the substitution of different sized particles of the gold for one another. At one time Dr. Faraday hoped he had changed one colour into another by means of gold, which would have been equivalent to a change in the number of vibrations; but although he has not yet confirmed that result, his researches are of the greatest interest.^[9]

The phenomenon of the coloured rings takes place in vacuo as well as in air, which proves that it is the distance between the lenses alone, and not the air, which produces the colours. However, if water or oil be put between them, the rings contract, but no other change ensues; and Newton found that the thickness of different media at which a given tint is seen is in the inverse ratio of their refractive indices, so that the thickness of laminÆ which could not otherwise be measured may be known by their colour; and, as the position of the colours in the rings is invariable, they form a fixed standard of comparison, well known as Newton’s scale of colours; each tint being estimated according to the ring to which it belongs from the central spot inclusively. Not only the periodical colours which have been described, but the colours seen in thick plates of transparent substances, the variable hues of feathers, of insects’ wings, mother-of-pearl, and of striated substances, all depend upon the same principle. To these may be added the coloured fringes surrounding the shadows of all bodies held in an extremely small beam of light, and the coloured rings surrounding the small beam itself when received on a screen.

When a very slender sunbeam, passing through a small pin-hole into a dark room, is received on a white screen, or plate of ground-glass, at the distance of a little more than six feet, the spot of light on the screen is larger than the pin-hole: and, instead of being bounded by shadow, it is surrounded by a series of coloured rings separated by obscure intervals. The rings are more distinct in proportion to the smallness of the beam (N.201). When the light is white there are seven rings, which dilate or contract with the distance of the screen from the hole. As the distance of the screen diminishes, the white central spot contracts to a point and vanishes; and, on approaching still nearer, the rings gradually close in upon it, so that the centre assumes successively the most intense and vivid hues. When the light is homogeneous—red, for example—the rings are alternately red and black, and more numerous; and their breadth varies with the colour, being broadest in red light and narrowest in violet. The tints of the coloured fringes from white light, and their obliteration after the seventh ring, arise from the superposition of the different sets of fringes of all the coloured rays. The shadows of objects are also bordered by coloured fringes when held in this slender beam of light. If the edge of a knife or hair, for example, be held in it, the rays, instead of proceeding in straight lines past its edge, are bent when quite close to it, and proceed from thence to the screen in curved lines called hyperbolas; so that the shadow of the object is enlarged, and, instead of being at once bounded by light, is surrounded or edged with coloured fringes alternating with black bands, which are more distinct the smaller the pin-hole (N.202). The fringes are altogether independent of the form or density of the object, being the same when it is round or pointed, when of glass or platinum. When the rays which form the fringes arrive at the screen, they are of different lengths, in consequence of the curved path they follow after passing the edge of the object. The waves are therefore in different phases or states of vibration, and either conspire to form coloured fringes or destroy one another in the obscure intervals. The coloured fringes bordering the shadows of objects were first described by Grimaldi in 1665; but, besides these, he noticed that there are others within the shadows of slender bodies exposed to a small sunbeam, a phenomenon which has already been mentioned to have afforded Dr. Young the means of proving, beyond all controversy, that coloured rings are produced by the interference of light.

It may be concluded that material substances derive their colours from two different causes: some from the law of interference, such as iridescent metals, peacocks’ feathers, &c.; others from the unequal absorption of the rays of white light, such as vermilion, ultramarine, blue, or green cloth, flowers, and the greater number of coloured bodies. The latter phenomena have been considered extremely difficult to reconcile with the undulatory theory of light, and much discussion has arisen as to what becomes of the absorbed rays. But that embarrassing question has been ably answered by Sir John Herschel in a most profound paper on the Absorption of Light by coloured Media, and cannot be better given than in his own words. It must, however, be premised, that, as all transparent bodies are traversed by light, they are presumed to be permeable to the ether. He says,—“Now, as regards only the general fact of the obstruction and ultimate extinction of light in its passage through gross media, if we compare the corpuscular and undulatory theories, we shall find that the former appeals to our ignorance, the latter to our knowledge, for its explanation of the absorptive phenomena. In attempting to explain the extinction of light on the corpuscular doctrine, we have to account for the light so extinguished as a material body, which we must not suppose annihilated. It may, however, be transformed; and among the imponderable agents, heat, electricity, &c., it may be that we are to search for the light which has become thus comparatively stagnant. The heating power of the solar rays gives a prim facie plausibility to the idea of the transformation of light into heat by absorption. But, when we come to examine the matter more nearly, we find it encumbered on all sides with difficulties. How is it, for instance, that the most luminous rays are not the most calorific, but that, on the contrary, the calorific energy accompanies, in its greatest intensity, rays which possess comparatively feeble illuminating powers? These and other questions of a similar nature may perhaps admit of answer in a more advanced state of our knowledge; but at present there is none obvious. It is not without reason, therefore, that the question, ‘What becomes of light?’ which appears to have been agitated among the photologists of the last century, has been regarded as one of considerable importance as well as obscurity by the corpuscular philosophers. On the other hand, the answer to this question, afforded by the undulatory theory of light, is simple and distinct. The question, ‘What becomes of light?’ merges in the more general one, ‘What becomes of motion?’ And the answer, on dynamical principles, is, that it continues for ever. No motion is, strictly speaking, annihilated; but it may be divided, and the divided parts made to oppose and in effect destroy one another. A body struck, however perfectly elastic, vibrates for a time, and then appears to sink into its original repose. But this apparent rest (even abstracting from the inquiry that part of the motion which may be conveyed away by the ambient air) is nothing else than a state of subdivided and mutually destroying motion, in which every molecule continues to be agitated by an indefinite multitude of internally reflected waves, propagated through it in every possible direction, from every point in its surface on which they successively impinge. The superposition of such waves will, it is easily seen, at length operate their mutual destruction, which will be the more complete the more irregular the figure of the body, and the greater the number of internal reflections.” Thus Sir John Herschel, by referring the absorption of light to the subdivision and mutual destruction of the vibrations of ether in the interior of bodies, brings another class of phenomena under the laws of the undulatory theory.

According to Mr. Rankin’s hypothesis of Molecular Vortices^[10] the absorption of light and radiant heat consists in the transference of motion from the molecules to their atmospheres, and conversely the emission of light and radiant heat is the transmission of motion from the atmospheres to the molecules. The great velocity of light and heat is a natural consequence of this hypothesis, according to which the vibratory masses must be extremely small compared with the forces exerted by them.

The ethereal medium pervading space is supposed to penetrate all material substances, occupying the interstices between their molecules; but in the interior of refracting media it exists in a state of less elasticity compared with its density in vacuo; and, the more refractive the medium, the less the elasticity of the ether within it. Hence the waves of light are transmitted with less velocity in such media as glass and water than in the external ether. As soon as a ray of light reaches the surface of a diaphanous reflecting substance, for example a plate of glass, it communicates its undulations to the ether next in contact with the surface, which thus becomes a new centre of motion, and two hemispherical waves are propagated from each point of this surface; one of which proceeds forward into the interior of the glass, with a less velocity than the incident waves; and the other is transmitted back into the air, with a velocity equal to that with which it came (N.203). Thus, when refracted, the light moves with a different velocity without and within the glass; when reflected, the ray comes and goes with the same velocity. The particles of ether without the glass, which communicate their motions to the particles of the dense and less elastic ether within it, are analogous to small elastic balls striking large ones; for some of the motion will be communicated to the large balls, and the small ones will be reflected. The first would cause the refracted wave, and the last the reflected. Conversely, when the light passes from glass to air, the action is similar to large balls striking small ones. The small balls receive a motion which would cause the refracted ray, and the part of the motion retained by the large ones would occasion the reflected wave; so that, when light passes through a plate of glass or of any other medium differing in density from the air, there is a reflection at both surfaces; but this difference exists between the two reflections, that one is caused by a vibration in the same direction with that of the incident ray, and the other by a vibration in the opposite direction.

A single wave of air or ether would not produce the sensation of sound or light. In order to excite vision, the vibrations of the molecules of ether must be regular, periodical, and very often repeated: and, as the ear continues to be agitated for a short time after the impulse by which alone a sound becomes continuous, so also the fibres of the retina, according to M. d’Arcet, continue to vibrate for about the eighth part of a second after the exciting cause has ceased. The interval of time during which the impression lasts is longer for the blue than for red or white light: it must not be less than 0·34. Every one must have observed, when a strong impression is made by a bright light, that an object remains visible for a short time after shutting the eyes, which is supposed to be in consequence of the continued vibrations of the fibres of the retina. Occasionally the retina becomes insensible to feebly illuminated objects when continuously presented. If the eye be turned aside for a moment, the object becomes again visible. It is probably on this account that the owl makes so peculiar a motion with its head when looking at objects in the twilight. It is quite possible that many vibrations may be excited in the ethereal medium incapable of producing undulations in the fibres of the human retina, which yet have a powerful effect on those of other animals or of insects. Such may receive luminous impressions of which we are totally unconscious, and at the same time they may be insensible to the light and colours which affect our eyes, their perceptions beginning where ours end.