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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 contaary, 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 lamina 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 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,