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the shadows of the knives are terminated, and which he noticed relating to it are well worthy distinguished from the first luminous fringes, by of attention. He exposed in the light of the the lines e is and rip, till the meeting and sun a cylinder of wood three feet long and six crossing of the fringes,; and then those lines lines and a half in diameter; when its shadow, cross the fringes in the form of dark lines termi- being received upon a paper held close to it, nating the first luminous fringes on the inside, was every where equally black and well defined, and distinguishing them from another light, and continued to be so to the distance of twentywhich begins to appear at i, and illuminates all three inches from it. . At a greater distance the the triangular space ip D Es, comprehended by shadow appeared to be of two different densities; these dark lines and the right line D E. Of these for the two extremities of the shadow, in the hyperbolas one asymptoie is the line D E, and direction of the length of the cylinder, were terthe other asymptotes are parallel to the lines CA minated by two dark strokes, a little more than and C B. The sun shining into his darkened a line in breadth. Within these dark lines there room, through the small hole mentioned above, was a faint light, equally dispersed through the he placed at the hole a prism to refract the light, shadow, which formed a uniform penumbra, and to form on the opposite wall the colored much lighter than the dark strokes at the eximage of the sun; and he found that the sha- tremity, or than the shadow received near the dows of all bodies held in the colored light, be- cylinder. As the cylinder was removed to a tween the prism and the wall, were bordered greater distance from the paper, the two black with fringes of the color of that light in which lines continued to be nearly of the same breadth, they were held; and, comparing the fringes made and the same degree of obscurity ; but the pein the several colored lighis, he found that those numbra in the middle grew lighter, and its made in the red light were the largest, those breadth diminished, so that the two dark lines made in the violet were the least, and those at the extremity of the shadow approached one made in the green were of a middle bigness. another, till, at the distance of sixty inches, they For the fringes with which the shadow of a man's coincided, and the penumbra in the middle hair were bordered, being measured across the entirely vanished. Ai a still greater distance a shadow, at six inches from the hair, the distance faint penumbra was visible; but it was ill defined, between the middle and most luminous part of and grew broader as the cylinder was removed the first or innermost fringe on one side of the farther off, but was sensible at a very great shadow, and that of the like fringe on the other distance. A narrow and faint penumbra was side of the shadow, was in the full red light sir

, of also seen on the outside of the dark shadow;

on the outside of this there was a tract an inch, and in the full violetto. The like distance between the middle and most luminous

more strongly illuminated than the rest of the parts of the second fringes, on either side of the paper. The breadth of the external penumbra shadow, was in the full red light ,, and the vio- increased with the distance of the shadow from let of an inch; and these distances of the the cylinder, and the breadth of the tract of fringes held the same proportion at all distances light on the outside of it was also enlarged; but from the hair without any sensible variation.

its splendor diminished with the distance.

59. He repeated these experiments with three 57. From these observations it was evident, other cylinders of different dimensions; and that the rays which made the fringes in the red from them all he inferred, that every opaque light, passed by the hair at a greater distance cylindrical body, exposed to the light of the sun, than those which made the like fringes in the makes a shadow which is black and dark to the violet; so that the hair, in causing these fringes, distance of thirty-eight to forty-five diameters of acted alike upon the red light or least refrangible the cylinder which forms it; and that, at a rays at a greater distance, and upon the violet or greater distance, the middle part begins to be most refrangible rays at a less distance; and illuminated in the manner described above. thereby occasioned 'fringes of different sizes, Other rays were deflected from the body, and without any change in the color of any sort of formed a strong light on the outside of the shalight. It may therefore be concluded, that when dow, and which might at the same time conthe hair in the first observation was held in the tribute to dilute the outer shadow, though he white beam of the sun's light, and cast a shadow supposed that penumbra to be occasioned prinwhich was bordered with three fringes of colored cipally by that part of the paper not being light, those colors arose not from any new enlightened, except by a part of the sun's disk modifications impressed upon the rays of light only, according to the known principles of by the hair, but only from the various inflections optics. The same experiments he made with whereby the several sorts of rays were separated globes of several diameters; but he found that, from one another, which before separation, by whereas the shadows of the cylinders did not the mixture of all their colors, composed the disappear but at the distance of forty-one of white beam of the sun's light; but, when sepa- their diameters, those of the globes were not rated, composed lights of the several colors visible beyond fifteen of their diameters; which which they are originally disposed to exhibit. he thought was owing to the light being inflected

58. The first person who pursued any experi- on every side of a globe, and consequently in inents similar to those of Newton on infected such a quantity as to disperse the shadows ight, was M. Maraldi; whose observations sooner than in the case of the cylinders. In all chiefly respect the inflection of light towards these cases the penumbra occasioned by the other bodies, whereby their shadows are partially inflected light began to be visible at a less disilluminated ; and many of the circumstances tance from the body in the stronger light of the

sun than in a weaker, on account of the greater cularly very near the plate, was illuminated by quantity of rays inflected in those circumstances. a faint light, equally dispersed, as in the pre

60. M. Maraldi, being sensible that the above ceding plate. But being received at thirteen mentioned phenomena of the shadows were feet from the plate, six small black streaks began caused by inflected light, was induced to give to be visible. At seventeen feet from the plate, more particular attention to this remarkable pro- the black streaks were broader, more distinct, perty, and to repeat the experiments of Grimaldi and more separated from the streaks that were and Sir Isaac Newton in a darkened room. In less dark. At forty-two feet from the plate, doing this, he observed that, besides the enlarged only two black streaks were seen in the middle shadow of a hair, a fine needle, &c, the bright of the penumbra. This middle penumbra begleam of light that bordered it, and the three tween the two black streaks was tinged with red. colored rings next to this enlightened part, Next to the black streaks there always appeared when the shadow was at a considerable distance the streaks of light which were broad, and the from the hair, the dark central shadow was di- colored streaks nexi to them. Receiving the vided in the middle by a mixture of light; and shadow of the same plate at the distance of what it was not of the same density, except when seventy-two feet, the appearances were the same A was very near the hair. This new appearance as in the former situation, except that the two is exactly similar to what he had observed with black streaks were broader, and the interval respect to the shadows in the open day-light between them, occupied by the penumbra, was above-mentioned.

broader also, and tinged with a deeper red. 61. Having placed a bristle in the rays of the 63. In the same rays of the sun he placed sun, admitted into a dark chamber by a small different plates, larger than the former, one of hole, at the distance of nine feet from the hole them a line and a half, another two lines, anois made a shadow, which, being received at five ther three lines broad, &c., but receiving their or six feet from the object, he observed to con- shadows upon paper, he could not perceive in sist of several streaks of light and shade. The them those streaks of faint light which he had middle part was a faint penumbra, bordered by observed in the shadows of the small plates, a darker shadow, and after that by a narrower though he received these shadows at the distance penumbra; next to which was a light streak of fifty-six feet. Nothing was seen but a weak broader than the dark part, and next to the light, equally diffused as in the shadows of the streak of light, the red, violet, and blue colors two smallest plates, received very near them. were seen as in the shadow of the hair. He also The streaks of ght in the shadows of veedles placed in the same rays, several needles of of a middling size, our author ascribed to the different sizes ; but the appearances were so rays of light which are inflected at different exceedingly various and singular, that he does distances from the bodies; and he imagined that not recite them. He exposed in the rays of the their crossing one another was sufficient to sun, admitted by a small hole into a dark cham- account for the variations observable in them at ber, a plate two inches long, and a little more different distances. The extraordinary size of than half a line broad. This plate being fixed the shadows of these small substances M. Maperpendicularly to the rays, at the distance of saldi thought to be occasioned by the shadow nine feet from the hole, a faint light was seen from the enlightened part of the sky, added to uniformly dispersed over the shadow, when it that which was made by the light of the sun, was received perpendicularly to it, and very and also to a vortex occasioned by the circulanear. The shadow of the same plate, being tion of the infle ed light behin

the object. received at the distance of two feet and a half, 64. M. Maraldi, having made the preceding was divided into four very narrow black streaks, experiments upon single long substances, had separated by small lighter intervals equal to the curiosity to place two of them so as to cross them. The boundaries of this shadow on each one another in a beam of the sun's light. The side had a penumbra, which was terminated by shadows of two hairs placed in this manner, and a very strong light, next to which were the received at some distance from them, appeared colored streaks of red, violet, and blue, as to be painted reciprocally one upon another, so before.

that the obscure part of one of them was visible 62. The shadow of the same plate, at four upon the obscure part of the other. The streaks feet and a half distance from it, was divided into of light also crossed one another, and the colored two black streaks only, the two outermost having streaks did the same. Having placed a needle disappeared ; but these two black streaks which and a hair crossing one another, their shadows, remained were broader than before, and sepa- at the same distance, exhibited the same aprated by a lighter shade, twice as broad as one pearances as the shadows of the two bairs, of the former black streaks, when the shadow though the shadow of the needle was the stronger. was taken at two feet and one-third. This pe- He also placed in the rays of the sun a bristle numbra in the middle had a tipge of red. After and a plate of iron a line thick, so that they the two black streaks there appeared a pretty crossed one another obliquely; and when their strong penumbra, terminated by the two streaks shadows were received at the same distance, the of light, which were now broad and splendid, light and dark streaks of the shadow of the after which followed the colored streaks. A bristle were visible so far as the shadow of the second plate, two inches long and a line broad, plate on the side of the acute angle, but not on being placed like the former fourteen feet from the side of the obtuse angle, whether the bristle the hole by which the rays of the sun were or the plate were placed next to the ray. The admitted, its shadow, being received perpendi- plate made a shadow sufficiently dark, livided

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into six black streaks; and these were again of the beam was parts of an inch. If the light divided by as many light ones equal to them; had not been bent, that breadth could not have and yet all the streaks belonging to the shadow exceeded 3%. Hence it must be concluded that of the bristle were visible upon it.

the light, being attracted by the sides of the hole, 65. M. Maraldi exposed several small globes is inflected, and of course caused to proceed in the light of the sun in his dark chanıber, and more divergingly than otherwise it would have compared their shadows with those of the long done. substances, as he had done in the day-light, and 69. With a hole one-tenth of an inch wide, or the appearances were still similar. There was wider, the centre of the beam was composed of much more light in the shadows of the globes the dense direct light of the sun unchanged in than in those of the cylinders, not only when its passage; but farther therefrom, towards the they were both of an equal diameter, but when borders of the beam, this light began to increase that of the globe was larger than that of the in density, and gradually decayed more and more cylinder, and the shadows of both the bodies in the approaches nearer and nearer to the borwere received at the same distance. He could ders, becoming at last considerably diluted and perceive no difference of light in the shadows of evanescent, and rendering the edge of the beam the plates which were a little more than one line ill-defined and indistinct. broad, though they were received at the distance 70. With a smaller hole than the last the cenof seventy-two feet; but he could easily see a tral dense light entirely disappeared, and, with difference of shades in those of the globes, taken a hole yet smaller than this, the external edges at the same distance, though they were two lines of the beam became more condensed and better and a quarter in diameter. To explain the defined; and the whole beam of light became, colors at the edges of these shadows, he contrived as before described, of more uniform density to throw some of the shadows upon others; in all its parts. With a hole smaller than any and the following observations, though they did of the foregoing, about tooth part of an inch not enable him to accomplish what he intended, wide, various colors began to appear in the are worth reciting :-Having thrown several of beam, the central parts of which became now, the similar colors upon one another, and thereby in their turn, more diluted than the rest, the exproduced a tinge more lively than before, he ternal parts denser than these, and bordered with threw the gleam of light, which always intervened tinges of yellow and red light on the very edge between the colors and the darker part of the or margin of the beam. shadow, upon different parts of other shadows; 71. All these appearances are to be ascribed and observed that, when it fell upon the exterior to the same attractions of the edges of the holes, penumbra made by another needle, it produced and of the different parts of the edges. These, a beautiful sky-blue color, almost like that which when the hole is large, affect only the parts of was produced by two blue colors thrown toge- the light passing nearest to them; when the hole ther. When the same gleam of light fell upon is reduced they attract and dilate the whole of the deeper shadow, in the middle, it produced a the passing light; when the hole is yet more red color. He placed two plates of iron, each considerably diminished, they act, not only each three or four lines broad, very near one another, part upon the light passing nearest to each, but but with a very small interval between them; each part also upon the light passing nearest to and having placed them in the rays of the sun, each opposite part of the edge, condensing by and received their shadows at fitteen or twenty diminishing the attraction and diffusion of the feet from them, he saw no light between them light on the edges of the beam, and rendering the but a continued shadow, in the middle of which whole more equably and uniformly divergent, and were some streaks of a lively purple, parallel to these at last, when the hole is in its most reduced one another, and separated by other black state, of about Idoth part of an inch wide, by their streaks; but between them there were other various actions produce colors in the passing streaks, both of a very faint green, and also of a light. pale yellow

72. In the beam of solar light passing through 66. If a solid opaque body, such as a hair, a the small hole goth part of an inch wide, the shaslender wire, &c., be placed in the stream of dows of very slender bodies, such as pins, needles, light within the room, the size of the shadow of straw, hairs, &c., were observed to be considerathat body will be found different from what it bly broader, as they ought to be in this divergent ought to be if the rays of light were not bent in light, than the bodies themselves; but, as each passing by it. This bending of the rays of light of these bodies exercises upon the light passing by passing, not through, but near the surface of by it the same attractions by which the light is a body, is called the inflection of light.

bent in passing through the hole, the author of 67. Let X, fig. 3, be the hole (about the fif- these experiments concluded that a part of the tieth part of an inch) of the light's passage into light would be in every case bent, in passing by, a darkened room, and let XX, X B, be lines towards the body into the shadow, and illuminate drawn from each external opposite edge on one

it and diminish its breadth, side of the solar disc, to each external opposite 73. Across a beam of solar light, admitted edge on the contrary side of the hole, crossing into a dark chamber through a small hole in a one another: XCD will represent the beam of thin piece of lead, nearly 35th of an inch wide, light after its passage through the hole, at ail a hair of a man's head was interposed, and the distances therefrom, considerably larger than the beam being received on a screen or sheet of penumbral cone E A B.

white paper, with an obliquity convenient for the 68. At seven feet from the hole the breadth purpose, the following appearances were noted :

74. At the termination of the shadow, whose that in certain distinct portions of light, and at intensity or darkness was not considerable, the different distances of observation, the more remote following orders and distinctions of colors ap- and the nearer rays of different colors contained peared. First and nearest to the dark or blue within each of those portions or divisions of the parts of the shadow might be seen a diluted blue, light, become variously intermingled with each changing into a breadth of white light, followed other, and, by their various intermixtures, form by breadths of yellow and red. To these suc each of these divisions into party-colored fringes ; ceeded an interval of diluted shade, then breadths whilst, the rays of different divisions never mixof diluted violet, blue, diluted green, yellow, ing with those of others, the intervals of the red; then green, diluted yellow, red; diluted divisions are preserved, and become the dark green, red; white, diluted red, and finally, white intervals which separate the fringes. light. These are the more general orders of the 80. The discoveries of M. A. Fresnel respectcolors. Of these orders the three first were suffi- ing the inflexion of light are in the highesi deciently obvious and distinct ; the last evanescent gree important, and cannot fail to be regarded and requiring accommodation of circumstances as affording a strong confirmation of the Huygeto produce, and attention to perceive them. nian theory of light. The following is a summary

75. When the distance of observation from of the principal results :the hair was very small, and before the first bright 81. (1.) M. Fresnel found that the fringes streak of light began to appear, the shadow of formed by inflexion may be examined by an eyethe hair was distinct and well-defined, and of glass, without receiving them upon a white surintense blackness. At a greater distance this face; and, by adapting a micrometer to the eyeshadow appeared to be divided by a parallel glass, he was able to determine their breadths, line of light throughout its whole length, into even to the 100th or 200th part of a millimetre. two parts, and resembled a double shadow, or 82. (2.) By following the external fringes to the shadows of two hairs, but was by no means their origin by means of a lens with a short nf the same degree of blackness as was the single focus, he perceived the third fringe at the disshadow observed close to the hair. At still tance of less than the 100th of a millimetre from greater distances it increased in breadth and di- the edge of the inflecting body. mioished in blackness, whilst the transverse 83. (3.) The inflexion of the passing light is dimensions of the dividing line of light increased influenced by the distance of the radiating or at the same time, until, at a considerable distance luminous point from the inflecting body, as apfrom the hair, this intermediate band or line of pears from the following results :light began to put on the appearance of colors on its edges, and to assume, on both sides externally, casts of yellowish and reddish light. By

Distance behind Angular deviafurther increase of distance this apparent shadow,

Distance of the the body where tion or inflexion radiating point the inflexion

of the red rays these dark intervals became more diluted, and

from the body.

was measured. of the first of nearly the same color throughout, the line of

fringe. light more and more diffused, and was at last extinguished by the extreme diffusion and ultimate

100 millimetres. 1 metre. 12' 6" invisibility of the light that produced it.

6 metres.

3' 55" 76. Whilst at all these different distances these changes proceed in the shadow, and in the light nearest to the body, in the other adjoining parts

84. Hence it follows that the ray suffers a of the light passing next in order of distance by less degree of inflexion in proportion to the disthe hair considerable changes are also produced. tance from which it diverges.

77. The shadow that first appeared close to 85. (4.) When the inflexion of the same the hair is perfectly and truly a shadow, being fringe is measured at different distances behind produced by the interception of the passing light the inflecting body, the distance of the radiant by the hair.

point remaining the same, it is found to be dif78. This shadow, however, quickly ceases to ferent at different distances; and hence it follows appear, the rays of light nearest to it on both that the successive positions of the same fringe sides of the hair being bent into it at considera- are not in a straight line, but form a curve whose ble angles of inflection and dispersion, and concavity is turned towards the inflecting body. crossing, illuminating, and extinguishing it. The lines which join the different positions of the

79. The rays of light are not only bent, they fringe of all the orders of colors are hyperbolas, are also distributed or divided into different rays having for their common foci the radiating point of different colors, in angles of dispersion greater and the edge of the inflecting body. In some as the distances are less, and less as the distances of M. Fresnel's experiments the sagitta of curare greater, in such a manner that of different vature was about one millimetre, or the twentycolors at the same distance, the purples, blues, fifth part of an inch, which is nearly fifty times greens, yellows, and reds, are bent towards the greater than the error of observation. body; the purples most, each of the others in 86. (5.) M. Fresnel measured the fringes produe succession less, and the reds least, accord- duced by various bodies, and found, by accuing to the order of their statement; and of colors rate measurement, that they all produced the of the same sorts, at different distances, the nearer same inflexion, the back of a razor giving the more than the more remote, and the more remote same fringes as its sharp edge. less than the nearer. So various, however, are the 87. Results of a similar kind were obtaincd bendings of different colors at different distances, by Dr. Brewster in two sets of experiments, one

1 metre.

of which was made in 1798, and the other in 91. It is by no means easy to explain to ge1812 and 1813. He compared the fringes formed neral readers the hypothesis by which M. Fresnel by gold leaf with those made by masses of gold; has accounted for the fringes upon the principle those formed by films which produced the colors of interference; but we shall attempt to make it of thin plates with those formed by masses of as intelligible as possible. the same substance. He examined the effects of 92. Let A ME, fig. 4, be a luminous wave or platinum, diamond, and cork, in inflecting the undulation, propagated from the radiant point light; the effects of grooves in metallic surfaces, C, and partly intercepted by the inflecting body &c.; and of cylinders of glass immersed in A G. Then, if we suppose it divided into an fluids of the same refractive power: and from infinity of small arcs Am, m'm, m M, Mn, nn', these he concluded that the Newtonian theory of n' n", &c., M. Fresnel obtains the intensity of inflexion could not be true; that the inflexion any point (P) of the wave AM E, when it has was not produced by any force inherent in the reached the position B P D, by supposing elebodies themselves, but arose from a property of mentary waves to be propagated from every the light itself, which always shows itself when point m, m', M, n, n', &c., of its preceding posidivergent light was stopped in its progress. tion at AM E. These elementary waves are

88. (6.) The fringes in the interior of the sha- propagated in all directions, and with intensities dow were first explained by Dr. Thomas Young. sensibly equal when they do not deviate much He showed, in the clearest manner, that they from the perpendicular. M. Fresnel does not were formed by the interference of two portions take into account the waves which are most inof light coming from the opposite sides of the clined, and which, according to his hypothesis, inflecting body. Having introduced the sun's destroy one another; and in this way he deterlight into a dark room, through two small holes mines the intensity of the light resulting from the very near each other, he received the admitted reciprocal influence of all the rays which are light upon a sheet of paper from each of the slightly inclined to the perpendicular. By thus holes separately, and observed no particular combining the principle of Huygens with Dr. effect. But when the light was admitted through Young's law of interference, he has obtained a both the holes at the same time, so as to inter- formula which represents the observations with fere, a series of obscure and brilliant fringes was surprising accuracy. produced.

93. (7) The phenomena of inflexion are con89. M. Fresnel obtained a similar effect by sidered by M. Fresnel to be inexplicable on the reflecting light from two metallic mirrors slightly Newtonian theory of the emission of luminous inclined to each other, and whose surfaces were particles; while almost all of them may be dinearly in the same plane. The formation of rectly deduced from the Huygenian Theory of these bands depends on the lengths of the paths Undulations. of two interfering portions of light. When the 94. There are two very important and compaths are exactly of the same length, the two paratively new branches of optical science to portions of light will form a very brilliant fringe, which we must now direct our readers' attention, having an intensity greater than that of either namely, the double refraction and polarisation of portion. If the next brilliant fringe corresponds light. to a difference of paths equal to d, then other 95. About the middle of the seventeenth cenbrilliant fringes will be formed when the differ- tury Dr. Erasmus Bartholinus, a physician at ences of the paths are 2 d, 3 d, 4 d, &c. When Copenhagen, and the author of several excellent the differences of the paths are id; d + } d; works on geometry, procured, from some of the 2 d + } d, or s d, d, 3 d, the interfering por- Danish merchants that frequented Iceland, a tions neutralise or destroy one another, and con- crystal stone like a rhombick or rhomboid sequently produce a black fringe. The quantity prism, which, when broken into small pieces, d has a different value for the rays of different kept the same figure. It was dug out of a very colors, and varies as the length of the fits in high mountain, not far from the Bay of Roerfiord, Newton's theory. M. Fresnel has found d to in 65° of lat. Its whole body was rather clear be moltooth of a millimetre for red light.

than bright, and of the color of limpid water ; 90. This beautiful theory of Dr. Young is em- but that color, when it was immersed in water braced by M. Fresnel. Both these philosophers and dried again, became dull. With this subhad ascribed the exterior fringes to the inter- stance, which from its locality was called Iceference of the direct rays with rays reflected from land crystal, Bartholinus made a number of the margin of the inflecting body. M. Fresnel, experiments both chemical and optical; and, however

, has since found that this explanation having discovered some of the singular effects is insufficient; for the real place of the fringe is which it produced upon light, he published an sometimes to oth of a millimetre different from account of them at Copenhagen in 1669, under what it should be upon this supposition; and the title of Experimenta Crystalli Islandici Dis at any rate, if the hypothesis were true, the ex- -diaclastici, quibus mira et insolita refractio tent and curvature of the margin of the inflecting detegitur. There does not appear to be a copy body would have an influence upon the inten- of this work in this country, but the want of it is sity of the fringes, which is contrary to experi- well supplied by an account of sundry experiment. He is therefore obliged to admit that the ments made and communicated by Dr. Erasmus rays which pass at a sensible distance from the Bartholinus, addressed to Dr. Oldenburgh, and inflecting body are made to deviate from their printed in the sixty-seventh number of the Philoprimitive direction, and concur also in the pro- sophical Transactions. From this account we duction of the colored fringes.

shall select those parts which relate to double

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