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I. A NEW THEORY OF LIGHT AND COLORS1 2
Sir,
Fulfilling my recent promise, I shall, without further preliminaries, begin with the fact that at the beginning of the year 1666 (at that time I was engaged in grinding optical glasses of forms other than spherical) I obtained a triangular glass prism, in order to make experiments with it on the celebrated phenomenon of colors3. For this purpose, having darkened my room and made a small hole in the window shutters to admit a suitable quantity of sunlight, I placed my prism where the light entered, so that it could be refracted toward the opposite wall. At first, the sight of the vivid and bright colors thus produced gave me very pleasant enjoyment. But then, forcing myself to look more attentively at the colors, I was struck by their elongated form: in accordance with the laws of refraction known to me, I expected that the form would be round. At the sides the colors were bounded by straight lines, while at the ends the diminution of the light was so gradual that it was difficult to define the figure; nevertheless, it seemed semicircular.
Comparing the length of the colored spectrum with its width, I found that it was approximately five times greater. The disproportion was so unusual that it aroused in me more than simple curiosity to learn whence this arose. It could hardly be supposed that the different thickness
glass, or a boundary with shadow or darkness, produces upon the light such an influence that the indicated effect is obtained (3). I considered it necessary, however, first to examine these circumstances and tried what would happen if the light were passed through parts of the glass of different thicknesses, or through openings in the window of different sizes, or if the prism were placed outside, so that the light passed through it and was refracted in it before being limited by the opening. But I found that none of these circumstances was essential. The appearance of the colors in all these cases remained the same.
Then I suspected whether the colors might not be spread out owing to some irregularities in the glass or to accidental imperfections. To check this, I took another prism, like the first, and placed it so that the light passing through both prisms could be refracted in the opposite way, the second prism returning the light to the path from which it had been deflected by the first. In this way, I thought, the regular actions of the first prism would be destroyed by the second, while the irregular ones would be increased through the increase in the number of refractions. In fact, what happened was that the light dispersed by the first prism into an elongated form was brought by the second prism back to a round form, as correctly as if it had not passed through prisms at all. Thus, whatever the cause of the elongation might be, it was not explained by accidental irregularities.
Next I proceeded to a more critical consideration of what effect might be produced by the difference in the incidence of rays coming from different parts of the sun. For this purpose I measured the various lines and angles corresponding to the image. The distance of the image from the opening was 22 feet; its greatest length \(13\frac{1}{4}\) inches, width \(2\frac{5}{8}\); the diameter of the opening \(\frac{1}{4}\) inch; the angle formed by the rays going to the middle of the image and by the line along which the rays would have gone without refraction was \(44^\circ 56'\); the vertical angle of the prism was \(63^\circ 12'\). The refractions on both sides of the prism, i.e. on the side of the incident and the emergent rays, were equal, so far as I could make them so, and therefore were approximately \(54^\circ 4'\). The rays fell upon the wall perpendicularly. If the diameter of the opening is subtracted from the length and width of the image, there remains 13 inches in length and \(2\frac{3}{8}\) inches in width, corresponding to the rays passing through the center of the opening. Consequently, the angle at the opening subtended by the indicated width was approximately \(31'\), corresponding to the diameter of the sun; but the angle subtended by the length of the opening was more than five times the solar diameter, namely \(2^\circ 49'\).
Having made these observations, I first of all calculated from them the refractive power of the glass and found that it is measured by the ratio of the sines 20 to 31. From this ratio I then calculated the refractions of two rays coming from opposite parts of the solar
disk and differed by \(31'\) in obliquity of incidence; I found that the emergent rays should make an angle of about \(31'\), as before incidence. This calculation was based on the hypothesis of the proportionality of the sines of incidence and refraction. However, on the basis of my own experiments, I could not imagine that this hypothesis was so erroneous that it would give an angle of \(31'\), whereas in reality it is equal to \(2^\circ 49'\). My curiosity made me take up the prism again. Placing it by the window, as before, I observed that when it was turned slightly about its axis to and fro, while its inclination to the light changed by more than \(4\)—\(5\) degrees, the colors did not noticeably move from their place on the wall. Consequently, under such a variation of the angle of incidence, the magnitude of the refraction did not noticeably change. From this experiment, and also on the basis of the preceding calculation, it was evident that the difference in incidence of the rays coming from different parts of the sun cannot, after their intersection, produce a divergence at an angle appreciably greater than that under which they previously converged; the magnitude of this angle is no more than \(31\)—\(32\) minutes; therefore it remained to find another cause by which an angle of \(2^\circ 49'\) would be obtained\(^{4}\).
Then I began to suspect whether the rays, after passing through the prism, might not move along curved lines, tending, according to greater or lesser curvature, toward different parts of the wall. This suspicion was strengthened when I recalled that I had often had occasion to see how a tennis ball, when struck obliquely by the racket, describes such a curved line. For in this case both a rotary and a translational motion are imparted to the ball. That side of the ball where the two motions agree must press and push the adjacent air more strongly than the other side and, consequently, will excite a proportionally greater resistance and reaction of the air\(^{5}\). For the same reason, if rays of light were spherical bodies and, in an oblique transition from one medium into another, acquired a rotational motion, then they would have to experience greater resistance from the surrounding ether on the side where the motions agree, and would continuously bend away to the other side. However, despite the plausible basis of this supposition, upon investigating it I could observe no curvature of the rays. And, moreover (for my purpose this was sufficient), I observed that the difference between the length of the image and the diameter of the aperture through which the light passed was proportional to their distance.
Gradually eliminating these suppositions, I finally came to the experimentum crucis, which consisted in the following. I took two boards; one of them I placed immediately behind the prism at the window, so that the light could pass through a small aperture made in the board for this purpose, and fall upon another board, which I placed at approximately a distance of 12 feet; in it too there had first been made
A NEW THEORY OF LIGHT AND COLORS
a small opening, so that part of the incident light could pass through it. Then, behind this second board, I placed another prism, so that the light passing through both boards could also pass through the prism, being refracted in it before reaching the wall. Having done this, I took the first prism in my hand and slowly turned it back and forth about its axis, so that different parts of the image falling on the second board could successively pass through the opening in this board, and I could see to what places on the wall the second prism refracted the rays. And I found, by changing these places, that the light directed toward that end of the image at which the greatest refraction by the first prism occurred underwent, in the second prism, considerably greater refraction than the light directed toward the other end. Thus the true cause of the length of the image was discovered, which consisted in the fact that light consists of rays of different refrangibility, which, independently of the difference of their incidence, proceed to different parts of the wall according to their degrees of refraction4.
Having understood this, I abandoned my above-mentioned work with glass, for I saw that the improvement of telescopes had until now been limited not so much by the absence of glasses of the proper form, corresponding to the prescriptions of optical authors (whatever those forms might be), as by the fact that light is a heterogeneous mixture of rays of different refrangibility. If glass were given so exact a form that it would collect all rays of one kind into one point, it would not collect at that same point the rays which, at equal incidence upon the same medium, would be capable of undergoing different refraction. Moreover, seeing so great a difference in refrangibility as I had found, I was surprised that telescopes had attained such perfection as they now have. Measuring the refractions in one of my prisms, I found that, if the common sine of incidence on one of its planes be supposed equal to 44 parts, then the sine of refraction of the extreme rays at the red end of the colors, in passing from glass into air, would be 68 parts, and the sine of refraction of the extreme rays at the other end—69 parts, so that the difference amounts to approximately one twenty-fourth or twenty-fifth part of the whole refraction. Consequently, the object glass of any telescope cannot collect all the rays proceeding from any point of the object into a focus within a space smaller than a circle whose diameter is the fiftieth part of the diameter of the aperture of the glass. This irregularity exceeds by several hundred times the irregularity which, in the case of homogeneous light, could be caused, owing to inaccuracy of form, by a spherical lens of as small a section as the object glasses of long telescopes.
This led me to turn to reflections. Finding that they occur regularly, so that the angle of reflection of all kinds of rays
I. NEWTON
equal to their angle of incidence, I understood that, by means of reflections, optical instruments could be brought to any conceivable degree of perfection. This is possible if a reflecting substance can be found which is polished as finely as glass and reflects as much light as glass transmits, and if a method is found for giving the substance a parabolic form. But here very great difficulties appeared; I considered them altogether insurmountable, reasoning that every irregularity of the reflecting surface causes the rays to deviate by a distance 5–6 times greater from the required path than in the case of similar irregularities of a refracting surface. Thus, here considerably greater precision is required than in shaping lenses for refraction.
In the midst of these occupations the outbreak of the plague forced me to leave Cambridge, and more than two years passed before I returned to further work. Having devised a finer method of polishing, suitable for metals, by means of which, I hoped, the form could be perfectly corrected, I began to try what could be done in this way. Gradually I improved the instrument (which in its essential parts resembles the one that I sent to London^7) to such an extent that I could distinguish the 4 satellites of Jupiter and sometimes showed them to two of my acquaintances. I could also distinguish the crescent phases of Venus, though not very clearly and not without some deterioration in the arrangement of the instrument.
From that time I was interrupted until last autumn, when I made another instrument. It proved considerably better than the first (especially with respect to terrestrial objects), so that I have no doubt that the instruments will be brought to still greater perfection by the efforts of those who, as you have informed me, have taken charge of it in London^7).
Fig. 1.
I also thought of making a microscope in which, in a similar way, a reflecting metal is placed instead of the objective glass. I hope that this too will receive attention. For such instruments can apparently be improved, like telescopes, and possibly even more, since in them only one reflecting metallic mirror is required. You can see this from the diagram, where $AB$ represents the objective metallic mirror, $CD$ the ocular glass, $F$ their common focus, and $O$ the other focus of the mirror, in which the object is placed.
After this digression let us return to what follows; I said that light is not uniform or homogeneous and consists of various rays—
...some of which are refracted more than others. Of the rays falling alike upon one and the same medium, some will be refracted more than others, not by virtue of any capacity in the glass or of any other external cause, but because of the disposition possessed by each separate ray to undergo its own degree of refraction.
I shall now acquaint you with another, more remarkable variety of rays, which reveals the origin of colors. In connection with this I shall first set forth the doctrine, and then, for its verification, give you one or two experimental examples, as a sample of the rest. The doctrine is set forth and explained by the following propositions:
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Just as rays differ in their degree of refrangibility, so also do they differ in their disposition to exhibit this or that particular color. Colors are not qualities of light arising in consequence of refractions or reflections in natural bodies (as is commonly thought), but are original and innate properties, different in different rays. Some rays are disposed to exhibit the color red and no other; some yellow and no other; some green and no other, and so on. There exist not only rays corresponding to the strongest colors, but also to all their intermediate gradations.
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To one and the same degree of refrangibility there always corresponds one and the same color, and to one and the same color there always belongs one and the same degree of refrangibility. All the least refrangible rays are disposed to exhibit the color red; and, conversely, the rays disposed to exhibit the color red are all the least refracted. Likewise, the most refrangible rays are all disposed to exhibit a deep violet color; and, conversely, those rays which are capable of exhibiting such a violet color are all refracted most strongly. The same holds also with respect to the intermediate colors. This analogy between colors and refrangibility is very exact and strict: rays either agree precisely in both respects, or disagree proportionally in both.
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The kind of color and the degree of refrangibility proper to each separate sort of rays are altered neither by refraction, nor by reflection from natural bodies, nor by any other cause that I have been able to observe. If any sort of rays was well separated from rays of another kind, then thereafter it obstinately retained its coloration, despite my utmost efforts to change it. I refracted a dark color with prisms, reflected it from bodies which in daylight had a different coloration. I blocked its path with a colored film of air between two compressed plates of glass8), passed it through colored media, through media illuminated by other sorts of rays, restricted it in various ways, and yet I could never produce in it a new coloration. On being compressed or
upon expansion it became more brilliant or weaker, and when many rays were lost, in some cases—very murky and dark; but I never noticed any change in its kind.
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However, changes of color, apparently, can occur where there is some mixture of different sorts of rays. For in such a mixture the component colors are not visible; overlapping one another, they compose an intermediate coloration. Therefore, if by refraction or owing to the other causes indicated, the various rays hidden in the dark mixture are separated, they will exhibit colors different from the coloration of the mixture. These colors are not created anew, but have only become visible through separation. For if they again mix completely and conceal one another, they will again compose the color which they had before separation. For the same reason the transformations that occur when different rays meet are not real; for if the different rays are again separated, they will exhibit exactly the same colors as before entering the mixture. As you know, blue and yellow powders, when finely mixed, appear green to the naked eye, and yet the colors of the constituent particles have not in reality changed, but have only concealed one another. For if one looks through a good microscope, they will again appear alternately blue and yellow.
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Therefore there are two kinds of colors. One is primary and simple, the other composed of them. The primary colors are: red, yellow, green, blue, and violet-purple, together with orange, indigo, and an infinite variety of intermediate gradations ⁹).
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The same colors in appearance as the primary ones can be obtained by mixing: for a mixture of yellow and blue gives green; of red and yellow—orange; of orange and yellowish-green—yellow. And in general, if any two colors in the series obtained by means of the prism, situated not far from one another, are mixed, then by their mutual union there will be formed a color lying in the above-mentioned series between them. Colors situated at a very great distance behave differently. Orange and indigo do not give the intermediate green; crimson and green do not give the intermediate yellow.
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But the most striking and wonderful mixture is that which gives whiteness. There is not a single sort of rays which, taken separately, could exhibit it. It is always composite, and to obtain it all the above-mentioned colors are required, mixed in the necessary proportion. Often I watched with delight how all the colors of the prism, when I made them converge and again mix in the same way as they had been in the light that fell upon the prism, reproduced a full and perfect white light, in no way differing from the direct light of the sun, provided only that the glasses I used were sufficiently transparent; otherwise the glass inclines them somewhat toward its own coloration.
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From this it follows that whiteness is the ordinary coloration of light; for light is a mixed aggregate of rays endowed with all sorts of colors, corresponding to their disorderly emission from the various parts of luminous bodies. Such a disorderly mixture, as I have said, produces whiteness if there is a proper proportion of ingredients. But if some ingredient predominates, the light inclines toward its coloration, as happens in the blue flame of sulphur, the yellow flame of a candle, and in fixed stars of various coloration.
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If one considers all these things, the manner in which colors arise in a prism will become obvious. For the rays that make up the incident light, differing in color, differ proportionally in refrangibility; therefore, owing to unequal refrangibility, they must separate and be dispersed into an elongated form in sequence, in order from the least refrangible crimson to the most refrangible violet. For the same reason, objects, when viewed through a prism, appear colored. For the different rays, because of their unequal refractions, diverge to different parts of the retina and there give colored images of objects, just as in the preceding case the image of the sun on the wall. Owing to this inequality of refractions, the images become not only colored, but also very confused and indistinct.
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From this it is likewise obvious why the colors of the rainbow appear in falling drops of rain. For drops that refract toward the observer’s eye the greatest quantity of rays capable of producing purple 9), refract rays of other sorts so much less that they appear in another place; such are the drops on the inner side of the primary rainbow and on the outer side of the secondary rainbow. Likewise, drops that refract toward the observer’s eye, with the greatest fullness, rays capable of appearing red refract rays of other sorts so much more that they pass off to the side; such are the drops on the outer part of the primary rainbow and on the inner part of the secondary.
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The strange phenomena of a tincture of lignum nephriticum 10), of gold leaf, pieces of colored glass, and other transparent colored bodies, which in one position appear of one color and in another of another, are no more mysterious on these grounds. For these substances are capable of reflecting one sort of light and transmitting another, as may be seen in a dark room by illuminating them with homogeneous or uncompounded light. For then they reveal only the color with which they are illuminated, but in one position this color is more vivid or bright than in another, according as these substances are disposed to a greater or lesser reflection or transmission of the incident color.
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From this also is clear the reason for one unexpected experiment, of which Mr. Hooke reports in his Micrographia. The experiment is made, as
he has, with other wedge-shaped vessels likewise filled, one with a red, another with a blue liquid. Although the vessels separately were sufficiently transparent, yet both together were opaque. For one vessel transmits only red rays, the other only blue; therefore no rays could pass through both vessels together ¹¹).
- I could add many examples of the same character. But I shall conclude with the following general fact: the colors of all natural bodies arise only from their having the capacity to reflect one sort of light more fully than others. I tested this in a dark room, illuminating natural bodies with unmixed light of various colors. For in this way any body may be made to appear with any coloration. They therefore have no color of their own and appear in the coloration of the color that falls upon them, but with this difference: that bodies seem most brilliant and vivid in the light of their own daylight coloration. Thus, red lead shows indiscriminately any coloration depending on the color with which it is illuminated, but the brightest in red light; likewise azure ¹¹ᵃ) shows indiscriminately any color with which it is illuminated, but it is brightest of all in blue. Therefore red lead reflects rays of all colors, but most abundantly the rays that produce the red color; when illuminated by daylight, i.e. by all sorts of rays, disorderly concealing one another, the rays having the quality of red will consequently be most abundant in the light reflected from red lead and, by their predominance, will produce the appearance of this coloration. For the same reason azure, reflecting blue most abundantly, will appear blue because of the excess of these rays in the reflected light; and so also with respect to other bodies. It is clear that herein lies the full and sufficient cause of the coloration of bodies, because they cannot alter or transform the colors of any sort of rays falling upon them, and indifferently take on all colors with which they are illuminated.
If this is so, then it is no longer possible to dispute whether colors exist in darkness, whether they are not qualities of visible objects, and whether light is not perhaps a body. For, since colors are qualities of light, having rays as their complete and immediate subject, can one think of rays as qualities, if only a quality cannot be the subject and support of another quality—which would mean calling it in reality a substance? We recognize bodies as substances only by their sensible qualities, and, once the chief qualities of something have been found, we have sufficient grounds to regard this something also as a substance ¹²).
Moreover, has anyone ever thought that any quality could be so heterogeneous an aggregate as this has been found to be with respect to light? But it is not so easy to determine more decisively,
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or actions it produces images of colors in our minds. And I shall not confuse conjectures with certainties ¹²).
Reviewing what I have written, I see that the reasoning itself leads to various experiments sufficient for investigating them; therefore I shall not detain you further and shall confine myself only to the description of one of the experiments that I have already mentioned.
Make an opening in the window shutter of a darkened room—an appropriate diameter for it is about one third of an inch—so that the necessary quantity of sunlight may pass through; place there a transparent and colorless prism so that it refracts the entering light toward the remote parts of the room. The light, as I have said, will thereby be dispersed into an elongated colored image. Then, at a distance of about four or five feet from there, place a lens with a radius of about three feet (say, the broad object glass of a three-foot telescope); all the colors must pass at once through the lens and, thanks to refraction in it, will come together at a distance of ten to twelve feet. If at this distance you intercept the light with a sheet of white paper, you will see that the colors, again by their mixture, have turned into whiteness. The prism
Fig. 2.
and the lens must be left motionless, while the paper on which the colors are displayed should be moved forward and backward; by means of such motion you will not only find at what distance the whiteness is most perfect, but will also see how the colors gradually come together and disappear into whiteness; and, having crossed at the place where the whiteness is formed, they are again dispersed and separated, preserving in reverse order those colors which they had before the mixture. You can also see that if any of the colors at the lens are stopped, then the whiteness changes into other colors. Therefore, in order to compose a perfect whiteness, care must be taken that not one of the colors falls to the side of the lens.
In the accompanying drawing of this experiment, \(ABC\) represents the prism, seen from the side of the base and placed at the aperture \(F\) in the window \(EG\). The vertical angle \(ABC\) is conveniently chosen at about 60 degrees; \(MN\) denotes the lens. Its width is \(2 \tfrac{1}{2}\)—3 inches. \(SF\) is one of the straight lines along which one may imagine successively moving—
various rays coming from the sun. \(FP\) and \(FR\) are two of these rays, refracted unequally. The lens makes them converge at \(Q\) and then diverge again after meeting; \(HI\) is paper at various distances, upon which the colors are projected; at \(Q\) whiteness is formed, but at \(R, r\) and \(\rho\) red and yellow are obtained, and at \(P, p\) and \(\pi\)—blue and purple.
If you should further wish to investigate the impossibility of changing simple colors (which I assert in propositions 3 and 13), then for this it is necessary that the room be very dark, for any scattered light, mixing with a simple color, spoils it and blends with it, making it compound, which runs counter to the purpose of the experiment. It is also necessary that the separation of the colors be more perfect than that which is obtained by refraction in a single prism in the manner described above. For those who consider the laws of refraction that have been discovered, it will hardly be difficult to obtain such a further separation¹³).
But if the experiment is carried out with colors that are not perfectly separated, changes of color proportional to the mixture will be observed. Thus, if a compound yellow color falls upon blue azure, the latter will not appear perfectly yellow, but rather green, since in the yellow mixture there are many rays that produce green; and the green color is contained in the ordinary blue paint of azure in greater quantity than yellow, and therefore is reflected more abundantly.
In the same way, if one arrests one of the prismatic colors, say red, in order to test the asserted impossibility of reproducing this color from the remaining colors that are allowed to pass, it is necessary first to separate the colors very well before arresting the red. Or else one must arrest together with the red the neighboring colors in which red is imperceptibly scattered (i.e., yellow, and perhaps even green). Otherwise one will have to accept the presence of red in the yellow-green, scattered in it and concealed by these colors. If all these conditions are observed, then a new production of red, or of another arrested color, will prove impossible.
I believe that this is sufficient as an introduction to experiments of this kind. If anyone from the Royal Society is curious to verify them, I shall be very glad to be informed of the success of the experiments. If anything should prove erroneous or contrary to this communication, then I shall have the opportunity to give further instructions, or else to acknowledge my errors, should I have made any¹⁴).