Opticks

_Sect._ IV. _Prop._ 31.

THE FIRST BOOK OF OPTICKS

_PART II._

_PROP._ I. THEOR. I.

_The Phaenomena of Colours in refracted or reflected Light are not caused by new Modifications of the Light variously impress"d, according to the various Terminations of the Light and Shadow_.

The PROOF by Experiments.

_Exper._ 1. For if the Sun shine into a very dark Chamber through an oblong hole F, [in _Fig._ 1.] whose breadth is the sixth or eighth part of an Inch, or something less; and his beam FH do afterwards pa.s.s first through a very large Prism ABC, distant about 20 Feet from the hole, and parallel to it, and then (with its white part) through an oblong hole H, whose breadth is about the fortieth or sixtieth part of an Inch, and which is made in a black opake Body GI, and placed at the distance of two or three Feet from the Prism, in a parallel Situation both to the Prism and to the former hole, and if this white Light thus transmitted through the hole H, fall afterwards upon a white Paper _pt_, placed after that hole H, at the distance of three or four Feet from it, and there paint the usual Colours of the Prism, suppose red at _t_, yellow at _s_, green at _r_, blue at _q_, and violet at _p_; you may with an Iron Wire, or any such like slender opake Body, whose breadth is about the tenth part of an Inch, by intercepting the Rays at _k_, _l_, _m_, _n_ or _o_, take away any one of the Colours at _t_, _s_, _r_, _q_ or _p_, whilst the other Colours remain upon the Paper as before; or with an Obstacle something bigger you may take away any two, or three, or four Colours together, the rest remaining: So that any one of the Colours as well as violet may become outmost in the Confine of the Shadow towards _p_, and any one of them as well as red may become outmost in the Confine of the Shadow towards _t_, and any one of them may also border upon the Shadow made within the Colours by the Obstacle R intercepting some intermediate part of the Light; and, lastly, any one of them by being left alone, may border upon the Shadow on either hand.

All the Colours have themselves indifferently to any Confines of Shadow, and therefore the differences of these Colours from one another, do not arise from the different Confines of Shadow, whereby Light is variously modified, as has. .h.i.therto been the Opinion of Philosophers. In trying these things "tis to be observed, that by how much the holes F and H are narrower, and the Intervals between them and the Prism greater, and the Chamber darker, by so much the better doth the Experiment succeed; provided the Light be not so far diminished, but that the Colours at _pt_ be sufficiently visible. To procure a Prism of solid Gla.s.s large enough for this Experiment will be difficult, and therefore a prismatick Vessel must be made of polish"d Gla.s.s Plates cemented together, and filled with salt Water or clear Oil.

[Ill.u.s.tration: FIG. 1.]

_Exper._ 2. The Sun"s Light let into a dark Chamber through the round hole F, [in _Fig._ 2.] half an Inch wide, pa.s.sed first through the Prism ABC placed at the hole, and then through a Lens PT something more than four Inches broad, and about eight Feet distant from the Prism, and thence converged to O the Focus of the Lens distant from it about three Feet, and there fell upon a white Paper DE. If that Paper was perpendicular to that Light incident upon it, as "tis represented in the posture DE, all the Colours upon it at O appeared white. But if the Paper being turned about an Axis parallel to the Prism, became very much inclined to the Light, as "tis represented in the Positions _de_ and _[Greek: de]_; the same Light in the one case appeared yellow and red, in the other blue. Here one and the same part of the Light in one and the same place, according to the various Inclinations of the Paper, appeared in one case white, in another yellow or red, in a third blue, whilst the Confine of Light and shadow, and the Refractions of the Prism in all these cases remained the same.

[Ill.u.s.tration: FIG. 2.]

[Ill.u.s.tration: FIG. 3.]

_Exper._ 3. Such another Experiment may be more easily tried as follows.

Let a broad beam of the Sun"s Light coming into a dark Chamber through a hole in the Window-shut be refracted by a large Prism ABC, [in _Fig._ 3.] whose refracting Angle C is more than 60 Degrees, and so soon as it comes out of the Prism, let it fall upon the white Paper DE glewed upon a stiff Plane; and this Light, when the Paper is perpendicular to it, as "tis represented in DE, will appear perfectly white upon the Paper; but when the Paper is very much inclin"d to it in such a manner as to keep always parallel to the Axis of the Prism, the whiteness of the whole Light upon the Paper will according to the inclination of the Paper this way or that way, change either into yellow and red, as in the posture _de_, or into blue and violet, as in the posture [Greek: de]. And if the Light before it fall upon the Paper be twice refracted the same way by two parallel Prisms, these Colours will become the more conspicuous.

Here all the middle parts of the broad beam of white Light which fell upon the Paper, did without any Confine of Shadow to modify it, become colour"d all over with one uniform Colour, the Colour being always the same in the middle of the Paper as at the edges, and this Colour changed according to the various Obliquity of the reflecting Paper, without any change in the Refractions or Shadow, or in the Light which fell upon the Paper. And therefore these Colours are to be derived from some other Cause than the new Modifications of Light by Refractions and Shadows.

If it be asked, what then is their Cause? I answer, That the Paper in the posture _de_, being more oblique to the more refrangible Rays than to the less refrangible ones, is more strongly illuminated by the latter than by the former, and therefore the less refrangible Rays are predominant in the reflected Light. And where-ever they are predominant in any Light, they tinge it with red or yellow, as may in some measure appear by the first Proposition of the first Part of this Book, and will more fully appear hereafter. And the contrary happens in the posture of the Paper [Greek: de], the more refrangible Rays being then predominant which always tinge Light with blues and violets.

_Exper._ 4. The Colours of Bubbles with which Children play are various, and change their Situation variously, without any respect to any Confine or Shadow. If such a Bubble be cover"d with a concave Gla.s.s, to keep it from being agitated by any Wind or Motion of the Air, the Colours will slowly and regularly change their situation, even whilst the Eye and the Bubble, and all Bodies which emit any Light, or cast any Shadow, remain unmoved. And therefore their Colours arise from some regular Cause which depends not on any Confine of Shadow. What this Cause is will be shewed in the next Book.

To these Experiments may be added the tenth Experiment of the first Part of this first Book, where the Sun"s Light in a dark Room being trajected through the parallel Superficies of two Prisms tied together in the form of a Parallelopipede, became totally of one uniform yellow or red Colour, at its emerging out of the Prisms. Here, in the production of these Colours, the Confine of Shadow can have nothing to do. For the Light changes from white to yellow, orange and red successively, without any alteration of the Confine of Shadow: And at both edges of the emerging Light where the contrary Confines of Shadow ought to produce different Effects, the Colour is one and the same, whether it be white, yellow, orange or red: And in the middle of the emerging Light, where there is no Confine of Shadow at all, the Colour is the very same as at the edges, the whole Light at its very first Emergence being of one uniform Colour, whether white, yellow, orange or red, and going on thence perpetually without any change of Colour, such as the Confine of Shadow is vulgarly supposed to work in refracted Light after its Emergence. Neither can these Colours arise from any new Modifications of the Light by Refractions, because they change successively from white to yellow, orange and red, while the Refractions remain the same, and also because the Refractions are made contrary ways by parallel Superficies which destroy one another"s Effects. They arise not therefore from any Modifications of Light made by Refractions and Shadows, but have some other Cause. What that Cause is we shewed above in this tenth Experiment, and need not here repeat it.

There is yet another material Circ.u.mstance of this Experiment. For this emerging Light being by a third Prism HIK [in _Fig._ 22. _Part_ I.][I]

refracted towards the Paper PT, and there painting the usual Colours of the Prism, red, yellow, green, blue, violet: If these Colours arose from the Refractions of that Prism modifying the Light, they would not be in the Light before its Incidence on that Prism. And yet in that Experiment we found, that when by turning the two first Prisms about their common Axis all the Colours were made to vanish but the red; the Light which makes that red being left alone, appeared of the very same red Colour before its Incidence on the third Prism. And in general we find by other Experiments, that when the Rays which differ in Refrangibility are separated from one another, and any one Sort of them is considered apart, the Colour of the Light which they compose cannot be changed by any Refraction or Reflexion whatever, as it ought to be were Colours nothing else than Modifications of Light caused by Refractions, and Reflexions, and Shadows. This Unchangeableness of Colour I am now to describe in the following Proposition.

_PROP._ II. THEOR. II.

_All h.o.m.ogeneal Light has its proper Colour answering to its Degree of Refrangibility, and that Colour cannot be changed by Reflexions and Refractions._

In the Experiments of the fourth Proposition of the first Part of this first Book, when I had separated the heterogeneous Rays from one another, the Spectrum _pt_ formed by the separated Rays, did in the Progress from its End _p_, on which the most refrangible Rays fell, unto its other End _t_, on which the least refrangible Rays fell, appear tinged with this Series of Colours, violet, indigo, blue, green, yellow, orange, red, together with all their intermediate Degrees in a continual Succession perpetually varying. So that there appeared as many Degrees of Colours, as there were sorts of Rays differing in Refrangibility.

_Exper._ 5. Now, that these Colours could not be changed by Refraction, I knew by refracting with a Prism sometimes one very little Part of this Light, sometimes another very little Part, as is described in the twelfth Experiment of the first Part of this Book. For by this Refraction the Colour of the Light was never changed in the least. If any Part of the red Light was refracted, it remained totally of the same red Colour as before. No orange, no yellow, no green or blue, no other new Colour was produced by that Refraction. Neither did the Colour any ways change by repeated Refractions, but continued always the same red entirely as at first. The like Constancy and Immutability I found also in the blue, green, and other Colours. So also, if I looked through a Prism upon any Body illuminated with any part of this h.o.m.ogeneal Light, as in the fourteenth Experiment of the first Part of this Book is described; I could not perceive any new Colour generated this way. All Bodies illuminated with compound Light appear through Prisms confused, (as was said above) and tinged with various new Colours, but those illuminated with h.o.m.ogeneal Light appeared through Prisms neither less distinct, nor otherwise colour"d, than when viewed with the naked Eyes.

Their Colours were not in the least changed by the Refraction of the interposed Prism. I speak here of a sensible Change of Colour: For the Light which I here call h.o.m.ogeneal, being not absolutely h.o.m.ogeneal, there ought to arise some little Change of Colour from its Heterogeneity. But, if that Heterogeneity was so little as it might be made by the said Experiments of the fourth Proposition, that Change was not sensible, and therefore in Experiments, where Sense is Judge, ought to be accounted none at all.

_Exper._ 6. And as these Colours were not changeable by Refractions, so neither were they by Reflexions. For all white, grey, red, yellow, green, blue, violet Bodies, as Paper, Ashes, red Lead, Orpiment, Indico Bise, Gold, Silver, Copper, Gra.s.s, blue Flowers, Violets, Bubbles of Water tinged with various Colours, Peac.o.c.k"s Feathers, the Tincture of _Lignum Nephritic.u.m_, and such-like, in red h.o.m.ogeneal Light appeared totally red, in blue Light totally blue, in green Light totally green, and so of other Colours. In the h.o.m.ogeneal Light of any Colour they all appeared totally of that same Colour, with this only Difference, that some of them reflected that Light more strongly, others more faintly. I never yet found any Body, which by reflecting h.o.m.ogeneal Light could sensibly change its Colour.

From all which it is manifest, that if the Sun"s Light consisted of but one sort of Rays, there would be but one Colour in the whole World, nor would it be possible to produce any new Colour by Reflexions and Refractions, and by consequence that the variety of Colours depends upon the Composition of Light.

_DEFINITION._

The h.o.m.ogeneal Light and Rays which appear red, or rather make Objects appear so, I call Rubrifick or Red-making; those which make Objects appear yellow, green, blue, and violet, I call Yellow-making, Green-making, Blue-making, Violet-making, and so of the rest. And if at any time I speak of Light and Rays as coloured or endued with Colours, I would be understood to speak not philosophically and properly, but grossly, and accordingly to such Conceptions as vulgar People in seeing all these Experiments would be apt to frame. For the Rays to speak properly are not coloured. In them there is nothing else than a certain Power and Disposition to stir up a Sensation of this or that Colour.

For as Sound in a Bell or musical String, or other sounding Body, is nothing but a trembling Motion, and in the Air nothing but that Motion propagated from the Object, and in the Sensorium "tis a Sense of that Motion under the Form of Sound; so Colours in the Object are nothing but a Disposition to reflect this or that sort of Rays more copiously than the rest; in the Rays they are nothing but their Dispositions to propagate this or that Motion into the Sensorium, and in the Sensorium they are Sensations of those Motions under the Forms of Colours.

_PROP._ III. PROB. I.

_To define the Refrangibility of the several sorts of h.o.m.ogeneal Light answering to the several Colours._

For determining this Problem I made the following Experiment.[J]

_Exper._ 7. When I had caused the Rectilinear Sides AF, GM, [in _Fig._ 4.] of the Spectrum of Colours made by the Prism to be distinctly defined, as in the fifth Experiment of the first Part of this Book is described, there were found in it all the h.o.m.ogeneal Colours in the same Order and Situation one among another as in the Spectrum of simple Light, described in the fourth Proposition of that Part. For the Circles of which the Spectrum of compound Light PT is composed, and which in the middle Parts of the Spectrum interfere, and are intermix"d with one another, are not intermix"d in their outmost Parts where they touch those Rectilinear Sides AF and GM. And therefore, in those Rectilinear Sides when distinctly defined, there is no new Colour generated by Refraction. I observed also, that if any where between the two outmost Circles TMF and PGA a Right Line, as [Greek: gd], was cross to the Spectrum, so as both Ends to fall perpendicularly upon its Rectilinear Sides, there appeared one and the same Colour, and degree of Colour from one End of this Line to the other. I delineated therefore in a Paper the Perimeter of the Spectrum FAP GMT, and in trying the third Experiment of the first Part of this Book, I held the Paper so that the Spectrum might fall upon this delineated Figure, and agree with it exactly, whilst an a.s.sistant, whose Eyes for distinguishing Colours were more critical than mine, did by Right Lines [Greek: ab, gd, ez,] &c. drawn cross the Spectrum, note the Confines of the Colours, that is of the red M[Greek: ab]F, of the orange [Greek: agdb], of the yellow [Greek: gezd], of the green [Greek: eethz], of the blue [Greek: eikth], of the indico [Greek: ilmk], and of the violet [Greek: l]GA[Greek: m]. And this Operation being divers times repeated both in the same, and in several Papers, I found that the Observations agreed well enough with one another, and that the Rectilinear Sides MG and FA were by the said cross Lines divided after the manner of a Musical Chord. Let GM be produced to X, that MX may be equal to GM, and conceive GX, [Greek: l]X, [Greek: i]X, [Greek: e]X, [Greek: e]X, [Greek: g]X, [Greek: a]X, MX, to be in proportion to one another, as the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5, 9/16, 1/2, and so to represent the Chords of the Key, and of a Tone, a third Minor, a fourth, a fifth, a sixth Major, a seventh and an eighth above that Key: And the Intervals M[Greek: a], [Greek: ag], [Greek: ge], [Greek: ee], [Greek: ei], [Greek: il], and [Greek: l]G, will be the s.p.a.ces which the several Colours (red, orange, yellow, green, blue, indigo, violet) take up.

[Ill.u.s.tration: FIG. 4.]

[Ill.u.s.tration: FIG. 5.]

Now these Intervals or s.p.a.ces subtending the Differences of the Refractions of the Rays going to the Limits of those Colours, that is, to the Points M, [Greek: a], [Greek: g], [Greek: e], [Greek: e], [Greek: i], [Greek: l], G, may without any sensible Error be accounted proportional to the Differences of the Sines of Refraction of those Rays having one common Sine of Incidence, and therefore since the common Sine of Incidence of the most and least refrangible Rays out of Gla.s.s into Air was (by a Method described above) found in proportion to their Sines of Refraction, as 50 to 77 and 78, divide the Difference between the Sines of Refraction 77 and 78, as the Line GM is divided by those Intervals, and you will have 77, 77-1/8, 77-1/5, 77-1/3, 77-1/2, 77-2/3, 77-7/9, 78, the Sines of Refraction of those Rays out of Gla.s.s into Air, their common Sine of Incidence being 50. So then the Sines of the Incidences of all the red-making Rays out of Gla.s.s into Air, were to the Sines of their Refractions, not greater than 50 to 77, nor less than 50 to 77-1/8, but they varied from one another according to all intermediate Proportions. And the Sines of the Incidences of the green-making Rays were to the Sines of their Refractions in all Proportions from that of 50 to 77-1/3, unto that of 50 to 77-1/2. And by the like Limits above-mentioned were the Refractions of the Rays belonging to the rest of the Colours defined, the Sines of the red-making Rays extending from 77 to 77-1/8, those of the orange-making from 77-1/8 to 77-1/5, those of the yellow-making from 77-1/5 to 77-1/3, those of the green-making from 77-1/3 to 77-1/2, those of the blue-making from 77-1/2 to 77-2/3, those of the indigo-making from 77-2/3 to 77-7/9, and those of the violet from 77-7/9, to 78.

These are the Laws of the Refractions made out of Gla.s.s into Air, and thence by the third Axiom of the first Part of this Book, the Laws of the Refractions made out of Air into Gla.s.s are easily derived.

_Exper._ 8. I found moreover, that when Light goes out of Air through several contiguous refracting Mediums as through Water and Gla.s.s, and thence goes out again into Air, whether the refracting Superficies be parallel or inclin"d to one another, that Light as often as by contrary Refractions "tis so corrected, that it emergeth in Lines parallel to those in which it was incident, continues ever after to be white. But if the emergent Rays be inclined to the incident, the Whiteness of the emerging Light will by degrees in pa.s.sing on from the Place of Emergence, become tinged in its Edges with Colours. This I try"d by refracting Light with Prisms of Gla.s.s placed within a Prismatick Vessel of Water. Now those Colours argue a diverging and separation of the heterogeneous Rays from one another by means of their unequal Refractions, as in what follows will more fully appear. And, on the contrary, the permanent whiteness argues, that in like Incidences of the Rays there is no such separation of the emerging Rays, and by consequence no inequality of their whole Refractions. Whence I seem to gather the two following Theorems.

1. The Excesses of the Sines of Refraction of several sorts of Rays above their common Sine of Incidence when the Refractions are made out of divers denser Mediums immediately into one and the same rarer Medium, suppose of Air, are to one another in a given Proportion.

2. The Proportion of the Sine of Incidence to the Sine of Refraction of one and the same sort of Rays out of one Medium into another, is composed of the Proportion of the Sine of Incidence to the Sine of Refraction out of the first Medium into any third Medium, and of the Proportion of the Sine of Incidence to the Sine of Refraction out of that third Medium into the second Medium.

By the first Theorem the Refractions of the Rays of every sort made out of any Medium into Air are known by having the Refraction of the Rays of any one sort. As for instance, if the Refractions of the Rays of every sort out of Rain-water into Air be desired, let the common Sine of Incidence out of Gla.s.s into Air be subducted from the Sines of Refraction, and the Excesses will be 27, 27-1/8, 27-1/5, 27-1/3, 27-1/2, 27-2/3, 27-7/9, 28. Suppose now that the Sine of Incidence of the least refrangible Rays be to their Sine of Refraction out of Rain-water into Air as 3 to 4, and say as 1 the difference of those Sines is to 3 the Sine of Incidence, so is 27 the least of the Excesses above-mentioned to a fourth Number 81; and 81 will be the common Sine of Incidence out of Rain-water into Air, to which Sine if you add all the above-mentioned Excesses, you will have the desired Sines of the Refractions 108, 108-1/8, 108-1/5, 108-1/3, 108-1/2, 108-2/3, 108-7/9, 109.

By the latter Theorem the Refraction out of one Medium into another is gathered as often as you have the Refractions out of them both into any third Medium. As if the Sine of Incidence of any Ray out of Gla.s.s into Air be to its Sine of Refraction, as 20 to 31, and the Sine of Incidence of the same Ray out of Air into Water, be to its Sine of Refraction as 4 to 3; the Sine of Incidence of that Ray out of Gla.s.s into Water will be to its Sine of Refraction as 20 to 31 and 4 to 3 jointly, that is, as the Factum of 20 and 4 to the Factum of 31 and 3, or as 80 to 93.

And these Theorems being admitted into Opticks, there would be scope enough of handling that Science voluminously after a new manner,[K] not only by teaching those things which tend to the perfection of Vision, but also by determining mathematically all kinds of Phaenomena of Colours which could be produced by Refractions. For to do this, there is nothing else requisite than to find out the Separations of heterogeneous Rays, and their various Mixtures and Proportions in every Mixture. By this way of arguing I invented almost all the Phaenomena described in these Books, beside some others less necessary to the Argument; and by the successes I met with in the Trials, I dare promise, that to him who shall argue truly, and then try all things with good Gla.s.ses and sufficient Circ.u.mspection, the expected Event will not be wanting. But he is first to know what Colours will arise from any others mix"d in any a.s.signed Proportion.

_PROP._ IV. THEOR. III.

_Colours may be produced by Composition which shall be like to the Colours of h.o.m.ogeneal Light as to the Appearance of Colour, but not as to the Immutability of Colour and Const.i.tution of Light. And those Colours by how much they are more compounded by so much are they less full and intense, and by too much Composition they maybe diluted and weaken"d till they cease, and the Mixture becomes white or grey. There may be also Colours produced by Composition, which are not fully like any of the Colours of h.o.m.ogeneal Light._

For a Mixture of h.o.m.ogeneal red and yellow compounds an Orange, like in appearance of Colour to that orange which in the series of unmixed prismatick Colours lies between them; but the Light of one orange is h.o.m.ogeneal as to Refrangibility, and that of the other is heterogeneal, and the Colour of the one, if viewed through a Prism, remains unchanged, that of the other is changed and resolved into its component Colours red and yellow. And after the same manner other neighbouring h.o.m.ogeneal Colours may compound new Colours, like the intermediate h.o.m.ogeneal ones, as yellow and green, the Colour between them both, and afterwards, if blue be added, there will be made a green the middle Colour of the three which enter the Composition. For the yellow and blue on either hand, if they are equal in quant.i.ty they draw the intermediate green equally towards themselves in Composition, and so keep it as it were in aequilibrion, that it verge not more to the yellow on the one hand, and to the blue on the other, but by their mix"d Actions remain still a middle Colour. To this mix"d green there may be farther added some red and violet, and yet the green will not presently cease, but only grow less full and vivid, and by increasing the red and violet, it will grow more and more dilute, until by the prevalence of the added Colours it be overcome and turned into whiteness, or some other Colour. So if to the Colour of any h.o.m.ogeneal Light, the Sun"s white Light composed of all sorts of Rays be added, that Colour will not vanish or change its Species, but be diluted, and by adding more and more white it will be diluted more and more perpetually. Lastly, If red and violet be mingled, there will be generated according to their various Proportions various Purples, such as are not like in appearance to the Colour of any h.o.m.ogeneal Light, and of these Purples mix"d with yellow and blue may be made other new Colours.