This is manifest by the 5th, 9th, 12th, and 15th Observations. For by those Observations it appears, that one and the same sort of Rays at equal Angles of Incidence on any thin transparent Plate, is alternately reflected and transmitted for many Successions accordingly as the thickness of the Plate increases in arithmetical Progression of the Numbers, 0, 1, 2, 3, 4, 5, 6, 7, 8, &c. so that if the first Reflexion (that which makes the first or innermost of the Rings of Colours there described) be made at the thickness 1, the Rays shall be transmitted at the thicknesses 0, 2, 4, 6, 8, 10, 12, &c. and thereby make the central Spot and Rings of Light, which appear by transmission, and be reflected at the thickness 1, 3, 5, 7, 9, 11, &c. and thereby make the Rings which appear by Reflexion. And this alternate Reflexion and Transmission, as I gather by the 24th Observation, continues for above an hundred vicissitudes, and by the Observations in the next part of this Book, for many thousands, being propagated from one Surface of a Gla.s.s Plate to the other, though the thickness of the Plate be a quarter of an Inch or above: So that this alternation seems to be propagated from every refracting Surface to all distances without end or limitation.

This alternate Reflexion and Refraction depends on both the Surfaces of every thin Plate, because it depends on their distance. By the 21st Observation, if either Surface of a thin Plate of _Muscovy_ Gla.s.s be wetted, the Colours caused by the alternate Reflexion and Refraction grow faint, and therefore it depends on them both.

It is therefore perform'd at the second Surface; for if it were perform'd at the first, before the Rays arrive at the second, it would not depend on the second.

It is also influenced by some action or disposition, propagated from the first to the second, because otherwise at the second it would not depend on the first. And this action or disposition, in its propagation, intermits and returns by equal Intervals, because in all its progress it inclines the Ray at one distance from the first Surface to be reflected by the second, at another to be transmitted by it, and that by equal Intervals for innumerable vicissitudes. And because the Ray is disposed to Reflexion at the distances 1, 3, 5, 7, 9, &c. and to Transmission at the distances 0, 2, 4, 6, 8, 10, &c. (for its transmission through the first Surface, is at the distance 0, and it is transmitted through both together, if their distance be infinitely little or much less than 1) the disposition to be transmitted at the distances 2, 4, 6, 8, 10, &c.

is to be accounted a return of the same disposition which the Ray first had at the distance 0, that is at its transmission through the first refracting Surface. All which is the thing I would prove.

What kind of action or disposition this is; Whether it consists in a circulating or a vibrating motion of the Ray, or of the Medium, or something else, I do not here enquire. Those that are averse from a.s.senting to any new Discoveries, but such as they can explain by an Hypothesis, may for the present suppose, that as Stones by falling upon Water put the Water into an undulating Motion, and all Bodies by percussion excite vibrations in the Air; so the Rays of Light, by impinging on any refracting or reflecting Surface, excite vibrations in the refracting or reflecting Medium or Substance, and by exciting them agitate the solid parts of the refracting or reflecting Body, and by agitating them cause the Body to grow warm or hot; that the vibrations thus excited are propagated in the refracting or reflecting Medium or Substance, much after the manner that vibrations are propagated in the Air for causing Sound, and move faster than the Rays so as to overtake them; and that when any Ray is in that part of the vibration which conspires with its Motion, it easily breaks through a refracting Surface, but when it is in the contrary part of the vibration which impedes its Motion, it is easily reflected; and, by consequence, that every Ray is successively disposed to be easily reflected, or easily transmitted, by every vibration which overtakes it. But whether this Hypothesis be true or false I do not here consider. I content my self with the bare Discovery, that the Rays of Light are by some cause or other alternately disposed to be reflected or refracted for many vicissitudes.

DEFINITION.

_The returns of the disposition of any Ray to be reflected I will call its_ Fits of easy Reflexion, _and those of its disposition to be transmitted its_ Fits of easy Transmission, _and the s.p.a.ce it pa.s.ses between every return and the next return, the_ Interval of its Fits.

PROP. XIII.

_The reason why the Surfaces of all thick transparent Bodies reflect part of the Light incident on them, and refract the rest, is, that some Rays at their Incidence are in Fits of easy Reflexion, and others in Fits of easy Transmission._

This may be gather'd from the 24th Observation, where the Light reflected by thin Plates of Air and Gla.s.s, which to the naked Eye appear'd evenly white all over the Plate, did through a Prism appear waved with many Successions of Light and Darkness made by alternate Fits of easy Reflexion and easy Transmission, the Prism severing and distinguishing the Waves of which the white reflected Light was composed, as was explain'd above.

And hence Light is in Fits of easy Reflexion and easy Transmission, before its Incidence on transparent Bodies. And probably it is put into such fits at its first emission from luminous Bodies, and continues in them during all its progress. For these Fits are of a lasting nature, as will appear by the next part of this Book.

In this Proposition I suppose the transparent Bodies to be thick; because if the thickness of the Body be much less than the Interval of the Fits of easy Reflexion and Transmission of the Rays, the Body loseth its reflecting power. For if the Rays, which at their entering into the Body are put into Fits of easy Transmission, arrive at the farthest Surface of the Body before they be out of those Fits, they must be transmitted. And this is the reason why Bubbles of Water lose their reflecting power when they grow very thin; and why all opake Bodies, when reduced into very small parts, become transparent.

PROP. XIV.

_Those Surfaces of transparent Bodies, which if the Ray be in a Fit of Refraction do refract it most strongly, if the Ray be in a Fit of Reflexion do reflect it most easily._

For we shewed above, in _Prop._ 8. that the cause of Reflexion is not the impinging of Light on the solid impervious parts of Bodies, but some other power by which those solid parts act on Light at a distance. We shewed also in _Prop._ 9. that Bodies reflect and refract Light by one and the same power, variously exercised in various circ.u.mstances; and in _Prop._ 1. that the most strongly refracting Surfaces reflect the most Light: All which compared together evince and rarify both this and the last Proposition.

PROP. XV.

_In any one and the same sort of Rays, emerging in any Angle out of any refracting Surface into one and the same Medium, the Interval of the following Fits of easy Reflexion and Transmission are either accurately or very nearly, as the Rectangle of the Secant of the Angle of Refraction, and of the Secant of another Angle, whose Sine is the first of 106 arithmetical mean Proportionals, between the Sines of Incidence and Refraction, counted from the Sine of Refraction._

This is manifest by the 7th and 19th Observations.

PROP. XVI.

_In several sorts of Rays emerging in equal Angles out of any refracting Surface into the same Medium, the Intervals of the following Fits of easy Reflexion and easy Transmission are either accurately, or very nearly, as the Cube-Roots of the Squares of the lengths of a Chord, which found the Notes in an Eight_, sol, la, fa, sol, la, mi, fa, sol, _with all their intermediate degrees answering to the Colours of those Rays, according to the a.n.a.logy described in the seventh Experiment of the second Part of the first Book._

This is manifest by the 13th and 14th Observations.

PROP. XVII.

_If Rays of any sort pa.s.s perpendicularly into several Mediums, the Intervals of the Fits of easy Reflexion and Transmission in any one Medium, are to those Intervals in any other, as the Sine of Incidence to the Sine of Refraction, when the Rays pa.s.s out of the first of those two Mediums into the second._

This is manifest by the 10th Observation.

PROP. XVIII.

_If the Rays which paint the Colour in the Confine of yellow and orange pa.s.s perpendicularly out of any Medium into Air, the Intervals of their Fits of easy Reflexion are the 1/89000th part of an Inch. And of the same length are the Intervals of their Fits of easy Transmission._

This is manifest by the 6th Observation. From these Propositions it is easy to collect the Intervals of the Fits of easy Reflexion and easy Transmission of any sort of Rays refracted in any angle into any Medium; and thence to know, whether the Rays shall be reflected or transmitted at their subsequent Incidence upon any other pellucid Medium. Which thing, being useful for understanding the next part of this Book, was here to be set down. And for the same reason I add the two following Propositions.

PROP. XIX.

_If any sort of Rays falling on the polite Surface of any pellucid Medium be reflected back, the Fits of easy Reflexion, which they have at the point of Reflexion, shall still continue to return; and the Returns shall be at distances from the point of Reflexion in the arithmetical progression of the Numbers 2, 4, 6, 8, 10, 12, &c. and between these Fits the Rays shall be in Fits of easy Transmission._

For since the Fits of easy Reflexion and easy Transmission are of a returning nature, there is no reason why these Fits, which continued till the Ray arrived at the reflecting Medium, and there inclined the Ray to Reflexion, should there cease. And if the Ray at the point of Reflexion was in a Fit of easy Reflexion, the progression of the distances of these Fits from that point must begin from 0, and so be of the Numbers 0, 2, 4, 6, 8, &c. And therefore the progression of the distances of the intermediate Fits of easy Transmission, reckon'd from the same point, must be in the progression of the odd Numbers 1, 3, 5, 7, 9, &c. contrary to what happens when the Fits are propagated from points of Refraction.

PROP. XX.

_The Intervals of the Fits of easy Reflexion and easy Transmission, propagated from points of Reflexion into any Medium, are equal to the Intervals of the like Fits, which the same Rays would have, if refracted into the same Medium in Angles of Refraction equal to their Angles of Reflexion._

For when Light is reflected by the second Surface of thin Plates, it goes out afterwards freely at the first Surface to make the Rings of Colours which appear by Reflexion; and, by the freedom of its egress, makes the Colours of these Rings more vivid and strong than those which appear on the other side of the Plates by the transmitted Light. The reflected Rays are therefore in Fits of easy Transmission at their egress; which would not always happen, if the Intervals of the Fits within the Plate after Reflexion were not equal, both in length and number, to their Intervals before it. And this confirms also the proportions set down in the former Proposition. For if the Rays both in going in and out at the first Surface be in Fits of easy Transmission, and the Intervals and Numbers of those Fits between the first and second Surface, before and after Reflexion, be equal, the distances of the Fits of easy Transmission from either Surface, must be in the same progression after Reflexion as before; that is, from the first Surface which transmitted them in the progression of the even Numbers 0, 2, 4, 6, 8, &c. and from the second which reflected them, in that of the odd Numbers 1, 3, 5, 7, &c. But these two Propositions will become much more evident by the Observations in the following part of this Book.

THE

SECOND BOOK

OF

OPTICKS

_PART IV._

_Observations concerning the Reflexions and Colours of thick transparent polish'd Plates._

There is no Gla.s.s or Speculum how well soever polished, but, besides the Light which it refracts or reflects regularly, scatters every way irregularly a faint Light, by means of which the polish'd Surface, when illuminated in a dark room by a beam of the Sun's Light, may be easily seen in all positions of the Eye. There are certain Phaenomena of this scatter'd Light, which when I first observed them, seem'd very strange and surprizing to me. My Observations were as follows.

_Obs._ 1. The Sun shining into my darken'd Chamber through a hole one third of an Inch wide, I let the intromitted beam of Light fall perpendicularly upon a Gla.s.s Speculum ground concave on one side and convex on the other, to a Sphere of five Feet and eleven Inches Radius, and Quick-silver'd over on the convex side. And holding a white opake Chart, or a Quire of Paper at the center of the Spheres to which the Speculum was ground, that is, at the distance of about five Feet and eleven Inches from the Speculum, in such manner, that the beam of Light might pa.s.s through a little hole made in the middle of the Chart to the Speculum, and thence be reflected back to the same hole: I observed upon the Chart four or five concentric Irises or Rings of Colours, like Rain-bows, encompa.s.sing the hole much after the manner that those, which in the fourth and following Observations of the first part of this Book appear'd between the Object-gla.s.ses, encompa.s.sed the black Spot, but yet larger and fainter than those. These Rings as they grew larger and larger became diluter and fainter, so that the fifth was scarce visible.

Yet sometimes, when the Sun shone very clear, there appear'd faint Lineaments of a sixth and seventh. If the distance of the Chart from the Speculum was much greater or much less than that of six Feet, the Rings became dilute and vanish'd. And if the distance of the Speculum from the Window was much greater than that of six Feet, the reflected beam of Light would be so broad at the distance of six Feet from the Speculum where the Rings appear'd, as to obscure one or two of the innermost Rings. And therefore I usually placed the Speculum at about six Feet from the Window; so that its Focus might there fall in with the center of its concavity at the Rings upon the Chart. And this Posture is always to be understood in the following Observations where no other is express'd.

_Obs._ 2. The Colours of these Rain-bows succeeded one another from the center outwards, in the same form and order with those which were made in the ninth Observation of the first Part of this Book by Light not reflected, but transmitted through the two Object-gla.s.ses. For, first, there was in their common center a white round Spot of faint Light, something broader than the reflected beam of Light, which beam sometimes fell upon the middle of the Spot, and sometimes by a little inclination of the Speculum receded from the middle, and left the Spot white to the center.

This white Spot was immediately encompa.s.sed with a dark grey or russet, and that dark grey with the Colours of the first Iris; which Colours on the inside next the dark grey were a little violet and indigo, and next to that a blue, which on the outside grew pale, and then succeeded a little greenish yellow, and after that a brighter yellow, and then on the outward edge of the Iris a red which on the outside inclined to purple.