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 space it passes 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 Glass, 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 circumstances; 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 Analogy 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 pass 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 pass 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 pass 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.