PROP. V. Theor. IV.
Homogeneal Light is refracted regularly without any Dilatation splitting or shattering of the Rays, and the confused Vision of Objects seen through refracting Bodies by heterogeneal Light arises from the different Refrangibility of several sorts of Rays.
The first Part of this Proposition has been already sufficiently proved in the fifth Experiment, and will farther appear by the Experiments which follow.
Exper. 12. In the middle of a black Paper I made a round Hole about a fifth or sixth Part of an Inch in diameter. Upon this Paper I caused the Spectrum of homogeneal Light described in the former Proposition, so to fall, that some part of the Light might pass through the Hole of the Paper. This transmitted part of the Light I refracted with a Prism placed behind the Paper, and letting this refracted Light fall perpendicularly upon a white Paper two or three Feet distant from the Prism, I found that the Spectrum formed on the Paper by this Light was not oblong, as when 'tis made (in the third Experiment) by refracting the Sun's compound Light, but was (so far as I could judge by my Eye) perfectly circular, the Length being no greater than the Breadth. Which shews, that this Light is refracted regularly without any Dilatation of the Rays.
Exper. 13. In the homogeneal Light I placed a Paper Circle of a quarter of an Inch in diameter, and in the Sun's unrefracted heterogeneal white Light I placed another Paper Circle of the same Bigness. And going from the Papers to the distance of some Feet, I viewed both Circles through a Prism. The Circle illuminated by the Sun's heterogeneal Light appeared very oblong, as in the fourth Experiment, the Length being many times greater than the Breadth; but the other Circle, illuminated with homogeneal Light, appeared circular and distinctly defined, as when 'tis view'd with the naked Eye. Which proves the whole Proposition.
Exper. 14. In the homogeneal Light I placed Flies, and such-like minute Objects, and viewing them through a Prism, I saw their Parts as distinctly defined, as if I had viewed them with the naked Eye. The same Objects placed in the Sun's unrefracted heterogeneal Light, which was white, I viewed also through a Prism, and saw them most confusedly defined, so that I could not distinguish their smaller Parts from one another. I placed also the Letters of a small print, one while in the homogeneal Light, and then in the heterogeneal, and viewing them through a Prism, they appeared in the latter Case so confused and indistinct, that I could not read them; but in the former they appeared so distinct, that I could read readily, and thought I saw them as distinct, as when I view'd them with my naked Eye. In both Cases I view'd the same Objects, through the same Prism at the same distance from me, and in the same Situation. There was no difference, but in the Light by which the Objects were illuminated, and which in one Case was simple, and in the other compound; and therefore, the distinct Vision in the former Case, and confused in the latter, could arise from nothing else than from that difference of the Lights. Which proves the whole Proposition.
And in these three Experiments it is farther very remarkable, that the Colour of homogeneal Light was never changed by the Refraction.
PROP. VI. Theor. V.
The Sine of Incidence of every Ray considered apart, is to its Sine of Refraction in a given Ratio.
That every Ray consider'd apart, is constant to it self in some degree of Refrangibility, is sufficiently manifest out of what has been said. Those Rays, which in the first Refraction, are at equal Incidences most refracted, are also in the following Refractions at equal Incidences most refracted; and so of the least refrangible, and the rest which have any mean Degree of Refrangibility, as is manifest by the fifth, sixth, seventh, eighth, and ninth Experiments. And those which the first Time at like Incidences are equally refracted, are again at like Incidences equally and uniformly refracted, and that whether they be refracted before they be separated from one another, as in the fifth Experiment, or whether they be refracted apart, as in the twelfth, thirteenth and fourteenth Experiments. The Refraction therefore of every Ray apart is regular, and what Rule that Refraction observes we are now to shew.[5]
The late Writers in Opticks teach, that the Sines of Incidence are in a given Proportion to the Sines of Refraction, as was explained in the fifth Axiom, and some by Instruments fitted for measuring of Refractions, or otherwise experimentally examining this Proportion, do acquaint us that they have found it accurate. But whilst they, not understanding the different Refrangibility of several Rays, conceived them all to be refracted according to one and the same Proportion, 'tis to be presumed that they adapted their Measures only to the middle of the refracted Light; so that from their Measures we may conclude only that the Rays which have a mean Degree of Refrangibility, that is, those which when separated from the rest appear green, are refracted according to a given Proportion of their Sines. And therefore we are now to shew, that the like given Proportions obtain in all the rest. That it should be so is very reasonable, Nature being ever conformable to her self; but an experimental Proof is desired. And such a Proof will be had, if we can shew that the Sines of Refraction of Rays differently refrangible are one to another in a given Proportion when their Sines of Incidence are equal. For, if the Sines of Refraction of all the Rays are in given Proportions to the Sine of Refractions of a Ray which has a mean Degree of Refrangibility, and this Sine is in a given Proportion to the equal Sines of Incidence, those other Sines of Refraction will also be in given Proportions to the equal Sines of Incidence. Now, when the Sines of Incidence are equal, it will appear by the following Experiment, that the Sines of Refraction are in a given Proportion to one another.
Fig. 26.
Exper. 15. The Sun shining into a dark Chamber through a little round Hole in the Window-shut, let S [in Fig. 26.] represent his round white Image painted on the opposite Wall by his direct Light, PT his oblong coloured Image made by refracting that Light with a Prism placed at the Window; and pt, or 2p 2t, 3p 3t, his oblong colour'd Image made by refracting again the same Light sideways with a second Prism placed immediately after the first in a cross Position to it, as was explained in the fifth Experiment; that is to say, pt when the Refraction of the second Prism is small, 2p 2t when its Refraction is greater, and 3p 3t when it is greatest. For such will be the diversity of the Refractions, if the refracting Angle of the second Prism be of various Magnitudes; suppose of fifteen or twenty Degrees to make the Image pt, of thirty or forty to make the Image 2p 2t, and of sixty to make the Image 3p 3t. But for want of solid Glass Prisms with Angles of convenient Bignesses, there may be Vessels made of polished Plates of Glass cemented together in the form of Prisms and filled with Water. These things being thus ordered, I observed that all the solar Images or coloured Spectrums PT, pt, 2p 2t, 3p 3t did very nearly converge to the place S on which the direct Light of the Sun fell and painted his white round Image when the Prisms were taken away. The Axis of the Spectrum PT, that is the Line drawn through the middle of it parallel to its rectilinear Sides, did when produced pass exactly through the middle of that white round Image S. And when the Refraction of the second Prism was equal to the Refraction of the first, the refracting Angles of them both being about 60 Degrees, the Axis of the Spectrum 3p 3t made by that Refraction, did when produced pass also through the middle of the same white round Image S. But when the Refraction of the second Prism was less than that of the first, the produced Axes of the Spectrums tp or 2t 2p made by that Refraction did cut the produced Axis of the Spectrum TP in the points m and n, a little beyond the Center of that white round Image S. Whence the proportion of the Line 3tT to the Line 3pP was a little greater than the Proportion of 2tT or 2pP, and this Proportion a little greater than that of tT to pP. Now when the Light of the Spectrum PT falls perpendicularly upon the Wall, those Lines 3tT, 3pP, and 2tT, and 2pP, and tT, pP, are the Tangents of the Refractions, and therefore by this Experiment the Proportions of the Tangents of the Refractions are obtained, from whence the Proportions of the Sines being derived, they come out equal, so far as by viewing the Spectrums, and using some mathematical Reasoning I could estimate. For I did not make an accurate Computation. So then the Proposition holds true in every Ray apart, so far as appears by Experiment. And that it is accurately true, may be demonstrated upon this Supposition. That Bodies refract Light by acting upon its Rays in Lines perpendicular to their Surfaces. But in order to this Demonstration, I must distinguish the Motion of every Ray into two Motions, the one perpendicular to the refracting Surface, the other parallel to it, and concerning the perpendicular Motion lay down the following Proposition.