Fig. 4.
Fig. 5.
Now these Intervals or Spaces subtending the Differences of the Refractions of the Rays going to the Limits of those Colours, that is, to the Points M, α, γ, ε, η, ι, λ, 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 Glass 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 Glass into Air, their common Sine of Incidence being 50. So then the Sines of the Incidences of all the red-making Rays out of Glass 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 Glass 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 Glass are easily derived.
Exper. 8. I found moreover, that when Light goes out of Air through several contiguous refracting Mediums as through Water and Glass, 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 passing on from the Place of Emergence, become tinged in its Edges with Colours. This I try'd by refracting Light with Prisms of Glass 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.