7/1 From the principles explained in the preceding pro positions, the lefractive powers of bodies, or their in dices of refraction, may be easily obtained. The me thod used by Ptolemy, and described in pag-c 591, is sufficiently simple ; and after we have measured one angle of incidence, and one angle of retraction, AVe have only to divide the sine of thc former by the sine of the latter, in order to obtain the index of refraction. This method, however, is never used, as a much more cor -ect result may be obtainod when the refraction is in creased by the action of two surfaces, as we shall after wards have occasion to describe. (Sec Prop. IX. p. 634.) In the meantime, we shall collect into one table the principal observations on refractive powers that have hitherto been made. Alany of these observations are very accurate ; but others, especially those on doubly refracting crystals, are less correct, in consequence of their having been made before the laws or double re fraction tbr crystals with two ztxes had been determined.
It may be ploper to state, that all the observations made by Dr. Wollaston arc, according to Dr. Young, appropriate to the extreme red rays, whereas those made by Dr. Brewster belong, in the case or fluids and soft substances, to the most luminous rays of the spec trum, and in minerals to the mean refrangible rays of the spectrum. The object of these last experiments was not to obtain measures of refractive powers for optical purposes, or for ascertaining the phenomena of double refraction, but solely to determine the general action of various bodies upon light. The accuracy of the num bers, therefore, dcpends entirely upon the nature nf the specimens which were used, and which were often of the worst description.
In order to convey to the reader an idea of the dif ferent degrees of refraction produced upon a ray of light when acted upon by different bodies, we ha.ve given a representation in Fig 3 of the difference of the effects of Air, Tabasheer, Water, Flint Glass, Diamond, and Chrom2te of Lead, upon the same incident ray AB ; CD being supposed to be the refracting surface of' each of these substances.
In the preceding Ta.ble the refractive powers of dif ferent bodies are given, without any consideration of their densities or specific gravities ; but it is evident, that if a body of small specific gravity has the same refractive power as another body of greater specific gravity, the former must have a greater absolute action upon light than the latter. Hence, if we wish to mea sure the absolute refractive powers of bodies, we must take their specific gravities into account.
Sir Isaac Newton has shown, that the refractive pow er is proportional to the square of the cosine of the an gle of refraction when it is a maximum ; so that if we call R the absolute refractive power, nz the index of re fraction, and S' the specific gravity, we shall have R= m2—I — from which the absolute refractive powers of S bodies may be calculated, when their specific gravities and their indices of refraction are known. In this way we have calculated the following Table, comprehend When a ray of light is transmitted through a medi um bounded by parallel surfaces, the emergent ray will be parallel to the incident ray.
Let AB b a, Fig. 4, be the medium, bounded by pa rallel surfaces AB, a b C ; and let DE be the incident ray refracted in the direction EF, and emerging in the direction FG; the ray FG will be parallel to DE. Through the points E, F, draw the perpendiculars l'Q, RS. Then since PQ and RS are parallel, the angle of refraction QEF at the first surface, is equal to EFR, the angle of incidence at the second surface ; but as the ratio of the sine of QEF to DEP is the same as that of EFR to SFG, by Prop. the angles DEP and SFG must be equal, and consequently their cotnplements AED, b FG ; and if we add to these the equal angles AEF, b FE, the whole angles DEF, GFE, will be equal, and consequently the rays DE, FG parallel.