Exact Determination of the Ratio of Refraction in Solid Substances.

34. THE manner in which we just now measured the ratio of refraction and recognised its constancy, can only be considered as an approximation, intended to indicate the general law of the phenomena. This ratio must now be exactly determined. For this purpose, the most simple method is, to construct a right, triangular prism of the transparent substance which we wish to observe, then to measure the deviations of the luminous ray in passing through it under different angles of incidence, and to see if they may all be calculated according to a constant ratio of refraction.

Let ABC be a section made in the prism by a plane perpen- Fig. 30. dicular to its edge. In this plane let us imagine a luminous ray SI, falling upon the prism at the point S, and refracted in the direction Il'. By the first law of refraction, the two straight lines SI, II, are situated in the same plane perpendicular to the refracting surface; they lie therefore in the plane ABC. The refracted ray, after passing through the substance of the prism, will meet the second surface in I', and as it passes into the air will be refracted anew in the direction l'O, comprehended also in the plane of the section ABC. Then an observer, situated any where in this direction, as at O, would receive at the same time the refracted ray I'O and the direct ray OS, coming immediately from the luminous object. If light suffered no deviation in passing through the prism, these two rays would be confounded in one. Their departure from each other, SOI, is therefore caused by the refraction of the first; and in any given position of the luminous object, the prism, and the observer, the deviation SOI will depend directly on the law of refraction. To prove this law, as stated by Descartes, we have only to employ it in calculation, and then to compare the results with observation. We may in fact thus determine the angle of emergence CIO, when we know the angle of incidence BIS, and the ratio of refraction; and reciprocally, we may calculate the ratio of refraction when we know these two angles. The calculation of this ratio, therefore, for different angles of incidence, will prove if it be indeed constant, as stated by Descartes; and this is in fact found to be the case with the utmost precision.

35. This truth being once established, a single measurement of the deviation I'OS, produced by a prism of a given angle, under a known angle of incidence, enables us to calculate the ratio of refraction of the substance of which the prism is composed. This measurement may be made in several ways. For example, if the substance be solid, we have only to form a prism of it, whose angles are measured by the reflection of light, then fixing its base on a support capable of being levelled with screws, we place it in relation to the distant signal S, as represented in figure 30, and then placing the instrument divided in O, so as to see successively with the same glass the object S, first directly, and then through the prism, we measure the angle of deviation SOS'. We also determine by observation the angles of incidence and emergence SIB, OFC; with these data and a knowledge of the refracting angle of the prism, we can calculate the ratio of refraction.

We may arrive at the same result without the distant signal, by using the circular goniometer employed to measure the angles of crystals. For this purpose we must apply the prism. to the glass GG, figure 31, using all the adjustments and verifications which we have pointed out to make the edge of the two faces coincide with the central axis of the circle; and observing, moreover, that the central glass used as a support must be thin and its two faces perfectly parallel. Then having placed the index S in such a situation that the light which enters through it shall be refracted by the prism, we move the other index O, till the eye placed behind the opening O', perceives the image of S' by refraction. When this takes place, the division of the circle will give the measure of the angles which the incident and refracted rays S'C'O'C', form with the two surfaces of the prism of which the position and inclination are known. With these data, we determine by calculation the ratio of refraction for the substance of which the prism is composed.

If the light of the sky, admitted through the hole in the index S, be too feeble to give, after refraction, a distinct image of this hole at O, we may invert the direction of the rays by placing the flame of a taper, lamp, or any bright light, beneath O, and then placing the eye at S', behind the other index which we move till the rays of refracted light pass through it.

We have recommended that the two faces of the central glass used as a support, should be perfectly parallel; otherwise, the prismatic form of the glass will cause a deviation in the refracted light, which we should falsely ascribe to the substance which we were examining. But if they are parallel, the ray will resume the same direction on passing into the air out of the glass which it had at its incidence, or it will penetrate a prism placed upon the glass in the same direction as if nothing were interposed. These facts we infer from the constancy of the ratio of refraction, and they are deduced from the calculus and confirmed by experiment.

It is also necessary that the glass should be thin, and that refraction should take place near the edge of the prism, that the incident and refracted rays may be considered as departing exactly from the centre of the circular division. If extreme exactness be required, it is easy to correct any little defect of centring. I have confined myself here to pointing out this mode of measuring the angles of refraction, because we have already made use of it in reflection.

In these experiments, the dispersion of light which always takes place, produces an infinite number of shades, among which may be distinguished seven stronger and more definite than the others, viz. red, orange, yellow, green, blue, indigo, and violet. Since these colours are separated in the emergent ray, it is evident that the different parts of this ray have different degrees of refrangibility, which may be estimated by the extent of their deviations. Thus we find the refrangibility least in the red rays, and that it goes on increasing in the order of the colours as we have named them, till it becomes greatest in the violet. We find, moreover, by varying the angles of incidence, that the ratio of the sine of incidence to the sine of the refraction, is constant for each of the different colours, though not the same for all; but it is difficult to determine this by the simple observation of the absolute deviations, because we are never sure of directing the eye in our different experiments to the same shade. For this reason I merely state in this place the constancy of the ratio of refraction as a thing very probable, and shall hereafter endeavour to establish it rigorously by other means.

Nevertheless the simple knowledge of the unequal refrangibility of the different colours, will furnish us now with a very

important remark respecting the manner in which they ought to appear when we look at a luminous point through a refracting Fig. 32 prism. Let SI be an infinitely thin white ray, proceeding from a point S at an infinite distance, and refracted by the prism ABC. After its emergence, it will be divided into a beam VIR, of which the most refracted side VI' is violet, and the least refracted RI' red, the other shades being distributed between these two. But if the eye of the observer be situated somewhere as at O, in the red ray produced, it is plain that it will receive no other of the coloured rays contained in the branch VIR. Now if through O we draw a line Oi, parallel to VI, it is plain that the observer will receive in this direction a violet ray from the white ray Si, which falls upon the prism parallel to SI', proceeding also from the point S; and with respect to the first refracted beam SI, the observer receives only the red ray I'R; so of the last, he will receive only the violet Oi. But other incident rays between SI and Si will send to the eye the intermediate shades, and it will thus perceive all the colours of the spectrum, as if the whole refracted beam RIV had been reeeived upon a piece of white pasteboard. The most refrangible rays will always be those which appear to deviate most from their primitive direction, and consequently those most distant from the base BC of the prism; this property will regulate the distribution of the colours with respect to the observer, and reciprocally, the order of the colours will indicate their greater or less refrangibility.

This remark, although very simple, it is highly essential to retain; for it will be of use in a great variety of cases, where we are obliged to infer from the order of the colours, this greater or less refraction.

Determination of the Ratio of Refraction in Liquids.

36. THE method which we have now explained might be equally applied to liquids if they could be formed into prisms. Now this is easily done by confining them within prismatic vessels of which the sides are formed of plane parallel plates of glass; for the definite directions of the rays not being changed

hy their passage through these plates, the refraction which takes place, and which we observe, is produced entirely by the liquid. Indeed, such vessels while empty do not sensibly affect the images of objects, at least when the glasses are well made, and the luminous point at a great distance compared with their thickness.

But to adjust these glasses to each other, and to form of them a vessel capable of containing liquids, they must be attached or luted together. If screws are used to confine them, it is difficult to prevent the liquid from escaping. If they are luted, the lute is often attacked by the liquid, and the refraction thus affected. The inconvenience is still greater if we wish to observe volatile liquids, as ammonia, the essential oils, and most of the acids. Happily all these difficulties may be avoided by a very simple method invented by M. Cauchoix and myself.

37. We begin with taking a square plate of glass, about of an inch in thickness, and two inches in breadth. It is of little importance whether the glass be pure or impure, opaque or transparent. The plate is perforated at its centre by a cylindrical canal of about of an inch in diameter; it is finally cut into a prism, as represented in figure 33, and the two sides are carefully reduced to plane surfaces and polished. Two plates of glass, also made plane and polished, being then laid upon these faces with a slight pressure, they adhere of themselves, by the effect of the attraction at a small distance, which is denominated capillary. We thus form a true hollow prism without lutes, in which we can enclose all kinds of liquids without their undergoing any alteration.

To introduce them with ease, and without being obliged every time to remove the glasses, we form in the thickness of the prism a lateral canal ab, which is closed with a glass stopple, made smooth with emery; and finally that the glass plates may adhere more perfectly, and not slide on the solid faces of the prism by the motions which we are obliged to give it, they are confined by triangular frames of copper which are slightly pressed against their surfaces by means of screws.

38. Supposing that the glass plates employed are perfectly parallel, it is evident that this apparatus offers us a true prism for liquids, through which the refraction of these substances may be observed as if they were solid, and with accurate results. The Fig. 31. prism is placed upon the goniometer, or upon any instrument