Page:Optics.djvu/187

 two in its passage through the rhomboid; and this may be easily shown to be the case, by presenting the crystal to a sunbeam, when it will give two distinct emergent beams. To measure the deviation of these rays, and determine their paths, Malus invented the following simple method: on the paper on which you place the rhomboid, draw, with very black ink, a right angle ABC, (Fig. 212.) of which let the least side BC be, for instance, one-tenth of AC. If this triangle be observed through the rhomboid, it will appear double, wherever the eye be placed; and for each position of the eye there will be found a point T, where the line A′C′, the extraordinary image of AC, will cut the line AB, which I suppose to belong to the ordinary image. Take then on the triangle itself a length AF′ equal to A′F, and the point F′ will be that of which the extraordinary image coincides with the ordinary one of F. The ordinary pencil proceeding from F, and the extraordinary one from F′ are therefore confounded together, on emerging from the crystal, and produce only one single pencil which meets the eye: hence, conversely, a natural pencil proceeding from where the eye is placed to the crystal, would be separated by the refraction into two pencils, one of which would go to F, and the other to F′. This may indeed be easily confirmed by experiment with the heliostat. If then the lines AB, AC be divided each into a thousand parts, for instance, and the divisions be numbered as represented in the Figure, a simple inspection will suffice to determine the points of AB, and AC, of which the images coincide; consequently, if the position of these lines and the triangle be known, relatively to the edges of the base of the crystal, it will be known in any case to what points of the base F and F′ correspond, so that to construct the refracted rays, it will only remain to determine, on the upper surface, the position of their common point of emergence (Fig. 213.). This might be done by marking on that surface the point I, where the images of AB and AC intersect; but as it is useful also to know the direction of the emergent pencil, it is better to make the observation with a graduated circle placed vertically in the plane of emergence IOV. The sights of this circle must be directed to the point I, and, if the precaution has been taken of levelling the plane on which the crystal lies, the same observation will determine at once the angle of emergence IOV, or NIO, measured from the normal, and the position of the point I on the rhomboid. The positions of