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general too difficult for an elementary Treatise like the present. As far as common practical results are concerned, we shall find it sufficient to substitute for surfaces of revolution, portions of spheres having the same curvature, and as to others, plane sections will generally give all the information desired.
Suppose, for instance, the mirror were cylindrical, and convex, and the object a circle placed directly in front of it. It will easily be seen that that diameter of the circle, which is parallel to the axis of the cylinder, will not be altered in the reflexion, but that the diameter perpendicular to that axis with all chords parallel to it, will have for their images portions of conic sections of less breadth than themselves, so that the image will appear diminished in breadth, and distorted into a form like that of the bowl of a spoon.
CHAP. VII.
OF REFRACTION AT PLANE SURFACES.
53.We must here recall to the Student's recollection, the details in the introduction about the manner or law of refraction, which is, that when light enters a transparent medium, its course is bent or broken in such a manner, that the sine of the angle of incidence, bears to the sine of the angle of refraction, a certain ratio which is the same however the angle of incidence be varied. The full and correct statement of the case is, that when a ray of light passes from one medium into another, as from air into water or glass, the refraction above described takes place at their common surface.
54.In either of the instances just mentioned, the angle of refraction is less than that of incidence. If the passage of the light were from water or glass into air, the contrary would be the case, and in general it is observed that when light passes from a rarer into a denser medium, the ray is brought nearer the perpendicular to the surface bounding them: when from a denser into a rarer, the converse.
