Page:The American Cyclopædia (1879) Volume XII.djvu/672

 658 OPTICS ditions to be kept in view are much more com- plex than in the case of reflection ; it is this : The paths of the ray before and after refrac- tion always lie in the same plane with the per- pendicular to the refracting surface drawn to the point of transmission, and on opposite sides of that perpendicular ; and in that plane the sines of the angle of incidence and of re- fraction have in all cases the same ratio for any two given media. This is " Snell's law ;" and it also is rigidly verified by measurements. Suppose the refraction be that of a ray passing from air into ordinary crown glass ; then, for all angles of incidence, the ratio = > very nearly. The angle of incidence is the greater, and the refraction is therefore toward the perpendicular. Thi3 is the case whenever the ray passes from a less to a more dense medium. And as, in all such cases, we have - > 1, this fact of a ratio greater than unity expresses a refraction toward the per- pendicular. The value which the ratio gine R may have, being constant for any two media, is called for such media the " index" or " co- efficient of refraction," c. From air to water, c=f ; from air to diamond, c=f ; from water to crown glass, |- ; from crown glass to dia- mond, f. When light passes successively from air through water, crown glass, and diamond, these refractions are not added ; but the ray has in any one of the media precisely the course it would have had if passed from vacuum or from air directly into the given medium. Thus, in the case supposed, the successive refractions would be fx|xf=c=f, the same as if the light had passed at once from air to diamond ; and so in all cases. When the ray passes, on the other hand, from a denser medium to a rarer, we always find the ratio = c < 1 ; and this signifies that the ray is then bent from the perpendicular. Thus, from crown glass to air, c=|; from water to air, c=f ; and so on. That is, in all these cases, sine I must be less than sine R, or sine R > sine I. But the angle of incidence may vary from up to 90 ; and the angle of refraction cannot exceed 90, be- cause this is the whole space between any surface and a perpendicular to it. Hence, for light going toward the rarer medium, there will be a limit of the angle of incidence beyond which no angle of refraction can be found suf- ficiently large. Rays meeting the surface at an angle greater than this limit cannot pass the surface. There is a mathematical impos- sibility, and hence a physical ; and the light is wholly thrown back into the medium, i. e., totally reflected. Fig. 11 gives a correct view of the paths of the rays proceeding from a ra- diant point R in the interior of a mass of water whose surface S S' is contiguous to air. R P is the path of the ray which is perpendicular to the surface S S 7. The rays which diverge are bent away from the perpendicular when they pass the surface S S' into the air, and their directions are shown by the lines 1, 2, 3, &c. ; but when the divergence has become so great that the sine of the angle of refraction (in air) must be greater than the radius in order Fm. 11. that the law of the constancy of the ratio of the sines shall hold, the rays do not pass through the surface S S', but are reflected from that surface, as shown by the lines a, &, c. This total reflection is readily observed on looking in certain directions into a prism ; its highly transparent surfaces serve as mirrors for ob- jects situated so that their light falls without a certain angle ; for crown glass, 41 48'. Any small transparent body of a density unlike that of the medium it is in, and bounded by a curved and a plane or by two curved surfaces, is termed a lens. The combination of spherical surfaces, either with each other or with plane surfaces, gives rise to six kinds of lenses, sections of which are represented in fig. 12 ; four are formed by two spherical surfaces, and two by a plane and a spherical surface. A is a double convex lens, B is a plano-convex, C is a con- verging concavo-convex, D is a double con- cave, E is a plano-concave, and F is a diverging concavo-convex. The lens C is also called the converging meniscus, and the lens F the di- verging meniscus. The first three, which are thicker at the centre than at the borders, are converging ; the others, which are thinner at the centre than at the borders, are diverging. Lenses are most conveniently made of glass,