A ray of light, in passing obliquely from one transparent body into another of different density, experiences at the point of the intersection of the common surface of the two planes, a sudden change of direction, to which the name of Refraction. refraction has naturally been given, in connection with the most familiar instance of the phenomenon, which is exhibited by a straight ruler with one half plunged into a basin of water while the other remains in the air. The ruler no longer appears straight, but seems to be bent or broken at the point where it enters the water. It may not be out of place to call attention to the laws which regulate the change of direction in the incident light, which are three in number.
1. Incidence and refraction, in uncrystallized media of homogeneous structure such as glass, always occur in a plane perpendicular to that of the refracting surface.
2. In the same substances, the angle formed with the perpendicular by the ray at its entering the surface of the second medium, has to the angle which it makes with the normal after it has entered the surface, such a relation, that their sines have a fixed ratio, which is called the refractive index. When a ray falls normally on the surface of any substance, it suffers no refraction.
3. The effect of passing from a rare to a dense medium, as from air into water or glass, is to make the angle of refraction less than the angle of incidence; and those angles are measured with reference to a normal to the plane which separates the media at the point of incidence. The converse phenomenon, of course, takes place in the passage from a dense to a rare medium, in which case the angle of incidence is less than the angle of refraction. To this rule there are a few exceptions; for there are certain combustible bodies, such as diamond, whose refractive powers are much greater than other substances of equal density.
Fig. 47.
The diagram ([fig. 47]) will serve to render those laws more intelligible. Let a ray of light a O meet a surface of water n m at O, it will be immediately bent into the direction O a′; and if, from the centre O, we describe any circle, and draw a line b O b′, perpendicular to nm; then ab and a′ b′, perpendiculars drawn to the normal bb′, from the points a and a′ where the circle cuts the incident and refracted rays, will be the sines of the angle of incidence b O a, and of the angle of refraction b′ O a′, and the ratio of those sines to each other, or b ab′ a′ will be the relative index of refraction for the two media.
4. It may perhaps be added, for convenience, as a fourth law, deducible from the others, that since rays passing from a dense into a rare medium, have their angle of refraction greater than the angle of incidence, there must be some angle of incidence whose corresponding angle of refraction is a right angle; beyond which no refraction can take place, because there is no angle whose sine can be greater than the radius. In such circumstances, total reflection ensues. For common glass, whose index of refraction is 1·5, we have (in the case of emergent rays) sine of incidence = sine of refraction1·5; but, as no sine can exceed radius or unity, the angle of incidence must be limited to 41° 49′; beyond which total reflection will take place, and the light will return inwards into the glass, being reflected at its surface.
Thus, if a ray proceed from a point O ([fig. 48]), within a piece of glass, to a point C, at its surface A B; and if O C b, its incidence, be less than 41° 49′, it will be refracted in some direction C f; but if this angle be greater than 41° 49′, as O C′ b′, the ray will be reflected back into the glass in the direction C′ O′.
Fig. 48.