Again, everyday experience tells us that the case is less simple when light actually crosses the bounding surface and passes into the other medium. Thus, if we look down into a bath filled with water, the bottom of the bath appears to have been raised up, and a stick plunged into the water seems to be bent just at the surface, except in the particular case when it is perfectly upright. Since the stick itself has not been bent, light evidently suffers some change in direction as it passes into the water or emerges therefrom. The passage of light from one medium to another was studied by Snell in the seventeenth century, and he enunciated the following laws:— 1. The refracted ray lies in the plane containing the incident ray and the normal to the plane surface separating the two media. It will be noticed that the reflected ray obeys this law also. 2. The angle _r_, which the refracted ray makes with the normal, is related to the angle _i_, which the incident ray makes with the same direction, by the equation _n_ sin _i_ = _n´_ sin _r_, (_a_) where _n_ and _n´_ are constants for the two media which are known as the indices of refraction, or the refractive indices. This simple trigonometrical relation may be expressed in geometrical language. Suppose we cut a plane section through the two media at right angles to the bounding plane, which then appears as a straight line, _SOS´_ (Fig. 14), and suppose that _IO_ represents the direction of the incident ray; then Snell’s first law tells us that the refracted ray _OR_ will also lie in this plane. Draw the normal _NON´_, and with centre _O_ and any radius describe a circle intersecting the incident and refracted rays in the points _a_ and _b_ respectively; let drop perpendiculars _ac_ and _bd_ on to the normal _NON´_. Then we have _n.ac = n´.bd_, whence we see that if _n_ be greater than _n´_, _ac_ is less than _bd_, and therefore when light passes from one medium into another which is less optically dense, in its passage across the boundary it is bent, or refracted, away from the normal. [Illustration: FIG. 14.—Refraction across a Plane Surface.] We see, then, that when light falls on the boundary of two different media, some is reflected in the first and some is refracted into the second medium. The relative amounts of light reflected and refracted depend on the angle of incidence and the refractive indices of the media. We shall return to this point when we come to consider the lustre of stones.