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LENSES 105
ratios'of these lines to the radius of the circle a n or b n are what mathematicians call the sines of the angles. Thus ad I an is the sine of i, and bf/bn the sine of r. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant.
This ratio is, when light leaves air for water, 4 to 3 ; that is, the sine bf/bn is three-quarter times as great as the sine ad/an, or the ratio ad/an is four-third times as great as bf/an. Light is still more refracted on entering glass. In this Flg* 25#
case the ratio of the sine is as 3 to 2. This ratio of the sines of the two angles is called the index of refraction.
If a ray of light I n falls upon a smooth sheet of glass (fig. 25), it experiences a similar refraction ; it continues in the direction n n' , and the sine of the angle of refraction at n in the glass becomes two-thirds of the sine of the angle of incidence.
On issuing from the other side of the sheet of glass, another refraction takes place ; but in this case the sine of the angle of refraction at n' in the air becomes one and a half times that of the angle in the glass, and as the angle at n is equal to the angle at n', the angle of emergence of n' r is of the same magnitude as the angle of incidence of I n — that is, the ray continues, after refraction, in its original direction. At all events, it only experiences a shifting parallel with itself. Therefore we see objects through our windows in the same direction in which they are really situated.
The result is entirely different when the spectator looks through a triangular glass (fig. 26). If the Flg* 2G* eye is at o, and an object at a, and
a triangular prism be held close to the eye, the object does not appear to be at a, but in the direction of a' '. The incident ray a d suffers a deflection at the