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 sine of refraction incidence = ------------------; 1·5 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′. [Illustration: Fig. 48.] The material hitherto employed in the construction of lighthouse apparatus is crown glass, which, although it possesses a lower refractive power than flint glass and has, besides, a slightly greenish tinge, offers the great practical advantages of being more easily obtained of homogeneous quality; and, being less subject to deterioration from atmospheric influences, it is peculiarly suitable for use in the exposed situations generally occupied by Lighthouses. The refractive index of crown glass, as already noticed, is about 1·5. Any one may easily satisfy himself by a careful protraction of the angles of _incidence_ and _refraction_, in the manner above described, as to the truth of the following general propositions resulting from those laws:-- 1. A ray of light passing through a plate of some diaphanous substance such as glass, with parallel surfaces, suffers no change of _direction_, but emerges in a line parallel to its original path, merely suffering a _displacement_, depending on the obliquity of the incident ray, and the refractive power and thickness of the plate. The effect of this displacement is merely to give the ray an apparent point of origin different from the true one. This will be easily understood by the diagram (fig. 49), in which _a b_ is a normal to the plate, whose surfaces _x x_ and _x′ x′_ are parallel, _r r r r_ shews the path of the ray, _r r_ the displacement, and _r′_ the apparent point of origin resulting from its altered _direction_. [Illustration: Fig. 49.]