We will proceed to consider the course of rays at different angles of incidence when light passes out from a medium into one less dense—for instance, from water into air. Corresponding to light with a small angle of incidence such as _I_{1}O_ (Fig. 15), some of it is reflected in the direction _OI´_{1}_ and the remainder is refracted out in the direction _OR_{1}_. Similarly, for the ray _I_{2}O_ some is reflected along _OI´_{2}_ and some refracted along _OR_{2}_. Since, in the case we have taken, the angle of refraction is greater than the angle of incidence, the refracted ray corresponding to some incident, ray _I_{c}O_ will graze the bounding surface, and corresponding to a ray beyond it, such as _I_{3}O_, which has a still greater angle of incidence, there is no refracted ray, and all the light is wholly or totally reflected within the dense medium. The critical angle _I_{c}ON_, which is called the angle of total-reflection, is very simply related to the refractive indices of the two media; for, since _r_ is now a right angle, sin _r_ = 1, and equation (_a_) becomes _n_ sin _i_ = _n´_ (_b_) Hence, if the angle of total-reflection is measured and one of the indices is known, the other can easily be calculated. [Illustration: FIG. 15.—Total-Reflection.] The phenomenon of total-reflection may be appreciated if we hold a glass of water above our head, and view the light of a lamp on a table reflected from the under surface of the water. This reflection is incomparably more brilliant than that given by the upper surface. The refractive index of air is taken as unity; strictly, it is that of a vacuum, but the difference is too small to be appreciated even in very delicate work. Every substance has different indices for light of different colour, and it is customary to take as the standard the yellow light of a sodium flame. This happens to be the colour to which our eyes are most sensitive, and a flame of this kind is easily prepared by volatilizing a little bicarbonate of soda in the flame of a bunsen burner. A survey of Table III at the end of the book shows clearly how valuable a measurement of the refractive index is for determining the species to which a cut stone belongs. The values found for different specimens of the species do in cases vary considerably owing to the great latitude possible in the chemical constitution due to the isomorphous replacement of one element by another. Some variation in the index may even occur in different directions within the same stone; it results from the remarkable property of splitting up a beam of light into two beams, which is possessed by many crystallized substances. This forms the subject of a later chapter.