The extent to which the rays undergo refraction depends upon the degree of density of the medium, and varies in the case of each individual substance; but it follows a definite law. If, as in Pl. XII. fig. 2, a circle be drawn around the point _b_, at which the ray _a_ is incident, _b r_ representing the refracted ray, the lines _s i_ and _t r_, drawn at right angles to the perpendicular _p_, will form respectively the sines, as they are called, of the angles _s b i_ and _t b r_; _s i_ being the sine of the angle of incidence _s b i_, or the angle formed by the incident ray with the perpendicular, and _t r_ the sine of the angle of refraction _t b r_, or of that formed by the refracted ray with the perpendicular. These sines, for brevity, are called the sines of incidence and of refraction; and they bear a constant ratio or proportion to each other. Taking the sine of refraction as the unit, or as = 1, the value of the sine of incidence represents the refractive index or the refractive power of the medium for a ray entering the medium from a vacuum; or, the refractive power of air being extremely small, the value of the sine of incidence may be considered as representing the refractive power from air into the medium. PLATE XII. [PAGE 168.] OPTICAL PRINCIPLES. Fig. 1. Refraction through a glass plate. 2. Law of refraction. 3. Reflexion from a plane surface. 4. Reflexion from a concave mirror. 5. Refraction at a curved surface. 6. A doubly convex lens. 7. A plano-convex lens. 8. A doubly concave lens. 9. A plano-concave lens. 10. A concavo-convex lens, or meniscus. 11. Refraction through a convex lens. 12. Relation of a convex lens to prisms. 13. Relation of a concave lens to prisms. 14. Refraction of parallel rays through a convex lens. 15. Refraction of converging rays through a convex lens. 16. Refraction of diverging rays through a convex lens. 17. Refraction of parallel rays through a concave lens. 18. Spherical aberration. 19. Dispersion and formation of a spectrum. 20. Chromatic aberration. 21. Formation of images in the eye. 22. Angle of vision. 23. Objects too near the eye. 24. Action of convex lens in vision. 25. Aplanatism. 26. Aberration produced by cover. 27. Course of rays through the microscope. 28. Achromatism. 29. Waves of light conspiring (_a_, _b_), and interfering (_b_, _c_). 30. Polarization: _t_, tourmaline; _d_, crystal; _s_, crystal of calcareous spar. [Illustration: Plate XII. W Bagg sculp London: John Van Voorst.] Although the ratio of the sines is constant, the refractive index varies in different media. Thus that of air is 1·0003; of water, 1·336; of Canada balsam, 1·549; of crown glass, from which window-panes are made, 1·535; of flint glass, from which bottles are made, 1·6; of Faraday’s heavy glass, composed of silicated borate of lead, 1·8; and of that consisting of borate of lead, 2·0.