A knowledge of this “law of the sines” is of practical importance in determining the direction which the rays will pursue when transmitted through glass lenses, &c. the refractive index of which is known; or in ascertaining the curve which should be given to their surfaces for producing a particular refraction and focal length. Thus, supposing the plate of glass in Pl. I. fig. 2 to consist of crown glass, the refractive index of which is 1·5, the length of the sine of refraction, _t r_, will be equal to one part or dimension, while the sine of incidence, _s i_, is equal to one part and a half. It must be remarked that when light is incident at a right angle to the surface of the medium, no refraction takes place, the transmitted ray pursuing its original course. When a ray of light leaves a denser medium, such as glass, to enter a rarer medium, such as air, it becomes refracted from the perpendicular. In such case, the angle of refraction being greater than the angle of incidence, its sine will also be greater than that of the latter; but the ratio is still preserved. _Reflexion._--When rays of light fall upon a plane surface, as the flat surface of the mirror, a greater or less number of them are reflected, and this according to a definite law, by which the angle of incidence, or that formed by the incident ray with the perpendicular, is equal to the angle of reflexion, or that formed by the reflected ray with the same. Thus, as shown in Pl. XII. fig. 3, the angle _i b p_, formed by the incident ray _i b_ with the perpendicular _p_, is equal to the angle _p b r_, formed by the reflected ray _b r_ with the perpendicular _p b_. If the body upon the surface of which the rays are incident be transparent, some of the rays will be refracted and will pass through it, whilst others will be reflected. The proportion of those reflected is smallest when the rays are incident perpendicularly to the surface; but this increases as the incident rays become more oblique, _i. e._ as the angle of incidence becomes greater, although at no degree of obliquity are the whole of the rays reflected. The case is different, however, with those rays which enter the substance and impinge upon its inner or second surface; for these at a particular angle of incidence undergo total reflexion, so that none of the rays are transmitted at the second surface. The angle of total reflexion is constant for the same medium, but different for different media: thus in crown glass it is equal to about 40°, in flint-glass 38°, &c.; and this internal reflexion from the second surface of transparent media is more perfect than that occurring at the surface of opake reflecting surfaces or mirrors.