In all cases where the light is incident from air upon the surface of a solid or a liquid, or, to speak more generally, when the incidence is from a less highly refracting to a more highly refracting medium, the reflection is partial.  In this case the most powerfully reflecting substances either transmit or absorb a portion of the incident light.  At a perpendicular incidence water reflects only 18 rays out of every 1,000; glass reflects only 25 rays, while mercury reflects 666 When the rays strike the surface obliquely the reflection is augmented.  At an incidence of 40 deg., for example, water reflects 22 rays, at 60 deg. it reflects 65 rays, at 80 deg. 333 rays; while at an incidence of 891/2 deg., where the light almost grazes the surface, it reflects 721 rays out of every 1,000.  Thus, as the obliquity increases, the reflection from water approaches, and finally quite overtakes, the perpendicular reflection from mercury; but at no incidence, however great, when the incidence is from air, is the reflection from water, mercury, or any other substance, total.

Still, total reflection may occur, and with a view to understanding its subsequent application in the Nicol’s prism, it is necessary to state when it occurs.  This leads me to the enunciation of a principle which underlies all optical phenomena—­the principle of reversibility.[5] In the case of refraction, for instance, when the ray passes obliquely from air into water, it is bent towards the perpendicular; when it passes from water to air, it is bent from the perpendicular, and accurately reverses its course.  Thus in fig. 5, if m E n be the track of a ray in passing from air into water, n E m will be its track in passing from water into air.  Let us push this principle to its consequences.  Supposing the light, instead of being incident along m E or m’ E, were incident as close as possible along C E (fig. 6); suppose, in other words, that it just grazes the surface before entering the water.  After refraction it will pursue say the course E n’’.  Conversely, if the light start from n’’, and be incident at E, it will, on escaping into the air, just graze the surface of the water.  The question now arises, what will occur supposing the ray from the water to follow the course n’’’ E, which lies beyond n’’ E?  The answer is, it will not quit the water at all, but will be totally reflected (along E x).  At the under surface of the water, moreover, the law is just the same as at its upper surface, the angle of incidence (D E n’’’) being equal to the angle of reflection (D E x).

[Illustration:  Fig. 6]