Many physicists, of whom may be especially mentioned Young, Fresnel, Poisson, Green, and Cauchy, have investigated the reflection of light or sound at the surface of separation of two uniform media of different mechanical properties. The transition from one medium to the other being treated as abrupt, the problem is of no great difficulty for the case of plane waves incident upon a plane surface of separation. It is of some interest to inquire what modifications would be caused by the substitution of a gradual for an abrupt transition, and the principal object of this paper is to give the details of one particular case, which admits of pretty simple treatment.

It is evident, from the first, that the transition may be supposed to be so gradual that no sensible reflection would ensue. No one would expect a ray of light to undergo reflection in passing through the earth's atmosphere as a consequence of the gradual change of density with elevation. At first sight, indeed, the case of so-called total reflection may appear to be an exception, as it is independent of the suddenness of transition; but this only shows that the phenomenon is inaccurately described by its usual title. It is, in strictness, a particular case of refraction, rather than of reflection, and must be so considered in theoretical work, although, no doubt, the name of total reflection will be retained whenever, as in constructing optical instruments, we have to deal with effects rather than with causes.