be
_a constant quantity_ for each particular substance, though it varied
in amount from one substance to another. He called the quotient the
_index of refraction_.

[Illustration Fig. 5]

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 f