Six Lectures on Light | Page 7

of the refracted beams let the
perpendiculars p _n_, _p'_ _n'_ be also drawn. Measure the lengths of o
m and of p _n_, and divide the one by the other. You obtain a certain
quotient. In like manner divide _m'_ _o'_ by the corresponding
perpendicular _p'_ _n'_; you obtain precisely the same quotient. Snell,
in fact, found this quotient to 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°, for example, water reflects 22 rays, at 60° it reflects 65 rays, at
80° 333 rays; while at an incidence of 89½°, 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]
Total reflection may be thus simply illustrated:--Place a shilling in a
drinking-glass, and tilt the glass so that the light from the shilling shall
fall with the necessary obliquity upon the water surface above it. Look
upwards through the water towards that surface, and you see the image
of the shilling shining there as brightly as the shilling itself. Thrust the
closed end of an empty test-tube into water, and incline the tube. When
the inclination is sufficient, horizontal light falling upon the tube
cannot enter the air within it, but is totally reflected upward: when
looked down upon, such a tube looks quite as bright as burnished silver.
Pour a little water into the tube; as the liquid rises, total reflection is
abolished, and with it the lustre, leaving a gradually diminishing
shining zone, which disappears wholly when the level of the water
within the tube reaches that without it. Any glass tube, with its end
stopped water-tight, will produce this effect, which is both beautiful
and instructive.
Total reflection never occurs except in the attempted passage of a ray
from a more refracting to a less refracting medium; but in this case,
when the obliquity is sufficient, it always occurs. The mirage of the
desert, and other phantasmal appearances in the atmosphere, are in part
due to it. When, for example, the sun heats an expanse of sand, the
layer of air in contact with the sand becomes lighter and less refracting
than the air above it: consequently, the rays from