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the
water. This is familiarly illustrated in looking into a glass of water
held above the eye, by the fact that the surface of the water appears
to be silvered and opaque, owing to the total reflection of a large
number of rays. The path of the rays is more fully illustrated in the
next figure, showing a ray of light, L A, passing out of the water by
refraction in the direction A R. If the angle of incidence, C A L, be
gradually increased, the angle of refraction will also increase, but
more rapidly than the angle of incidence until it becomes equal to 90°,
when the ray will graze the surface of the water at A M. If the source
of light be still further removed as to I, the ray can no longer pass out, but is reflected to r. The
incident angle at which internal reflection will thus take the place
of refraction is called for every substance the critical or limiting
angle, and is a constant angle for each different substance. For water
(with reference to air) this angle is 48°35', for flint glass 37°36',
and for diamond 23° 53'. Substances with a low critical angle—or in
other words, highly refracting substances—will appear more brilliant
than those of low refractive power, because the amount of light
striking upon them becomes concentrated into a smaller part of the
surface. This can be proved by a mathematical calculation, but it is
too abstruse for these pages. The fact, however, can be made evident by
observation. A large amount of total reflection, such as is afforded by
substances of high refractive power, has, moreover, the advantage of
returning light to the eye which would otherwise pass through the stone
and be lost. How this is done is shown by the following figure after
Bauer, representing the path of a ray of light in a diamond cut as a
brilliant. The ray enters in the direction a b and being totally reflected from the various points of the interior comes back in somewhat the general direction m g in
which it started. It does not come back, however, as a single ray, but
is broken up by the refraction into its differently colored components.
Hence the particular ray which reaches the eye may be red or blue, or
some other color. To this refractive power, therefore, the diamond owes
the property of flashing colored lights which gives it so much of its
beauty and attractiveness. When refraction, or reflection, of a ray of
light takes place, the ray
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