m, n be the sine of the angle of incidence, and p q the
sine of the angle of refraction. Now, it is found that whatever the
direction of the incident ray, that of the corresponding refracted ray
is so conditioned that the quotient of the sine of the angle of
refraction into the sine of the angle of incidence is a constant
quantity for the same media. This quotient is called the index of
refraction. It is to be found in the instance above quoted by dividing m n by p q. The greater the refractive power of the substance the smaller will be the value of p q, and
the larger the quotient, which is the index of refraction. Hence
substances with a high refractive power have a large index of
refraction, as diamond, whose index of refraction is 2.42. That of
water is only 1.336. Garnet has an index of refraction varying from
1.75 to 1.81 in different varieties. Zircon is another gem mineral
which possesses a high index of of refraction, this being 1.96. Diamond
is the most highly refractive of the gems, however.
It
is to be noted that the amount of refraction of the different
component colors of a ray of white light is a variable quantity, and
hence in every refraction the ray is broken up in a way similar to that
in which it is separated into the colors of the spectrum in passing
through a prism. This variation in the refraction of the different
colors is called dispersion. The red waves, for example, suffer
less change of velocity than the blue, and hence the refractive index
for a given substance is greater for blue than for red light.
Substances differ in the degree of refraction which the waves of the
different colors suffer in passing through them, and hence in the
degree to which they separate the component colors; that is, they
differ in what is called dispersive power. Diamond has high
dispersive power, its index of refraction for red light being 2.407+,
and for violet light 2.464+, while spinel, which has only an average
dispersive power, has a difference in indices between red and violet
light only between 1.712+ for red, and 1.726 for violet.
A
particular phase of the relations of the incident and refracted rays
should be noted here, as it has much to do with increasing the
brilliancy of gems.
When
a ray of light attempts to pass from a denser into a rarer medium there
are conditions under which the angle of refraction cannot be greater
than the angle of incidence. Under such circumstances the ray cannot
emerge from the denser medium, but will be wholly reflected at the
point of incidence. Thus, in the following figure, if the luminous
rays from A passing out of the water be traced it will be found that
since the angle of refraction increases more rapidly than that of
incidence certain rays cannot emerge at all, but are refracted or
reflected back into
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