118 PHYSICS. 
from their true position; in any other position of the refracting edge, they 
are displaced towards it, and likewise exhibit colored borders. If a beam 
of solar light, coming in the direction vd (fig. 28), through a small aperture 
in the window-shutter of a darkened room, be received on a prism with its 
refracting edge uppermost, an elongated space, crossed transversely by the 
various colors of the rainbow, will be observed. This colored space is 
called the solar spectrum. Without the prism there would have been seen 
at d, above 7, a white and circular image of the sun. 
To follow the course of the rays in a prism, it becomes necessary to 
consider their direction in the plane of a principal section. In fig. 29, let 
as and a's be the refracting surfaces, s the refracting edge of a glass prism, 
i the incident, 72’ the refracted ray (refracted towards the perpendicular), 
and i’c’ the ray emerging from the prism (now refracted from the 
perpendicular). For air and glass the limiting angle is 402° ; an emergence 
of a ray from the prism is then impossible, when the ray, Ji, strikes the 
prism in such a manner, that the angle of refraction is less than the amount 
by which the refracting angle of the prism exceeds that limiting angle. In 
a prism whose refracting angle is twice as great, or still greater than the 
limiting angle, an emergence of the rays from the prism is impossible. Ifa 
ray of light pass in such a manner through a prism, as to make equal angles 
with both refracting surfaces, the total deflection produced on the ray by 
the prism is a minimum, that is, less than in any other position of the 
refracted ray. Suppose the ray, di (pl. 21, fig. 80), to be refracted in such 
a manner, that the refracted ray. ii’, shall make equal angles with the 
surfaces sa and sa, then will nz'2 = the angle of refraction n2i’ =, and 
the angle of deviation, d, of the ray at 7 = that at 2’; the total deviation 
thus = D=2d. If the direction of the incident ray be changed, so as, for 
instance, to fall along /’7, then the refracted ray will be am, and the angle, 
nim, less than x; the angle made by zm, with the perpendicular through m, 
will be just so much greater than 2: the deviation thus increases on one 
side and diminishes on the other. If the decrease = a, then the deviation 
= d—a,; as, however, it must have increased at m just so much more than 
x, as already seen, we may indicate the deviation at m by d+«+; the 
total deviation here, then, is D’ = d—a+td+a+8=2d+4, thus greater 
than D. The same may be proved by any other case of the kind. If the 
refracting angle of the prism be of small amount, then, in the case of the 
minimum of deviation, this is proportional to the refracting angle. If an 
object be observed through a prism, the direction in which the deviation is 
the least is easily found. If this minimum of deviation, d, be known, and 
the refracting angle of the prism, the index of refraction of the material of 
which the prism is composed, may be asceriained for air from the formula 
_ sin, sin. § (d (d+ 8) 
sin. 3g 
To obtain the index of refraction of any body, it becomes necessary then 
to form it into a prism. To give a liquid the prismatic shape, a hole is to 
oe bored through two sides of a glass prism, and a smaller one through the 
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