Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics.

270 UNDULATORY THEORY OF OPTICS.
B'D in the proportion in which the velocity is diminished.
Let u be the number expressing this proportion: then
B'b = -B'D.
Similarly C has reached the surface still longer before, and
has therefore diverged into a sphere whose radius
Cc = -CE.
The sane holds for every intermediate point. Now the
front of the grand wave formed by all these little waves
is evidently the plane which touches all the spheres; and
therefore makes with the refracting surface an angle whose
Cc
sine is C' This angle is equal to the angle which the
direction of the wave (or the perpendicular to its front)
makes with the perpendicular to the refracting surface: it
is therefore the angle of refraction. Consequently
Cc
sin. refraction = C.
CE
Similarly sin. incidence = CAsin refraction Cc 1
Therefore = --
sin incidence CE /J
35. It is easily seen that a similar demonstration applies when the waves are transmitted in the second medium
with greater velocity than in the first: which we suppose
to represent the circumstances of light coming out of a refracting medium into vacuum. If in this case, fig. 10, the
angle of incidence is so great that Cc (the radius of the
wave diverging from C) is greater than CA', that is, if
AA'
AA'. M is greater than CA' or sin ACA' or sin ACA' is
or sin. incidence greater than
greater than -, or sin. incidence greater than -, no plane
~~CL 1~~L