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.

POLARIZATION BY REFLECTION FROM GLASS. 343
Eliminating b,
(sin 2i + sin 2i) c - sin 2i. ac - (sin 2 - sin 2i) a = 0,
or (c - a) (sin 2i'+ sin 2i)c + (sin 2i'- sin2i)a} = 0.
This equation is satisfied by c= a: but that would give
b = o, and therefore expresses only total reflection, which
would require exactly the same niathematical conditions as
those that we have used, but would not correspond to the
physical circumstances of the problem now before us. The
other is the only solution which we want: it gives
tan (i'- i)
C a — a
cosi tan (i i))
and b=a.o 1 + >.
cos ' tan (i' + i)
Hence if the displacement produced by the incident wave is. 2r
a sin (vt - x),
that produced by the reflected wave is
tan (i'-i) 2 r
- a. sin - (vt - c),
tan(i'+i) k
and that by the refracted wave is
cos i tan(i'-i)l. 2r
a - 1 + - si ln - (t - x).
cos z talr ( i+ -)
130. One of the most remarkable inferences from this
expression is obtained by making i'+ i = 90~. The displacement produced by the reflected wave is then = 0. Suppose
now light consisting of transversal vibrations in all directions
to be incident at this angle on a surface of glass. Resolve
the vibrations into two sets, one parallel to the plane of incidence and the other perpendicular to it. The former (as
we have just seen) will furnish no reflected ray: the latter,
by (128), will produce a reflected ray. Consequently the