
3.4.
Fermat's Principle and Reflecting Surfaces 37
following different paths. This is most easily done by means of a specific
example.
If, in Fig. 3.3, we choose n = I, n' = ^J5/2, then the stationary path is that
for which
P2
is at (2, 2) when Pj is at (0,
— 1)
and
PQ
is at
(1,
0). The optical path
length between P^ and P2 is then a minimum. In order for another wave
originating at P^ to reach
P2
half a cycle after the wave following the minimum
path, we need
AJ^Q
of 1475 wavelengths for light of
500
nm, when the coordinates
of the points are given in meters. One-half cycle difference for two waves
corresponds to destructive interference. ...