
28 3. Fermat's Principle: An Introduction
3.1.
FERMAT'S PRINCIPLE IN GENERAL
The simplest case illustrating Fermat's Principle is shown in Fig.
3.1.
A surface
Z lies between two points,
PQ
and
P^,
with a
ray
joining these points consisting of
straight line segments. The solid line is the actual ray path and the dashed line
some other path. If the time of travel from
PQ
to P^ is denoted by T, then the
condition that
T
have a stationary value for the actual path is
dT/dx = dx/dy = 0,
(3.1.1)
where x, y are the generalized coordinates of the point where the ray intersects the
surface.
An equivalent statement of Fermat's Principle is obtained b ...