Fermat's principle explains why light rays traveling between
air and water undergo bending {refraction). Imagine that we
have two uniform media (such as air and water) and a light
ray traveling from a source A in one medium to an observer B
in the other medium (see the figure below). It is known that
light travels at a constant speed in a uniform medium, but
more slowly in a dense medium (such as water) than in a thin
medium (such as air).
Consequently, the path of shortest time from A to B is not
necessarily a straight line, but rather some broken line path
A to P to B allowing the light to take greatest advantage of
its higher speed through the thin medium. Snell's law of
refraction states that the path of the light ray will be such
that
Show that this follows
from the assumption that the path of minimum time occurs when
dt/dx = 0.
