The
Fermat principle is a very important
concept in geometrical
optics. In
1657, Fermat stated this principle by saying that "
light is propagating from a point to another on a trajectory such that its travel time is minimal". Today, Fermat principle is stated somewhat differently:
Between two points A and B reached by light, the optical path along the light's trajectory is stationary.
The main difference lies in the use of the stationarity of the optical path instead of the minimal duration of light's travel. This new statement is less restrictive than Fermat's original principle since it encompasses some physical singularities, such as discontinuities. For example, reflected light between points A and B can follow a much longer path than a straight line; however, unless points A and B are the foci of an elliptic reflector, trying to change the reflected light's path by a small amount results in an augmented optical path. Thus, we say that the trajectory followed by the reflected light is stationary.
Immediate consequences of the Fermat principle include rectilinear propagation of light in an homogenous medium, and inverse return of light (i.e. light's trajectory does not depend on the direction of propagation). One can also deduce the iconal equation and Snell-Descartes's Law from the Fermat principle using the differential of the optical path.