How can Fermat’s principle be used to explain reflection from mirrors?

Fermat’s principle, formulated by the French mathematician Pierre de Fermat, states that light traveling between two points follows a path that requires the least, greatest, or a stationary amount of time compared to neighboring paths.123

When applied to reflection from mirrors, this principle explains the laws of reflection by identifying the specific point on a surface where the travel time is minimized or maximized. For a flat mirror, the path taken by a light ray is the shortest possible distance—and thus the shortest time—between two points.3

In more complex scenarios, such as an elliptical mirror, the principle demonstrates that all paths from one focal point to the mirror and then to a second focal point take the same amount of time, resulting in perfect focusing. If a surface is curved more strongly than an ellipse, the path taken may represent the longest time among neighboring paths. Ultimately, this extremal approach allows for the deduction of optical behavior by treating light as a wave seeking the most efficient path.31