Fermat's principle
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Light takes the path of stationary travel time.
Light travels along the path of stationary (usually minimum) travel time between two points. Both reflection and refraction laws follow.
A lifeguard problem: run along the beach and swim.
Stationary doesn't always mean minimum.
In more detail
Fermat's principle states that light travels along the path that takes the least time between two points. It explains reflection and refraction as consequences of this principle.
Real-world uses
- Designers use Fermat's principle to trace rays through complex optical systems.
- It explains mirages and ray bending in the atmosphere.
- Fermat's principle explains why light bends at a boundary, since it takes the route of least time.
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Frequently asked questions
Does light really choose the fastest path?
It takes a path where time is stationary, which is usually the minimum time.
How does it give Snell's law?
Minimising travel time across a boundary leads directly to Snell's law.
Does light really test every path?
No. The principle says light follows the path where the travel time is stationary, which gives the observed route.
Related topics in Optics
Optical activity · Coherence and lasers · Holography · Fresnel and Fraunhofer diffraction · Fibre optics numerical aperture · Colour and the eye