Pierre de Fermat
French mathematician known for Fermat's principle of least time.
Pierre de Fermat, a French mathematician, first proposed Fermat's principle in 1662 as a means of explaining the ordinary law of refraction of light. Fermat's principle, also known as the principle of least time, states that the path taken by a ray between two given points is the path that can be traveled in the least time. This principle is the link between ray optics and wave optics. Fermat's principle was initially controversial because it seemed to ascribe knowledge and intent to nature. Not until the 19th century was it understood that nature's ability to test alternative paths is merely a fundamental property of waves.
- field
- Mathematics, physics, law
- nationality
- French
- known_for
- Fermat's principle
Lore & Background
Fermat's principle was first proposed by the French mathematician Pierre de Fermat in 1662, as a means of explaining the ordinary law of refraction of light. The principle was initially controversial because it seemed to ascribe knowledge and intent to nature. Not until the 19th century was it understood that nature's ability to test alternative paths is merely a fundamental property of waves. In its original 'strong' form, Fermat's principle states that the path taken by a ray between two given points is the path that can be traveled in the least time. In order to be true in all cases, this statement must be weakened by replacing the 'least' time with a time that is 'stationary' with respect to variations of the path – so that a deviation in the path causes, at most, a second-order change in the traversal time.
Reader's Guide
Fermat's principle is most familiar in the case of visible light: it is the link between geometrical optics, which describes certain optical phenomena in terms of rays, and the wave theory of light (or physical optics), which explains the same phenomena on the hypothesis that light consists of waves. The principle applies to waves in general, including sound waves in fluids and elastic waves in solids. In a modified form, it even works for matter waves: in quantum mechanics, the classical path of a particle is obtainable by applying Fermat's principle to the associated wave – except that, because the frequency may vary with the path, the stationarity is in the phase shift (or number of cycles) and not necessarily in the time. All the conclusions that Huygens drew from his geometric construction – including the laws of rectilinear propagation of light, ordinary reflection, ordinary refraction, and the extraordinary refraction of 'Iceland crystal' (calcite) – are also consequences of Fermat's principle.
Did You Know?
- Fermat's principle was first proposed by Pierre de Fermat in 1662.
- Fermat's principle was initially controversial because it seemed to ascribe knowledge and intent to nature.
- Not until the 19th century was it understood that nature's ability to test alternative paths is merely a fundamental property of waves.
- Fermat's principle applies to waves in general, including sound waves in fluids and elastic waves in solids.
- All the conclusions that Huygens drew from his geometric construction are consequences of Fermat's principle.
Frequently Asked Questions
What was Fermat's day job?
He served as a magistrate in the French judicial system, holding a seat on the Parliament of Toulouse. Mathematics was a private pursuit he carried on in his spare time, and he published very little of his work during his own lifetime.
How did Fermat contribute to the development of calculus?
He devised a method called adequality for determining tangents to curves and locating maxima and minima, which is essentially an early form of differentiation. This placed him among the key forerunners of Newton's and Leibniz's later formalization of calculus.
What is Fermat's principle in optics?
It states that light traveling between two points follows the path that requires the least travel time. This single rule accounts for both reflection and refraction and became a cornerstone of geometric optics.
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