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The ordinary law of refraction was at that time attributed to René Descartes (d. 1650), who had tried to explain it by supposing that light was a force that propagated instantaneously, or that light was analogous to a tennis ball that traveled faster in the denser medium, [44] [45] either premise being inconsistent with Fermat's.
Fermat's principle states that light takes a path that ... Snell's law for refraction requires that these terms be equal. As this calculation demonstrates, Snell's ...
Snell's law (also known as the Snell–Descartes law, the ibn-Sahl law, [1] and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
In the generalized Fermat’s principle [6] the time is used as a functional and together as a variable. It is applied Pontryagin’s minimum principle of the optimal control theory and obtained an effective Hamiltonian for the light-like particle motion in a curved spacetime. It is shown that obtained curves are null geodesics.
According to Fermat’s principle, the actual path between two points taken by a beam of light (which obeys Snell's law of refraction) is one that takes the least time. In 1697 Johann Bernoulli used this principle to derive the brachistochrone curve by considering the trajectory of a beam of light in a medium where the speed of light increases ...
The angle between this ray and the normal is known as the angle of refraction, and it is given by Snell's law. Conservation of energy requires that the power in the incident ray must equal the sum of the power in the refracted ray, the power in the reflected ray, and any power absorbed at the surface.
The earlier geometrical ideas in optics were generalized by Pierre de Fermat, who, in the 17th century, refined the principle to "light travels between two given points along the path of shortest time"; now known as the principle of least time or Fermat's principle. Fermat showed that principle predicts the observed law of refraction. His ...
Pierre de Fermat (French: [pjɛʁ də fɛʁma]; [a] 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.