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  2. Fermat's principle - Wikipedia

    en.wikipedia.org/wiki/Fermat's_principle

    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.

  3. Fermat's and energy variation principles in field theory

    en.wikipedia.org/wiki/Fermat's_and_energy...

    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.

  4. Snell's law - Wikipedia

    en.wikipedia.org/wiki/Snell's_law

    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.

  5. History of variational principles in physics - Wikipedia

    en.wikipedia.org/wiki/History_of_variational...

    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 ...

  6. Geometrical optics - Wikipedia

    en.wikipedia.org/wiki/Geometrical_optics

    A light ray is a line or curve that is perpendicular to the light's wavefronts (and is therefore collinear with the wave vector). A slightly more rigorous definition of a light ray follows from Fermat's principle, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time. [1]

  7. Calculus of variations - Wikipedia

    en.wikipedia.org/wiki/Calculus_of_Variations

    A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends upon the material of the medium. One corresponding concept in mechanics is the principle of least/stationary action.

  8. Parents charged with abuse after child's botched circumcision ...

    www.aol.com/parents-charged-abuse-childs-botched...

    A couple has been arrested after authorities say they performed a botched circumcision on their son at their central Missouri home last week.. Prosecutors charged Tyler Wade Gibson, 35, with one ...

  9. Brachistochrone curve - Wikipedia

    en.wikipedia.org/wiki/Brachistochrone_curve

    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 ...