KnowraFermat's principleLinked fromLinked fromThe 17 pages that link to Fermat's principle, each with the reason it gives.All 17Broader topic 1Related 13Compared with 3RefractionRelated: Its least-time formulation yields the law governing refraction at an interface.Gravitational lensingRelated: Lensed images correspond to stationary travel-time paths through the gravitational field.Snell's lawRelated: Applying it to travel across an interface yields the sine relation in Snell's law.Atmospheric refractionRelated: It explains curved atmospheric ray paths through variation in light’s speed.Euler–Lagrange EquationCompared with: It is a physical variational principle, while the Euler–Lagrange equation is the condition derived from such principles.Optical path lengthRelated: Stationary travel time is equivalent to stationary optical path length in a given medium.Pierre de FermatBroader topic: Fermat applied mathematical reasoning to optics, extending his work beyond number theory.Geometrical opticsRelated: It provides a variational rule from which reflection and refraction laws can be derived.Principle of least actionRelated: It is an optical stationary-time principle analogous to stationary action.WavefrontRelated: Its stationary paths determine how optical wavefronts advance.Hamilton's principleRelated: It is a related variational principle, with travel time replacing mechanical action.Law of reflectionRelated: Its least-time construction derives equal incidence and reflection angles.Fermat pointCompared with: It shares Fermat's name but concerns light paths, not a triangle's distance-sum minimum.Pierre Louis MaupertuisCompared with: Its earlier use of an extremum principle prompted comparisons with Maupertuis’s proposal for mechanics.Brachistochrone curveRelated: The analogy with light refraction offers a route to the brachistochrone solution.Ibn SahlRelated: It offers a later variational account of refraction that can be compared with Ibn Sahl's construction.Fagnano's problemRelated: The equal-angle reflection rule mirrors the path condition used in optical ray tracing.
KnowraFermat's principleLinked fromLinked fromThe 17 pages that link to Fermat's principle, each with the reason it gives.All 17Broader topic 1Related 13Compared with 3RefractionRelated: Its least-time formulation yields the law governing refraction at an interface.Gravitational lensingRelated: Lensed images correspond to stationary travel-time paths through the gravitational field.Snell's lawRelated: Applying it to travel across an interface yields the sine relation in Snell's law.Atmospheric refractionRelated: It explains curved atmospheric ray paths through variation in light’s speed.Euler–Lagrange EquationCompared with: It is a physical variational principle, while the Euler–Lagrange equation is the condition derived from such principles.Optical path lengthRelated: Stationary travel time is equivalent to stationary optical path length in a given medium.Pierre de FermatBroader topic: Fermat applied mathematical reasoning to optics, extending his work beyond number theory.Geometrical opticsRelated: It provides a variational rule from which reflection and refraction laws can be derived.Principle of least actionRelated: It is an optical stationary-time principle analogous to stationary action.WavefrontRelated: Its stationary paths determine how optical wavefronts advance.Hamilton's principleRelated: It is a related variational principle, with travel time replacing mechanical action.Law of reflectionRelated: Its least-time construction derives equal incidence and reflection angles.Fermat pointCompared with: It shares Fermat's name but concerns light paths, not a triangle's distance-sum minimum.Pierre Louis MaupertuisCompared with: Its earlier use of an extremum principle prompted comparisons with Maupertuis’s proposal for mechanics.Brachistochrone curveRelated: The analogy with light refraction offers a route to the brachistochrone solution.Ibn SahlRelated: It offers a later variational account of refraction that can be compared with Ibn Sahl's construction.Fagnano's problemRelated: The equal-angle reflection rule mirrors the path condition used in optical ray tracing.