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- https://phys.libretexts.org/Bookshelves/Optics/BSc_Optics_(Konijnenberg_Adam_and_Urbach)/02%3A_Geometrical_Optics/2.04%3A_Some_Consequences_of_Fermats_PrincipleLet the x-axis be the intersection of the mirror and the plane through the points P and Q and perpendicular to the mirror. Let (x P , y P ) and (x Q , y Q ) with y P > 0 and y Q < 0 be the coordinates...Let the x-axis be the intersection of the mirror and the plane through the points P and Q and perpendicular to the mirror. Let (x P , y P ) and (x Q , y Q ) with y P > 0 and y Q < 0 be the coordinates of two points P and Q are shown in Figure \(\PageIndex{3}\). where \(θ_i\) and \(θ_t\) are the angles between the ray and the normal to the surface in the upper half space and the lower half space, respectively (\(\PageIndex{3}\)).
- https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_I_(Raymond)/03%3A_Geometrical_Optics/3.05%3A_Fermats_PrincipleIf a light ray originates at point O in Figure \(\PageIndex{12}\):, reflects off of the ellipsoidal mirror surface at point A, and returns to point O, the elapsed time isn’t much different from that e...If a light ray originates at point O in Figure \(\PageIndex{12}\):, reflects off of the ellipsoidal mirror surface at point A, and returns to point O, the elapsed time isn’t much different from that experienced by a ray which reflects off the mirror a slight distance from point A and returns to O.
- https://phys.libretexts.org/Bookshelves/Optics/Physical_Optics_(Tatum)/01%3A_Reflection_and_Refraction_via_Fermat's_Principle_and_Huygens'_Construction/1.01%3A_Reflection_and_RefractionReflection of light from a smooth, shiny surface is called specular reflection. (Latin speculum a mirror.) At the other extreme we have the sort of diffuse scattering that occurs when you shine light ...Reflection of light from a smooth, shiny surface is called specular reflection. (Latin speculum a mirror.) At the other extreme we have the sort of diffuse scattering that occurs when you shine light on blotting paper. And there are lots of situations in between these extremes. In this chapter I am going to deal solely with specular reflection, the law of specular reflection being that the angle of reflection is equal to the angle of incidence.
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Graduate_Classical_Mechanics_(Fowler)/03%3A_Fermat's_Principle_of_Least_Time/3.03%3A_Fermats_PrincipleSince the times along the paths are different, the signals along the different paths will arrive at B with different phases, and to get the total wave amplitude we must add a series of unit 2D vectors...Since the times along the paths are different, the signals along the different paths will arrive at B with different phases, and to get the total wave amplitude we must add a series of unit 2D vectors, one from each path. (Representing the amplitude and phase of the wave by a complex number for convenience -- for a real wave, we can take the real part at the end.)
