Editing Fermat's principle (section)

=== A ray as an energy path (beam) ===

[[File:Concave lens.jpg|thumb|320px|'''Fig.{{nnbsp}}3''':{{big|&nbsp;}}An experiment demonstrating refraction (and partial reflection) of ''rays'' &ndash; approximated by, or contained in, narrow beams]]

If the corridor of paths reinforcing a ray path from ''A'' to ''B'' is substantially obstructed, this will significantly affect the ''energy''<ref group=Note>More precisely, the [[energy flux density]].</ref> reaching ''B'' from ''A'' &ndash; unlike a similar-sized obstruction outside any such corridor. Thus the ray path marks an ''energy'' path &ndash; as does a beam.

Suppose that a wavefront expanding from point ''A'' passes point ''P'', which lies on a ray path from point ''A'' to point ''B''. By definition, all points on the wavefront have the same propagation time from ''A''. Now let the wavefront be blocked except for a window, centered on ''P'', and small enough to lie within the corridor of paths that reinforce the ray path from ''A'' to ''B''. Then all points on the unobstructed portion of the wavefront will have, nearly enough, equal propagation times to ''B'', but ''not'' to points in other directions, so that ''B'' will be in the direction of peak intensity of the beam admitted through the window.<ref>This is the essence of the argument given by Fresnel ([[#SecMem|1827, tr.&nbsp;Hobson]], {{nowrap|pp.{{tsp}}310–11}}).</ref> So the ray path marks the beam. And in optical experiments, a beam is routinely considered as a collection of rays or (if it is narrow) as an approximation to a ray (Fig.{{nnbsp}}3).<ref>See (e.g.) [[#Opticks|Newton, 1730]], p.{{nnbsp}}55; [[#ToL|Huygens, 1690, tr.&nbsp;Thompson]], pp.{{nnbsp}}40–41,{{tsp}}56.</ref>