Editing Fermat's principle (section)

=== Homogeneous media: rectilinear propagation ===

In a homogeneous medium (also called a ''uniform'' medium), all the secondary wavefronts that expand from a given primary wavefront {{mvar|W}} in a given time {{math|Δ''t''}} are [[congruence (geometry)|congruent]] and similarly oriented, so that their envelope {{mvar|W&prime;}} may be considered as the envelope of a ''single'' secondary wavefront which preserves its orientation while its center (source) moves over {{mvar|W}}. If {{mvar|P}} is its center while {{mvar|P&prime;}} is its point of tangency with {{mvar|W&prime;}}, then {{mvar|P&prime;}} moves parallel to {{mvar|P}}, so that the plane tangential to {{mvar|W&prime;}} at {{mvar|P&prime;}} is parallel to the plane tangential to {{mvar|W}} at {{mvar|P}}. Let another (congruent and similarly orientated) secondary wavefront be centered on {{mvar|P&prime;}}, moving with {{mvar|P}}, and let it meet its envelope {{mvar|W&Prime;}} at point {{mvar|P&Prime;}}. Then, by the same reasoning, the plane tangential to {{mvar|W&Prime;}} at {{mvar|P&Prime;}} is parallel to the other two planes. Hence, due to the congruence and similar orientations, the ray directions {{mvar|PP&prime;}} and {{mvar|P&prime;P&Prime;}} are the same (but not necessarily normal to the wavefronts, since the secondary wavefronts are not necessarily spherical). This construction can be repeated any number of times, giving a straight ray of any length. Thus a homogeneous medium admits rectilinear rays.<ref>[[#deWitte|De Witte, 1959]] (p.{{nnbsp}}295, col.{{nnbsp}}1 and Figure&nbsp;2), states the result and condenses the explanation into one diagram.</ref>