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This animation demonstrates the reflection property of parabolae. (See notes below.)
A planar light wave entering a reflector formed by rotating a parabola about its axis is reflected by the parabola to its focus. Because every photon travels exactly the same distance (see The Dandelin construction; focus-directrix definition of a parabola and Focus-directrix definition of parabola), they all arrive at the focus simultaneously. If you watch carefully, you can follow the tracks of individual photons in this animation.
This animation shows a central cross-section (that is, a cross-section that contains the axis of the paraboloid) of a parabolic mirror.