WOLFRAM|DEMONSTRATIONS PROJECT

A Double Parabola with Retroreflection Properties

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number of rays n
10
entry angle φ
-45
focal length p
1
p=1
This Demonstration shows the reflective behavior of a two-dimensional shape formed by similar arcs of two parabolas. An interesting and unexpected reflective behavior arises when this shape takes a specific configuration, with two parabolas of unit focal length. In this particular configuration it is found that, except for the rays with absolute value of the entry angle
ϕ
less than
ϕ
0
=arctan
2
4≈19.47°
, a ray emerges from the cavity with a trajectory that is nearly opposite to its entry trajectory. This characterizes a cavity with retroreflective behavior. Even in the case of trajectories with entry angle
ϕ
below
ϕ
0
(shown as dashed trajectories), the exit direction does not appear to vary greatly from the entry direction.