A Double Parabola with Retroreflection Properties

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.