Ellipse: Reflective Property and Distance

Topic:
Ellipse
Each ray starting from will travel, hit the ellipse at some point and reflect to . The distance traveled equals the sum of the distance from to and from to , in other words: . By the definition of an ellipse, we have that this quantity is a constant for all points on the ellipse, no matter which path the ray takes. This means the 12 rays pointing in different directions will all travel the same distance by the time they reach . If they are moving at the same speed, they will arrive simultaneously. Animate the diagram to see this happen.