Reflective Properties of Ellipses


Introduction

If the interior of ellipse is silvered to produce a mirror, rays originated at ellipse's focus are reflected to the other focus of the ellipse.

Proof

1.
Point P is a point on the ellipse.
L is a tangent line of the ellipse at point P.
Point Q moves on L.
If Q = P , AQ + BQ = minimum.
2.
There are two point A, B, a line L and a moving point Q on L.
When AQ + BQ = minimum at Q = P,
angles made by AP, BP and L are equal to each other.

Applet

  • Press "Beam" button to shoot the beams from the point B.
  • The ellipse reflects the beams to the other focus.
  • Press "+f" or "-f" to change the distance of two forci.