Reflections Inside an Ellipse
- Author:
- Clint Givens
- Topic:
- Conic Sections, Ellipse, Hyperbola
In the GeoGebra applet below, you can drag the points A, B, and C to reposition the ellipse, and you can drag D and E on the circumference of the ellipse. The other segments drawn inside the ellipse are the path of a light ray which starts at D, travels to E, and then is reflected a large number of times by the interior of the ellipse.
You will notice right away that the space filled up by the light ray's path, also known as its orbit, takes the shape of a hyperbola. As you move points D and E around, you will find that you can also arrange it to take the shape of a different ellipse situated inside the original ellipse. These shapes--the hyperbola or ellipse traced out by the light ray's orbit--are called envelopes.