Optical (Reflective) Property of an Ellipse

This video is a part of the Ellipse playlist:    • Ellipse  

See more about ellipse: https://math-stuff.com/pages/standard...

In this video, we show what the optical (or reflective) property of an ellipse is. We also show some corollaries of that property, not only for light waves but for sound waves as well. To prove that a ray of light starting at one focus of an ellipse, after reflecting off of the ellipse, goes through the other focus, we use (a modified version of) the law of reflection.

Timestamps:

00:00 - What Optical or Reflective Property of an Ellipse Is
00:22 - Some Corollaries of Optical (Reflective) Property
01:21 - Optical (Reflective) Property Applied to Sound
01:43 - The Law of Reflection
02:27 - The Law of Reflection for Curved Surfaces
02:11 - Applying the Law of Reflection to the Ellipse
03:22 - Using the Definition of an Ellipse
04:23 - A Neat “Trick”
05:15 - Finishing the Proof

Software used for animations: Manim CE