Optical Illusions and Parabolic Ghosts

[S2 Maths Topic: Graphs & Quadratic Equations] Optical illusions. They are a rare occurrence in Nature, and sometimes observed over deserts in the form of mirages, or the Brocken spectre when the sun casts your own shadow among moving clouds to name a few.

But with the help of Physics (and Maths), we can recreate a "mirage" [Parabolic Ghost] of an object by placing it carefully between two special, non-Euclidean convex mirrors.

A Do-It-Yourself mirage? How does it work? Professor Burkard Polster works out the mathematics behind the phenomenon so that you can try to make one yourself.

(Hint: Some old flashlight heads have the perfect geometry to replicate the [y = x^2] shape depicted in the video. Look around your house for one!)

The Secrets of Parabolic Ghosts