The coffee cup caustic

Exhibit: table of content

Mathematics Math21a, Spring 2006
Multivariable Calculus
Oliver Knill, SciCtr 434,

The coffeecup caustic

Next time you drink coffee, look from above into the cofee mug. You might see a crescent of light on the surface of the drink. Typically, this bright part will form a curve with a cusp.

Light does not need to reflect first to form a caustic. If you have a light or sound wave front and light propagates perpendicular to a surface. For each point on the surface, there will be an instance, where the light ray will focus with neighboring rays.This place is called the caustic. In the animation to the left, you see this. One can compute the caustic by drawing at every point of the curve a line perpendicular to the curve and chose the point on that line with distance 1/kappa(t) from the original front. You see the cusp also in the coffecup caustic. It is stable. If you change the shape of the initial wave front a bit, then the cusp will still be there.

Here is an applet. Click into the red area to clear the screen. Click into the yellow area to shoot a light ray from there. The applet is by Roy Williams Clickery.

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Oliver Knill, Math21a, Multivariable Calculus, Spring 2006, Department of Mathematics, Faculty of Art and Sciences, Harvard University