Coffee Cup Caustic

The light source is at C. Rays are reflected in the circle. Observe what happens as you drag C inside the circle.

The phantom curve made up by the reflected rays is mathematically the envelope of the family of lines. This curve is called the circle caustic. It is sometimes referred to as the coffee-cup caustic as it can be seen reflected in the surface of a cup of coffee.

When C lies on the circumference of the circle, the curve is a cardioid, from Greek καρδίᾱ [kardiā]. If C is at infinity, then the curve is a nephroid, from Greek νεφρός [nephros]. From heart to kidney...