The bottom of a teacup

Once you know what to look for you start seeing singularities everywhere. For instance you'll often find some lurking in the bottom of a tea-cup. Take a clean shiny tea-cup, and pear into the bottom of it. If your lucky you'll see a pattern something like this.

This pattern's caused by the light reflecting from the sides of the cup. At some points on the bottom there are more reflected rays than at other points. If we draw some of the rays things become a little clearer.

Here the blue lines are light rays coming from a point source a little distance away. The red lines are the reflected rays. Note how you can see a cusp shape formed by these red lines.

The mathematics of what is happening here is explained in more detail in the page on Caustics.