I'm very interested in topics that are math and optics related. There
are two main topics that I'm very interested in so far: Caustics and
Multiple Reflections.

Topics in Caustics: 

1. Rainbow
2. Circles of Light
3. Gravitational Lensing
4. Patterns on the bottom of the swimming pool
5. Patterns from in wine glasses

Topics in Multiple Reflections:
1. Reflections between two mirrors

Here are some sites that you might want to look at:

Circle of Light
http://www.taracanada.com/CircleofLight.html

Multiple Reflections
http://www.hands-on-optics.org/docs/reflections.pdf