The mirrors do not touch.  I would like to be able to draw mirrors of various size at any place around the light.

Think of it this way...  There is a light in the middle of a room emitting light in all directions.  We want to place flat mirrors of any length at any point around the light.  Ideally, we want to use the mirrors to reflect the light back onto itself so that it does not escape into infinity.  The mirrors should be able to reflect on both sides. 

It's similar to the Multiple Reflection from two plane mirrors applet except we do not want the mirrors to touch and we want to be able to put any size mirror in ourselves in any location around the light source.  We would like to be able to place as many mirrors as possible. 

I hope this helps!