Just remember that whatever you use, the brighter it is, the better it will work.
A half silvered mirror (beamsplitter) that has a 50/50 coating on it (without accounting for absorption and using a theoretical "perfect" mirror) is going to let:
50% through on the first "ring"
25% on the second
12.5% on the third
6.25% on the fourth
3.125% on the fifth
and so on.......
In reality, it will be less. How much less depends on the quality of coatings used.
I'm thinking that PJ's idea of mounting superbright (10,000mcd) white LEDs through from the back of the mirror would be an interesting thing to try. When you look at those things straight on, you see green spots for about 15 minutes afterward

Oh, and you'll want to use a first-surface mirror and make sure the reflective coating on the beam-splitter is facing inside.
RandyT