I created a test blend to verify the concept. You can find it here:
There is a 'laser emitter' which has a simple particle system enabled, along with three 'mirrors' with very simple collision enabled. Also, the scene has had gravity disabled.
Once you open the blend, immediately look at the particles property page on the right side. Look for and click the 'Bake' button. Then go to the Timeline at the bottom and click the play button.
You should see a flow of 'photons' being emitted from the 'laser', bouncing off the mirrors.
Adjust the mirrors to your liking. Make copies of the mirrors to add more.
After any adjustment of the mirrors, click the 'Free Bake' button. It will free the computed particles and the button will revert to the 'Bake' button once again. Click the 'Bake' button to 'apply' the new mirror configuration, then play to watch the new laser beam path through your mirrors.
Hope this helps.