I just create a simulation for you according to your description. However, I think you did not think carefully about your problem. Because you have too many possibility: light in all direction?(infinity), mirrors of any length at any point.

The following is what I have created.

VIEW or DOWNLOAD ejs xml source
then click to translate strings for selected locale.

Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.

You can use mouse drag and drop to create mirrors (maximum number=36).The first mouse click will be the starting point for the mirror, drag your mouse and drop it at the place you want.
You can place mirror at any different locations.
(You can drag both end points to change the mirrors later.)

And you can change number of rays (uniform distribution in 360 degree).
I also add an option for light to be bounded at the boundary.
I will leave the rest of work to you! Enjoy it.