Points A, B, and C lie in the plane such that A B=13, B C=14, and C A=15. A peculiar laser is fired from A perpendicular to \overline{B C}. After bouncing off B C, it travels in a direction perpendicular to C A. When it hits C A, it travels in a direction perpendicular to A B, and after hitting A B its new direction is perpendicular to B C again. If this process is continued indefinitely, the laser path will eventually approach some finite polygonal shape T_{\infty}. What is the ratio of the perimeter of T_{\infty} to the perimeter of \triangle A B C?