Question 14
A beam of light strikes $\overline{BC}$ at point $C$ with angle of incidence $\alpha=19.94^\circ$ and reflects with an equal angle of reflection as shown. The light beam continues its path, reflecting off line segments $\overline{AB}$ and $\overline{BC}$ according to the rule: angle of incidence equals angle of reflection. Given that $\beta=\frac{\alpha}{10}=1.994^\circ$ and $AB=BC,$ determine the number of times the light beam will bounce off the two line segments. Include the first reflection at $C$ in your count.
