2. Two plane mirrors serve as the faces of a dihedral angle. A light ray, perpendicular to the edge of the angle and parallel to the first mirror, is reflected from the second mirror, then from the first, then again from the second, again from the first, and finally, reflecting for the fifth time from the second mirror, returns along the same straight line. What is the magnitude of the dihedral angle between the mirrors?

(Remember, according to the laws of reflection, the incident and reflected rays lie in a plane perpendicular to the mirror plane and form equal angles with the mirror plane.)
2. Since the light ray falls perpendicular to the edge of the dihedral angle, all reflections occur in one plane perpendicular to the edge (Fig. 81). Since after the third reflection the ray returns along the same path, at this reflection it must be directed perpendicular to the mirror plane. The exterior angle of the isosceles triangle $A_{1} A_{2} O$ is $2 \alpha$ ( $\alpha$ is the given angle). Therefore, in the right triangle $A_{2} A_{3} O$, one angle is $\alpha$, the other is $2 \alpha$. Thus, $3 \alpha=90^{\circ} ; \alpha=30^{\circ}$.