When a light ray passes through the center of curvature (C) of a spherical mirror, it strikes the mirror along the normal (perpendicular) to the surface at that point. According to the law of reflection, the angle of incidence is equal to the angle of reflection. Since the incident ray is along the normal, the angle of incidence is 0°. Therefore, the reflected ray must also have a 0° angle of reflection, meaning it retraces the exact same path back through the center of curvature.

Final answer: retrace its path.