Final answer:
The center of curvature is reflected on itself because a light ray hitting a spherical mirror at this point does so perpendicularly, causing it to reflect back along its original path.
Step-by-step explanation:
The center of curvature is reflected on itself in a spherical mirror because when a ray of light traveling towards the center of curvature strikes the mirror, it hits the surface at a perpendicular angle. This means the angle of incidence is zero, and according to the law of reflection, the angle of reflection will also be zero, causing the light to reflect directly back along its original path. This property is particular to spherical mirrors and is essential to their function in devices like telescopes and headlights, where precise control over the direction of light is necessary.