What does the radius of curvature refer to in optics?

The radius of curvature in optics is defined as the distance from the vertex of a spherical mirror (or lens) to its center of curvature. The center of curvature is the point at the center of the sphere from which the mirror or lens is a part. In practical terms, this means that if you were to extend the surface of a spherical mirror or lens into a full sphere, the radius of curvature would be the radius of that sphere. This distance plays a critical role in determining how light rays reflect off or refract through the lens or mirror, influencing the focus and magnification of images produced.

Understanding the radius of curvature is key for the application of the mirror and lens equations, which help in predicting the behavior of light as it interacts with curved surfaces. It is especially relevant when designing optical instruments and understanding the principles of image formation.