radius of curvature

Meaning: R is the distance from a curved surface to its center of curvature, C, the center of the sphere the surface was cut from. A more strongly curved surface has a smaller R. A flat mirror has R approaching infinity, so it does not focus light. For a spherical mirror, rays close to the axis focus halfway between the mirror and C, so the focal point lies at R/2. This is a physics (optics) idea rather than an organic chemistry one.

Equation: f = R/2, and 1/o + 1/i = 1/f = 2/R. Here f is the focal length (m), R is the radius of curvature (m), o is the object distance (m), and i is the image distance (m).

On the MCAT: A passage gives R for a concave or convex mirror. You find f, then use the mirror equation to place the image and judge whether it is real or virtual, upright or inverted. Sign convention: a concave mirror has positive f and R, and a convex mirror has negative f and R. An object placed at C (o = R) gives an image at C that is real, inverted and the same size.

Common confusion: Students treat R as the focal length. The focal point is at R/2, not at R. This relation holds for a spherical mirror with rays near the axis. For a lens, f is not simply R/2, because it also depends on the refractive index.