Radius of curvature (optics)

Radius of curvature (ROC) has specific meaning and sign convention in optical design.

A spherical lens or mirror surface has a center of curvature located either along or decentered from the system local optical axis.

The vertex of the lens surface is located on the local optical axis.

][2] The sign convention for the optical radius of curvature is as follows: Thus when viewing a biconvex lens from the side, the left surface radius of curvature is positive, and the right radius of curvature is negative.

Note however that in areas of optics other than design, other sign conventions are sometimes used.

In particular, many undergraduate physics textbooks use the Gaussian sign convention in which convex surfaces of lenses are always positive.

These surfaces are typically designed such that their profile is described by the equation where the optic axis is presumed to lie in the z direction, and

is the sag—the z-component of the displacement of the surface from the vertex, at distance