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. The distance from the vertex to the center of curvature is the radius of curvature of the surface.^{[1]}^{[2]}
The sign convention for the optical radius of curvature is as follows:
 If the vertex lies to the left of the center of curvature, the radius of curvature is positive.
 If the vertex lies to the right of the center of curvature, the radius of curvature is negative.
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.^{[3]} Care should be taken when using formulas taken from different sources.
YouTube Encyclopedic

1/3Views:4 21835 76728 042

Radii of curvature for lenses

Radius of Curvature.mp4

Centre, radius of Curvature, Pole and Principal axis of Spherical Mirror  Physics Class X
Transcription
Aspheric surfaces
Optical surfaces with nonspherical profiles, such as the surfaces of aspheric lenses, also have a radius of curvature. 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 zcomponent of the displacement of the surface from the vertex, at distance from the axis. If and are zero, then is the radius of curvature and is the conic constant, as measured at the vertex (where ). The coefficients describe the deviation of the surface from the axially symmetric quadric surface specified by and .^{[2]}
See also
 Radius of curvature (applications)
 Radius
 Base curve radius
 Cardinal point (optics)
 Vergence (optics)
References
 ^ "Radius of curvature of a lens". 20150306.
 ^ ^{a} ^{b} Barbastathis, George; Sheppard, Colin. "Real and Virtual Images" (Adobe Portable Document Format). MIT OpenCourseWare. Massachusetts Institute of Technology. p. 4. Retrieved 8 August 2017.