Concept

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. The distance from the vertex to the center of curvature is the radius of curvature of the surface. 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. Care should be taken when using formulas taken from different sources. Optical surfaces with non-spherical 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 z-component 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 .

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related lectures (5)
Concave Mirrors: Focal Length and Reflection Laws
Explores the focal length of concave mirrors and reflection laws.
Camera Calibration: Basics
Introduces camera calibration basics, including parameters estimation, pinhole model limitations, lens imaging, depth of field, and lens distortions.
Show more
Related publications (5)
Related concepts (6)
Cardinal point (optics)
In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the focal points, the principal points, and the nodal points. For ideal systems, the basic imaging properties such as image size, location, and orientation are completely determined by the locations of the cardinal points; in fact only four points are necessary: the focal points and either the principal or nodal points.
Focal length
The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly.
Dioptre
A dioptre (British spelling) or diopter (American spelling), symbol dpt, is a unit of measurement with dimension of reciprocal length, equivalent to one reciprocal metre, 1 dpt = 1 m−1. It is normally used to express the optical power of a lens or curved mirror, which is a physical quantity equal to the reciprocal of the focal length, expressed in metres. For example, a 3-dioptre lens brings parallel rays of light to focus at metre. A flat window has an optical power of zero dioptres, as it does not cause light to converge or diverge.
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.