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Radius of curvature sign convention for optical design. 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.
A concave mirror diagram showing the focus, focal length, centre of curvature, principal axis, etc. A concave mirror, or converging mirror, has a reflecting surface that is recessed inward (away from the incident light). Concave mirrors reflect light inward to one focal point. They are used to focus light. Unlike convex mirrors, concave mirrors ...
For a spherically-curved mirror in air, the magnitude of the focal length is equal to the radius of curvature of the mirror divided by two. The focal length is negative for a concave mirror, and positive for a convex mirror. In the sign convention used in optical design, a concave mirror has negative radius of curvature, so
[5] [6] The mirror to be tested is placed vertically in a stand. The Foucault tester is set up at the distance of the mirror's radius of curvature (radius R is twice the focal length.) with the pinhole to one side of the centre of curvature (a short vertical slit parallel to the knife edge can be used instead of the pinhole).
= / effective radius of curvature in the sagittal plane (vertical direction) R = radius of curvature, R > 0 for concave, valid in the paraxial approximation θ is the mirror angle of incidence in the horizontal plane.
Radius of curvature and center of curvature. In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or ...
A concave mirror with light rays Center of curvature. In geometry, the center of curvature of a curve is a point located at a distance from the curve equal to the radius of curvature lying on the curve normal vector. It is the point at infinity if the curvature is zero. The osculating circle to the curve is centered at the centre of curvature.
A concave-convex cavity has one convex mirror with a negative radius of curvature. This design produces no intracavity focus of the beam, and is thus useful in very high-power lasers where the intensity of the light might be damaging to the intracavity medium if brought to a focus.