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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.
The sign of the weight of a tensor density, such as the weight of the determinant of the covariant metric tensor. The active and passive sign convention of current, voltage and power in electrical engineering. A sign convention used for curved mirrors assigns a positive focal length to concave mirrors and a negative focal length to convex mirrors.
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 show different image types depending on the distance between the object and the mirror.
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 positive for a concave mirror, and negative for a convex mirror. In the sign convention used in optical design, a concave mirror has negative radius of curvature, so
For optics like convex lenses, the converging point of the light exiting the lens is on the input side of the focal plane, and is positive in optical power. For concave lenses, the focal point is on the back side of the lens, or the output side of the focal plane, and is negative in power.
The signs are reversed for the back surface of the lens: R 2 is positive if the surface is concave, and negative if it is convex. This is an arbitrary sign convention; some authors choose different signs for the radii, which changes the equation for the focal length. For a thin lens, d is much smaller than one of the radii of curvature (either ...
The cardinal points were all included in a single diagram as early as 1864 (Donders), with the object in air and the image in a different medium. Cardinal point diagram for an optical system with different media on each side. F for Focal point, P for Principal point, NP for Nodal Point, and efl for effective focal length. The chief ray is shown ...
A convex secondary mirror is placed just to the side of the light entering the telescope, and positioned afocally so as to send parallel light on to the tertiary. The concave tertiary mirror is positioned exactly twice as far to the side of the entering beam as was the convex secondary, and its own radius of curvature distant from the secondary.