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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.
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
Each optical element (surface, interface, mirror, or beam travel) is described by a 2 × 2 ray transfer matrix which operates on a vector describing an incoming light ray to calculate the outgoing ray. Multiplication of the successive matrices thus yields a concise ray transfer matrix describing the entire optical system.
Convex mirror lets motorists see around a corner. Detail of the convex mirror in the Arnolfini Portrait. The passenger-side mirror on a car is typically a convex mirror. In some countries, these are labeled with the safety warning "Objects in mirror are closer than they appear", to warn the driver of the convex mirror's distorting effects on distance perception.
The Houghton telescope or Lurie–Houghton telescope is a design that uses a wide compound positive-negative lens over the entire front aperture to correct spherical aberration of the main mirror. If desired, the two corrector elements can be made with the same type of glass, since the Houghton corrector's chromatic aberration is minimal.
where R is the radius of curvature of the optical surface. The sag S ( r ) is the displacement along the optic axis of the surface from the vertex, at distance r {\displaystyle r} from the axis. A good explanation of both this approximate formula and the exact formula can be found here .
Types of two-mirror optical cavities, with mirrors of various curvatures, showing the radiation pattern inside each cavity. Light confined in a resonator will reflect multiple times from the mirrors, and due to the effects of interference, only certain patterns and frequencies of radiation will be sustained by the resonator, with the others being suppressed by destructive interference.
From top: Parabolic mirror showing Foucault shadow patterns made by knife edge inside radius of curvature R (red X), at R and outside R. Foucault testing is commonly used by amateur telescope makers for figuring primary mirrors in reflecting telescopes. [5] [6] The mirror to be tested is placed vertically in a stand. The Foucault tester is set ...