# fundamental paraxial equation

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## paraxial equation, fundamental

Equation based on gaussian theory and dealing with refraction at a spherical surface:
where n and n′ are the refractive indices of the media on each side of the spherical surface, r is the radius of curvature of the surface and l and l′ the distances of the object and the image from the surface, respectively. n/l and n′ /l′ are the vergences (or reduced vergences) of the incident and refracted light rays respectively. L′ − L corresponds to the change produced by the surface in the vergence of the light and is called the focal power (or vergence power, or refractive power) F of the surface. Thus
L′ − L = F
Focal power is usually expressed in dioptres and can be either positive or negative.At a reflecting surface or a mirror the equation becomes
L′ − L = 2/r
where r is the radius of curvature of the surface or mirror. Syn. general refraction formula. See image distance; object distance; sign convention; gaussian theory; vergence.
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