Radius of curvature (ROC) has specific meaning and sign convention in optical design. A spherical

lens A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements'') ...

mirror A mirror, also known as a looking glass, is an object that Reflection (physics), reflects an image. Light that bounces off a mirror forms an image of whatever is in front of it, which is then focused through the lens of the eye or a camera ...

surface has a center of curvature located either along or decentered from the system local

optical axis An optical axis is an imaginary line that passes through the geometrical center of an optical system such as a camera lens, microscope or telescopic sight. Lens elements often have rotational symmetry about the axis. The optical axis defines ...

. 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 Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

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.

Aspheric surfaces

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 :

z(r)=\frac+\alpha_1 r^2+\alpha_2 r^4+\alpha_3 r^6+\cdots ,

where the optic axis is presumed to lie in the z direction, and

z(r)

is the ''sag''—the z-component of the

displacement Displacement may refer to: Physical sciences Mathematics and physics *Displacement (geometry), is the difference between the final and initial position of a point trajectory (for instance, the center of mass of a moving object). The actual path ...

of the surface from the vertex, at distance

r

from the axis. If

\alpha_1

and

\alpha_2

are zero, then

R

is the ''radius of curvature'' and

K

is the conic constant, as measured at the vertex (where

r=0

). The coefficients

\alpha_i

describe the deviation of the surface from the axially symmetric

quadric surface In mathematics, a quadric or quadric surface is a generalization of conic sections (ellipses, parabolas, and hyperbolas). In three-dimensional space, quadrics include ellipsoids, paraboloids, and hyperboloids. More generally, a quadric hyper ...

specified by

R

and

K

References

{{DEFAULTSORT:Radius Of Curvature (Optics) Geometrical optics Physical optics Optical quantities Radii

Aspheric surfaces

See also

References