Atoric lens is alens with differentoptical power andfocal length in two orientations perpendicular to each other. One of the lens surfaces is shaped like a "cap" from atorus (see figure at right), and the other one is usuallyspherical. Such a lens behaves like a combination of aspherical lens and acylindrical lens. Toric lenses are used primarily ineyeglasses,contact lenses andintraocular lenses to correctastigmatism.

A torus is the surface of revolution resulting when a circle with radiusr rotates around an axis lying within the same plane as the circle, at a distanceR from the circle's centre (see figure at right). IfR > r, aring torus is produced. IfR = r, ahorn torus is produced, where the opening is contracted into a single point.R < r results in aspindle torus, where only two "dips" remain from the opening; these dips become less deep asR approaches 0. WhenR = 0, the torus degenerates into asphere with radiusr.^{[citation needed]}

The greatestradius of curvature of the toric lens surface,R +r, corresponds to the smallestrefractive power,S, given by

${\displaystyle S=\frac{n-1}{R+r}}$,

wheren is theindex of refraction of the lens material.

The smallest radius of curvature,r, corresponds to the greatest refractive power,s, given by

${\displaystyle s=\frac{n-1}{r}}$.

SinceR +r >r,S <s. The lens behaves approximately like a combination of a spherical lens with optical powers and acylindrical lens with powers −S. Inophthalmology andoptometry,s −S is called thecylinder power of the lens^[a].

Note that both the greatest and the smallest curvature have acircular shape. Consequently, in contrast with a popular assumption, the toric lens isnot anellipsoid of revolution.

Light rays within the (x,y)-plane of the torus (as defined in the figure above) arerefracted according to the greatest radius of curvature,R +r, which means that it has the smallest refractive power,S.

Light rays within a plane through the axis of revolution (thez axis) of the torus are refracted according to the smallest radius of curvature,r, which means that it has the greatest refractive power,s.

As a consequence, there are two different refractive powers at orientations perpendicular to each other. At intermediate orientations, the refractive power changes gradually from the greatest to the smallest value, or reverse. This will compensate for the astigmatic aberration of the eye.

With modern computer-controlled design, grinding and polishing techniques, good vision corrections can be achieved for even wider angles of view by allowing certain deviations from the toric shape. This is called anatoric lens (literally, non-toric lens).^[1][2] They are related to toric lenses in the same way thataspheric lenses are related to spherical lenses.^{[citation needed]}

• Geometrical optics
• Corrective lenses

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