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Concept
Toric lens
Summary
A toric lens is a lens with different optical power and focal length in two orientations perpendicular to each other. One of the lens surfaces is shaped like a "cap" from a torus (see figure at right), and the other one is usually spherical. Such a lens behaves like a combination of a spherical lens and a cylindrical lens. Toric lenses are used primarily in eyeglasses, contact lenses and intraocular lenses to correct astigmatism.
Torus
A torus is the surface of revolution resulting when a circle with radius r rotates around an axis lying within the same plane as the circle, at a distance R from the circle's centre (see figure at right). If R > r, a ring torus is produced. If R = r, a horn torus is produced, where the opening is contracted into a single point. R < r results in a spindle torus, where only two "dips" remain from the opening; these dips become less deep as R approaches 0. When R = 0, the torus degenerates into a sphere with radius r.
The greatest radius of curvature of the toric lens surface, R + r, corresponds to the smallest refractive power, S, given by
where n is the index of refraction of the lens material.
The smallest radius of curvature, r, corresponds to the greatest refractive power, s, given by
Since R + r > r, S < s. The lens behaves approximately like a combination of a spherical lens with optical power s and a cylindrical lens with power s − S. In ophthalmology and optometry, s − S is called the cylinder power of the lens.
Note that both the greatest and the smallest curvature have a circular shape. Consequently, in contrast with a popular assumption, the toric lens is not an ellipsoid of revolution.
Light rays within the (x,y)-plane of the torus (as defined in the figure above) are refracted 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 (the z axis) of the torus are refracted according to the smallest radius of curvature, r, which means that it has the greatest refractive power, s.
Official source
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