How to find the curvature of the radius in a lens

Updated March 23, 2017

A lens' "radius of curvature" is the distance between the centre of the lens and the point in space outside the lens that marks the centre of the curve of the lens' bounding materials. A lens thus has two radii of curvature -- one measuring the distance toward the centre of curvature in front of the lens, and one to the centre of curvature behind it. Rene Descartes developed an equation -- the Lens-Maker's Formula -- relating a lens' two radii of curvature to the focal length and refraction index of the lens.

Obtain the focal length of your lens. This is the distance between the centre of the lens and the point in space at which light rays passing through the lens converge. It is usually marked on the lens in millimetres -- this is what people mean when they talk about, for example, a "400mm lens."

Obtain the refractive index of your lens. This is a measurement of how severely the material the lens is made of bends light. Glass lenses have a refractive index of about 1.52; standard plastic ones, about 1.5. If you have a lens made of a different material or a special plastic, contact the source of the lens for the refraction measurement.

Plug your numbers into the following formula:

1/f = (n - 1) * ((1/Rf) - (1/Rb))

where "f" is the focal length, "n" is the refractive index and "Rf" and "Rb" are the front and back radii of curvature. Keep in mind that, by convention, Rf is positive and Rb is negative -- that's why, in a lens with identical front and back radii, the right half of Decartes' equation does not equal zero.

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About the Author

Theon Weber has been a professional writer and critic since 2006, writing for the Village Voice, the Portland Mercury, and the late Blender Magazine. He was a staff writer at the Web-based Stylus Magazine from 2005 to its closure in 2007.