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Lensmaker's Equation Calculator

Find a thin lens's focal length and optical power from the refractive index and radii of curvature of its two surfaces, 1/f = (n-1)(1/R1 - 1/R2).

Focal length
20 cm
Optical power
5 diopters
Lens type
Converging (convex)

How it works

The lensmaker's equation gives a thin lens's focal length from its material and shape alone: 1/f = (n−1)×(1/R1 − 1/R2), where n is the lens material's refractive index and R1/R2 are the radii of curvature of the surface light reaches first and second. This is the same relationship this site's existing Thin Lens Equation calculator takes as a given (f) — this one derives that f from the physical lens itself.

Radii follow the standard sign convention: positive when that surface's center of curvature sits on the far (outgoing-light) side of the lens, negative when it sits on the near (incoming-light) side, and 0 for a flat surface (an infinite radius, whose 1/R term is exactly zero). A symmetric biconvex lens (R1 positive, R2 the same magnitude but negative) with n=1.5 and R=20cm, the calculator's defaults, works out to f=20cm exactly — a standard textbook check.

Optical power in diopters (1/f with f measured in meters) is reported alongside the focal length, since diopters are the fixed real-world unit optometrists and lens datasheets actually publish, independent of whichever length unit the radii were entered in.

FAQ

What does it mean if the two surfaces give zero net power?

If (n−1)×(1/R1 − 1/R2) works out to exactly zero — for example, two flat surfaces, or two surfaces with the same radius and sign — the lens has no focusing power at all; light passes through undeviated, the same as a flat pane of glass. There's no finite focal length to report in that case.

Does this account for the lens's thickness?

No — this is the thin-lens form of the equation, which assumes the lens is thin enough that light's path length through the glass itself is negligible compared to the radii of curvature. A thick lens needs an extra correction term involving the center thickness and n, which real camera and microscope lenses account for but which this calculator, like most everyday lens calculations, omits.

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