By Zencalcy Editorial TeamLast reviewed About us
The lens maker's equation predicts a lens's focal length from the refractive index of its glass and the radii of its two surfaces. It lets an optical designer choose curvatures before grinding any glass.
Focal length from lens curvature and refractive index.
1/f = (n − 1)(1/R₁ − 1/R₂)
R₁ and R₂ are the radii of the first and second surfaces, positive when the centre of curvature lies on the outgoing side. R₂ is negative for the back surface of a biconvex lens.
| Symbol | Meaning |
|---|---|
| f | Focal length of the lens. |
| n | Refractive index of the lens material. |
| R₁, R₂ | Radii of the two lens surfaces, with signs. |
1/f = 0.5 × (10 + 10) = 10 m⁻¹, so f = 0.1 m. This symmetric biconvex lens has a focal length equal to its radius of curvature here.
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The sign tracks which side the centre of curvature lies on. For the back surface of a biconvex lens the centre lies in front of the surface, so R₂ is negative.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026