By Zencalcy Editorial TeamLast reviewed About us
For a spherical mirror the focal point sits halfway between the pole and the centre of curvature, so the focal length is half the radius. A shallow, large-radius mirror has a long focal length and a gentle curve.
Focal length from the radius of curvature.
f = R / 2
f is the focal length and R the radius of curvature. The relation is exact only in the paraxial approximation, for rays close to the axis.
| Symbol | Meaning |
|---|---|
| f | Focal length of the mirror. |
| R | Radius of curvature of the mirror surface. |
A concave mirror with a 0.4 m radius has a focal length of 0.2 m. Its focal point lies 0.2 m in front of the mirror, halfway to the centre of curvature.
Continue with the Numerical Aperture Calculator, Optical Path Length Calculator, or the Prism Deviation Calculator — or browse more optics and light tools and all physics calculators.
A ray parallel to the axis hits the surface and reflects as if from the centre of curvature. Geometry puts the crossing point midway between the pole and that centre for small angles.
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