Focal Length from Radius (f = R/2)
For spherical mirror: f = R/2. For thin lens: 1/f = (n−1)(1/R₁ − 1/R₂) (lensmaker).
Result
Mirror focal length
15.0000 cm
R / 2 = 30 / 2 = 15.0000 cm.
- R30 cm
- f = R/215.0000 cm
- TypeConcave (converging)
Step-by-step
- Spherical mirror: f = R/2 = 30/2 = 15.0000 cm.
How to use this calculator
- Pick mirror or lens.
- Enter R (mirror) or R₁, R₂, n (lens).
- Read focal length.
About this calculator
For a spherical mirror, focal length is exactly half the radius of curvature: f = R/2. For a thin lens, the lensmaker's equation links f to lens material (n) and surface curvatures: 1/f = (n−1)(1/R₁ − 1/R₂). Sign convention: R positive if center of curvature is on the outgoing side. Biconvex lens: R₁ > 0, R₂ < 0 (both faces convex). Concave: opposite.
Frequently asked
Geometric optics: parallel rays converge halfway between mirror and center of curvature. Derives from small-angle approximation.
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