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
General calculation reads
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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
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M = -d_i/d_o = h_i/h_o. Linear magnification of a lens or mirror.
F_c = m × v² / r. Force required to keep object in circular motion.
n₁ sin θ₁ = n₂ sin θ₂. Refraction angle from indices and incidence.
1/f = 1/d_o + 1/d_i. Solve for any of focal length, object distance, image distance.
c = λ × ν. Wavelength in vacuum from frequency or vice versa. c = 3×10⁸ m/s.