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
Loading calculator…
—
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
Why f = R/2 for mirrors?+
Geometric optics: parallel rays converge halfway between mirror and center of curvature. Derives from small-angle approximation.
Camera lens 50mm?+
Focal length of the lens system in millimeters. Determines field of view + magnification on a given sensor.
Eye focal length?+
Adjustable! Cornea + lens system: ~17 mm. Lens flexes to focus near and far.
Plano-convex lens?+
One flat face (R = ∞). f = R/(n−1) where R is the curved face's radius. Common in flashlights, basic optics.
Telescope diameter vs. focal length?+
Diameter = light gathering. Focal length × eyepiece = magnification. Different things; both matter.
Related calculators
Thin Lens Equation Calculator
1/f = 1/d_o + 1/d_i. Solve for any of focal length, object distance, image distance.
Mirror Equation Calculator
1/f = 1/d_o + 1/d_i. Same form as lens but with mirror sign conventions.
Magnification Calculator
M = -d_i/d_o = h_i/h_o. Linear magnification of a lens or mirror.
Snell's Law Calculator
n₁ sin θ₁ = n₂ sin θ₂. Refraction angle from indices and incidence.
Wavelength ↔ Frequency Calculator
c = λ × ν. Wavelength in vacuum from frequency or vice versa. c = 3×10⁸ m/s.
Centripetal Force Calculator
F_c = m × v² / r. Force required to keep object in circular motion.