Thin-lens lensmaker equation
1/f = (n−1)(1/R₁ − 1/R₂)
Signed surface curvatures determine ideal optical power in air.
Lens Focal Length Calculator
Estimate thin-lens focal length for the same spherical lens forms used by the Multi-Stage Lens Ray Simulator.
Access: Free to use, no installation, and No account required.
Inputs
The result uses the simulator’s thin-lens lensmaker estimate. Finite thickness, wavelength dispersion, aspheres, aberrations, aperture, and surrounding media other than air require a fuller optical model.
Results
Lensmaker estimate
For a thin lens in air, optical power depends on refractive index and the signed curvatures of the two surfaces. Positive focal length indicates convergence; negative focal length indicates divergence.
Engineering reference
Lens Focal Length Calculator: background and worked detail
Use the Lens Focal Length Calculator to estimate thin-lens focal length and optical power for the spherical biconvex, biconcave, plano, and meniscus geometries used by the Lens Ray Simulator.
The lensmaker equation
Optical power
Φ = 1/f
When f is expressed in metres, optical power is in diopters.
Engineering theory and interpretation
The thin-lens lensmaker relation connects refractive index with the signed radii of the two refracting surfaces. The sign of optical power determines whether the idealized lens converges or diverges paraxial rays.
The focused model assumes a thin lens in air and uses a compact geometry parameterization. Real optical design can require finite center thickness, wavelength-dependent refractive index, aspheric surfaces, aperture, aberrations, decenter/tilt, and surrounding media.
Symmetric biconvex lens
Choose biconvex, R = 250 mm, refractive index n = 1.517, and no flip.
- The simulator geometry maps the two surfaces to +250 mm and −250 mm radii.
- 1/f = (1.517−1)(1/250 − 1/−250) mm⁻¹.
- The resulting focal length is about +242 mm, corresponding to about +4.14 D.
Result: The positive sign indicates a converging thin lens in the simulator's sign convention.
Thin-lens, paraxial, single-wavelength
Assumptions
- Thin lens in air.
- Spherical surfaces and the simulator's signed-radius convention.
- Refractive index is treated as constant at the wavelength of interest.
Limitations
- Does not include finite thickness, chromatic dispersion, aberrations, aspheres, aperture diffraction, decenter/tilt, or non-air surrounding media.
- The simple geometry parameter does not replace an optical prescription with independently specified surfaces.
Lens Focal Length Calculator FAQ
What does a negative focal length mean?
In this sign convention, negative focal length indicates a diverging lens.
Why does refractive index affect focal length?
A larger refractive-index contrast bends rays more strongly at the same surface curvature, increasing optical power and reducing focal-length magnitude.
Is this accurate for thick camera lenses?
Not by itself. Multi-element photographic optics require surface-by-surface ray tracing with thickness, spacing, glass dispersion, aperture, and aberration analysis.
Validation checks
Index near unity
Case: Move refractive index toward 1 while keeping curvature fixed.
Expected: Optical power should approach zero and focal length magnitude should grow very large.
Curvature scaling
Case: Double both signed radius magnitudes for the same lens form and index.
Expected: Focal length magnitude should approximately double in the thin-lens model.
Where this calculation comes from
Shared with the Geometrical Optics Workbench, which traces rays surface by surface.
Open the source workbench →Read calculation and source methodology →