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Lensmaker’s Equation Calculator — result sheet
Calculate thin-lens focal length and optical power from refractive indices and the two surface radii.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: 1/f=(lens index/medium index−1)×(1/R₁−1/R₂); optical power=1/f.
The thin-lens form connects surface curvature and refractive-index contrast with focal length under a stated sign convention.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Lens refractive index — minimum 1.0E-6; maximum 1000000
- Surrounding-medium index — minimum 1.0E-6; maximum 1000000
- First surface radius — m; minimum -1000000000; maximum 1000000000
- Second surface radius — m; minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Lens refractive index | 1.5 |
| Surrounding-medium index | 1 |
| First surface radius | 0.1 |
| Second surface radius | -0.1 |
Focal length =0.1 m; optical power =10 D.
Assumptions and limits
- Radii use a consistent Cartesian sign convention and are nonzero where the curvature term requires it.
- The lens is thin, spherical, centered, and surrounded by a uniform medium.
- Thickness, aberrations, dispersion, aperture, coatings, and prescription suitability are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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