Calculator
Example data table
Sample inputs and results are shown for quick reference.
| Case | Model | nm | nlens | R1 (mm) | R2 (mm) | d (mm) | f (approx, mm) | P (approx, D) |
|---|---|---|---|---|---|---|---|---|
| 1 | Thin | 1.000 | 1.500 | 50 | -50 | — | 50 | 20.0 |
| 2 | Thick | 1.000 | 1.600 | 60 | -60 | 5 | ~50 | ~20 |
| 3 | Thin (in water) | 1.333 | 1.500 | 80 | -80 | — | Longer | Lower |
Formula used
This tool uses the lens maker equation with a medium correction via the relative refractive index nrel = nlens / nm.
Radii and thickness must share the same length unit. The calculator converts them internally to meters, then reports focal length in your chosen unit and meters.
How to use this calculator
- Select your length unit for radii and thickness.
- Choose thin or thick lens model based on your design.
- Enter medium index and lens refractive index values.
- Enter R1 and R2 using a consistent sign convention.
- Use plano checkboxes if a surface is flat.
- If solving, enter a target focal length value.
- Click Calculate to view results above the form.
- Use Download buttons to export CSV or PDF.
Focal length and power in practice
The calculator reports focal length f and optical power P in diopters, where P = 1/f(m). A 50 mm focal length equals 0.05 m, giving P = 20 D. Positive f indicates a converging design; negative f indicates a diverging design.
Curvature inputs and sign convention
Lens power depends on surface curvatures 1/R1 and 1/R2. With the sign convention used here, a biconvex lens commonly uses R1 positive and R2 negative. Marking a surface as plano sets curvature to zero, which reduces power and increases |f|.
Refractive index and relative index
The medium matters. The tool uses the relative index nrel = nlens / nm. In air (nm≈1.000) a glass lens with nlens=1.50 has nrel=1.50. In water (nm≈1.333) the same glass gives nrel≈1.125, so the lens becomes noticeably weaker.
Thin versus thick lens modeling
The thin model ignores center thickness d and is ideal for lenses where d is small compared with radii. The thick model adds a correction term involving d, R1, and R2. For typical small lenses (d≈5 mm), the correction is modest but measurable when curvatures are steep.
Solving for refractive index
If you know the desired focal length and the two radii, choose “solve n”. The solver searches for the lens index that matches your target in the selected medium. This is useful when comparing common materials: plastics near 1.49–1.59 and crown glasses near 1.50–1.53.
Solving for one radius
In thin mode, you can solve for R1 or R2 when the other radius, indices, and target f are known. This helps quick design iteration: keep one surface fixed for manufacturing, then compute the matching curvature for the second surface to hit a focal length requirement.
Quality checks before exporting
Always sanity-check units and magnitudes. Radii near the focal length typically produce moderate powers, while very small radii create high diopters. If results seem extreme, verify sign choices, ensure R is not zero, and confirm whether a surface should be plano. For thick lenses, keep thickness and radii units consistent throughout calculations always.
Why does the calculator ask for medium index?
Lens power depends on the relative index nrel = nlens / nm. A higher-index medium, like water, reduces nrel and makes the same lens weaker, increasing the focal length magnitude.
What does marking a surface as plano do?
Plano means the radius is infinite, so curvature 1/R is zero. This removes that surface’s contribution to power and usually increases focal length compared with a similarly curved surface.
Can I use centimeters or millimeters safely?
Yes. Pick one unit and use it for R1, R2, thickness, and target focal length. The tool converts internally to meters and reports results back in your chosen unit.
Why is my focal length negative?
Negative focal length occurs when the net curvature term produces negative power, typical for diverging lenses. Also check radius signs; swapping sign convention can flip the focal length sign.
When should I choose thick lens mode?
Use thick mode when thickness is not negligible compared with radii or when you need a closer estimate for steep curvatures. The thickness correction can slightly shift focal length and power.
Why can radius solving only work in thin mode?
The thin equation is linear in 1/R, so solving for one radius is direct. The thick equation couples radii and thickness in a nonlinear way, so a simple closed-form radius solution is avoided here.