Lens Maker Equation Calculator
Ideal thin lens maker1/f=(nrel−1)(1/R1−1/R2), actual signed optical convention, infinite/zero cases refused. No thick lens/dispersion. Actual independently established compatible SI units/model context; conditional arithmetic, not code compliance, engineering design or safe operation approval.
Description
The thin-lens maker relation depends on relative refractive index and signed surface radii.
The thin-lens maker relation depends on relative refractive index and signed surface radii.1
This tool calculates finite focal length under that convention without modeling thickness or dispersion.
When to use Lens Maker Equation Calculator
Use this tool to calculate finite focal length under that convention without modeling thickness or dispersion.
How to use Lens Maker Equation Calculator and how it works
- Prepare relativeIndex, firstSignedRadiusMeters, secondSignedRadiusMeters, with the units, conventions and assumptions below.
- Enter the required fields and run Lens Maker Equation Calculator.
- Read result.value using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| relativeIndex | Relative Index. Use the units and matching context stated in the calculation below. | number | Required; strictly positive; finite; other constraints below |
| firstSignedRadiusMeters | First Signed Radius Meters. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
| secondSignedRadiusMeters | Second Signed Radius Meters. Use the units and matching context stated in the calculation below. | number | Required; finite; other constraints below |
Supply positive relative refractive index different from one and finite nonzero distinct curvature radii under a consistent signed-radius convention. Return the reciprocal of (index-1)*(1/R1-1/R2), in the radii's length unit. This is the thin-lens expression, without a thickness correction.
focalLength=1/((relativeIndex-1)*(1/R1-1/R2)) Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Signed thin-lens focal length in meters. | number |
{
"input": {
"relativeIndex": 2,
"firstSignedRadiusMeters": 2,
"secondSignedRadiusMeters": -2
},
"output": {
"result": {
"value": 1
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Keystone Correction Angle Calculator for a complementary operation: A projected trapezoid's side angle can be calculated from its measured top and bottom widths and height.
Use Optical Magnification Calculator for a complementary operation: Thin-lens transverse magnification has a signed distance-ratio convention.
References
-
Lens Maker Equation Calculator — tool.io
Similar or alternative tools
- Keystone Correction Angle Calculator
A projected trapezoid's side angle can be calculated from its measured top and bottom widths and height.
- Optical Magnification Calculator
Thin-lens transverse magnification has a signed distance-ratio convention.