Source: https://guthlabs.ai/docs/instruments/thin-lens-equation-calculator/mechanism/

instrument mechanism / verified-clean

# Thin Lens Equation Calculator mechanism

The inspectable method record for Thin Lens Equation Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The thin-lens equations and honest-label claim are appropriate, but the instrument needs an explicit sign convention, unit policy, input constraints, singularity behavior, and classification rules before it can receive PASS.

- The formulas are standard only under an explicitly stated sign convention: f>0 for converging lenses, f<0 for diverging lenses, do>0 for a real object, and di>0 for a real image.

- The formulas do not specify the classification rules that convert the sign of di and m into real/virtual and upright/inverted outputs.

- The specification does not define behavior at the focal-plane boundary do=f, where the image is at infinity and finite di and m do not exist.

## Units and conventions

- f and do must use the same length unit before substitution; di is returned in that same unit.

- This review assumes the real-is-positive convention: converging f>0, diverging f<0, real object do>0, real image di>0.

- Under this convention, di>0 means real and di<0 means virtual; m<0 means inverted and m>0 means upright.

- The thin-lens and paraxial approximations apply, so object and image distances are measured from the lens's principal plane.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "f": 50,
    "do": 300,
    "unit": "mm"
  },
  "expected_outputs": {
    "di": 60,
    "m": -0.2,
    "image_type": "real",
    "orientation": "inverted"
  },
  "working": "1/di = 1/f - 1/do = 1/50 - 1/300 = 6/300 - 1/300 = 5/300 = 1/60. Therefore di = 60 mm. m = -di/do = -60/300 = -0.2. Since di>0, the image is real. Since m<0, it is inverted."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The singular inputs do = f and do = 0 require explicit rejection or infinity handling, and the signed-distance convention is unspecified. Without validation and a documented sign convention, the calculator can produce undefined results or a different image type and magnification for the same physical setup.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/thin-lens-equation-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/thin-lens-equation-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/thin-lens-equation-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`