Source: https://guthlabs.ai/docs/instruments/brewster-s-angle-calculator/mechanism/

instrument mechanism / verified-clean

# Brewster's Angle Calculator mechanism

The inspectable method record for Brewster's Angle Calculator, kept separate from implementation and qualification.

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

## Model scope

The core formula is standard under its stated physical assumptions. Review is required because the specification omits angle units, wavelength/index-selection requirements, medium assumptions, polarization, and validation behavior for invalid or equal indices.

- The formula θB = atan(n2/n1) is correct for the Brewster incidence angle at an interface between isotropic, nonmagnetic, lossless dielectrics, measured from the normal, but those applicability conditions are not stated.

- The output angle unit and atan convention are unspecified: radians are the mathematical default, while optics interfaces commonly report degrees.

- Refractive indices are wavelength-dependent, but no wavelength or index-table selection is specified. The equal-index case produces 45° mathematically, but there is no reflected interface when n1 = n2, so a physical Brewster angle is not meaningful in that case.

## Units and conventions

- n1 and n2 are dimensionless refractive indices at the same wavelength and for the relevant polarization/material conditions.

- θB is computed as atan(n2/n1) in radians internally; degree values require multiplication by 180/π.

- Both refractive indices must be positive real values, with incidence defined from medium 1 into medium 2 and the angle measured from the surface normal.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "n1": 1,
    "n2": 1.5
  },
  "expected_outputs": {
    "thetaB_rad": 0.982793723,
    "thetaB_deg": 56.309932
  },
  "working": "1. Compute the index ratio: n2/n1 = 1.5/1.0 = 1.5. 2. Apply the formula: θB = atan(1.5) = 0.982793723 rad. 3. Convert to degrees: 0.982793723 × 180/π = 56.309932°."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The exact input n1=0 produces a division-by-zero undefined result. The instrument must reject it rather than returning a numeric angle. A second hazard is convention ambiguity: the formula gives the angle from the normal, while some interfaces may display the complementary angle from the surface.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/brewster-s-angle-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/brewster-s-angle-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/brewster-s-angle-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`