Brewster's Angle Calculator mechanism

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

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