Critical Angle / Total Internal Reflection Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

Tranche

tranche-5

Evidence ID

t5-140

Ledger rows

1

No ledger note is attached.

Review findings

The core critical-angle formula is standard, but the specification needs an explicit angle-unit contract, the strict TIR comparison rule, validation behavior for n1<=n2, and wavelength-qualified refractive-index data. The honest label should not be n/a: the panel should state its assumptions and identify refractive indices as wavelength- and condition-dependent.

Formula and scope findings

• The critical-angle formula θc=asin(n2/n1) is correct only for n1>n2, with incidence measured from the surface normal and both refractive indices dimensionless.
• The TIR decision rule is omitted: TIR occurs only when the incidence angle θi is strictly greater than θc; equality is the critical-angle case and should not be labeled TIR.
• The angle unit is unspecified. The calculator must explicitly define whether inputs and outputs use degrees or radians and convert consistently.

Unit assumptions

• n1 and n2 are dimensionless phase refractive indices at the same wavelength, temperature, and material conditions.
• n1 is the refractive index of the incident medium and n2 is the refractive index of the transmitted medium.
• Incidence angle is measured from the interface normal, not from the interface surface.
• Test vectors below use degrees unless the input key explicitly ends in _rad; asin is converted to the stated output unit.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The specification does not define handling for n1 <= n2, out-of-domain asin arguments, or signed incidence angles. Invalid-index inputs can produce undefined results, and retaining a negative incidence sign changes the TIR branch unless an unsigned-from-normal convention is enforced.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "n1": 1.5,
    "n2": 1,
    "incidence_angle_deg": 50
  },
  "expected_outputs": {
    "critical_angle_deg": 41.8103,
    "tir": true
  },
  "working": "n2/n1 = 1.0/1.5 = 0.6666667. θc = asin(0.6666667) = 41.8103°. Compare incidence angle: 50.0° > 41.8103°, so TIR = yes."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json