Critical Angle
Resolve optical total-internal-reflection critical angle for a caller higher-to-lower-index interface; not seismic critical-angle appearance, prism/rainbow geometry or actual stone light return.
Description
Total internal reflection requires travel from higher to lower refractive index.
Total internal reflection requires travel from higher to lower refractive index. Its critical internal angle is measured from the interface normal.1
Resolve optical total-internal-reflection critical angle for a caller higher-to-lower-index interface; not seismic critical-angle appearance, prism/rainbow geometry or actual stone light return.
When to use Critical Angle
Use this tool to resolve optical total-internal-reflection critical angle for a caller higher-to-lower-index interface; not seismic critical-angle appearance, prism/rainbow geometry or actual stone light return.
Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
How to use Critical Angle and understand its results
- Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.
- Enter internalRefractiveIndex, externalRefractiveIndex using the field table and calculation rules, then run the tool.
- Read criticalInternalAngleDegrees. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| internalRefractiveIndex | Internal refractive index | number | Required |
| externalRefractiveIndex | External refractive index | number | Required |
Enter positive optical indices with internal strictly greater than external. Return the real critical angle in degrees.
critical angle=asin(external index/internal index) × 180/π Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| criticalInternalAngleDegrees | Critical internal angle degrees | number |
{
"input": {
"internalRefractiveIndex": 2,
"externalRefractiveIndex": 1
},
"output": {
"criticalInternalAngleDegrees": 30.000000000000004
}
}Limitations and assumptions
Equal or reversed indices are rejected. A critical angle alone does not determine a gemstone's light return.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Fresnel Reflection Loss: Compute lossless real-index oblique Fresnel s/p energy reflection and transmission with explicit TIR; not normal-only lustre proxy, absorbing media or integrated gemstone light return. For a complementary task, use Light Return Tilt Check: Trace supplied meridional entry and exit-facet normals measured relative to the same entry-face normal under declared tilt/index; zero exit angle is unused for TIR flags, and this local-interface screen is not full gemstone light-return simulation.
References
-
Critical Angle — tool.io
Similar or alternative tools
- Fresnel Reflection Loss
Compute lossless real-index oblique Fresnel s/p energy reflection and transmission with explicit TIR; not normal-only lustre proxy, absorbing media or integrated gemstone light return.
- Light Return Tilt Check
Trace supplied meridional entry and exit-facet normals measured relative to the same entry-face normal under declared tilt/index; zero exit angle is unused for TIR flags, and this local-interface screen is not full gemstone light-return simulation.