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.

Description

A local entry/exit ray screen applies Snell's law to supplied meridional facet normals.

A local entry/exit ray screen applies Snell's law to supplied meridional facet normals. Total internal reflection at an exit needs a separate flag because no transmitted angle is then available.^[1]

When to use Light Return Tilt Check

Use this tool to 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.

Prepare the gemstone measurements, spectra or comparison data and any supplied calibration parameters. Check units, reference conditions and record alignment.

How to use Light Return Tilt Check 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 sampleIndex, outsideIndex, externalEntryIncidenceDegrees, exitFacetNormalOffsetsDegrees, appliedTiltDegrees using the field table and calculation rules, then run the tool.
Read internalExitIncidencesDegrees, totalInternalReflectionFlags, transmittedExitAnglesDegrees. 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
sampleIndex	Sample index	number	Required
outsideIndex	Outside index	number	Required
externalEntryIncidenceDegrees	External entry incidence degrees	number	Required
exitFacetNormalOffsetsDegrees	Exit facet normal offsets degrees	list of number	Required
appliedTiltDegrees	Applied tilt degrees	number	Required

Use positive indices with sample>outside, nonnegative entry incidence below 90° and |tilt|<90°. Require tilted entry inside (−90°,90°) and a nonempty list of exit incidences below 90° from normals relative to the same entry-face normal. For s≥1 flag TIR and return exit-angle placeholder 0; otherwise return asin(s) in degrees.

internal entry=asin(outside/sample index × sin(external incidence+tilt)); exit s=sample/outside index × sin(exit incidence)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
internalExitIncidencesDegrees	Internal exit incidences degrees	list of number
totalInternalReflectionFlags	Total internal reflection flags	list of number
transmittedExitAnglesDegrees	Transmitted exit angles degrees	list of number

json

{
  "input": {
    "sampleIndex": 2,
    "outsideIndex": 1,
    "externalEntryIncidenceDegrees": 0,
    "exitFacetNormalOffsetsDegrees": [
      0,
      45
    ],
    "appliedTiltDegrees": 0
  },
  "output": {
    "internalExitIncidencesDegrees": [
      0,
      45
    ],
    "totalInternalReflectionFlags": [
      0,
      1
    ],
    "transmittedExitAnglesDegrees": [
      0,
      0
    ]
  }
}

Limitations and assumptions

The zero angle on TIR rows is unused. This local-interface model does not simulate complete gemstone light return.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use 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. For a complementary task, 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.

References

Light Return Tilt Check — tool.io

Similar or alternative tools

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.
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.