Refractive Index Snell

Infer optical index from independent measured refracted rays and incident-medium index; no mineral identity, normal-incidence division or ocean-wave speed/refraction alias.

Description

Snell's law relates incident and refracted ray angles measured from an interface normal.

Snell's law relates incident and refracted ray angles measured from an interface normal. Nonzero acute angles are needed for this index-ratio inversion.^[1]

Infer optical index from independent measured refracted rays and incident-medium index; no mineral identity, normal-incidence division or ocean-wave speed/refraction alias.

When to use Refractive Index Snell

Use this tool to infer optical index from independent measured refracted rays and incident-medium index; no mineral identity, normal-incidence division or ocean-wave speed/refraction alias.

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

How to use Refractive Index Snell 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 incidentMediumIndex, measuredIncidenceDegrees, measuredRefractionDegrees using the field table and calculation rules, then run the tool.
Read inferredSampleRefractiveIndices, meanInferredRefractiveIndex. 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
incidentMediumIndex	Incident medium index	number	Required
measuredIncidenceDegrees	Measured incidence degrees	list of number	Required
measuredRefractionDegrees	Measured refraction degrees	list of number	Required

Use positive incident index and aligned measured ray angles strictly between 0° and 90°. Infer an index for every pair and return the arithmetic mean.

Paired lists must be nonempty and have equal lengths.

sample index=incident-medium index × sin(incidence)/sin(refraction)

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

Output field	Meaning	Value type
inferredSampleRefractiveIndices	Inferred sample refractive indices	list of number
meanInferredRefractiveIndex	Mean inferred refractive index	number

json

{
  "input": {
    "incidentMediumIndex": 1,
    "measuredIncidenceDegrees": [
      30,
      30
    ],
    "measuredRefractionDegrees": [
      30,
      30
    ]
  },
  "output": {
    "inferredSampleRefractiveIndices": [
      1,
      1
    ],
    "meanInferredRefractiveIndex": 1
  }
}

Limitations and assumptions

Normal-incidence division is rejected. The optical model does not identify a mineral or infer principal indices from unobserved directions.

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 Single Reading Refractometer Estimate: Calibrate a single curved-surface spot reading against caller instrument references with propagated reading bounds/extrapolation flag; not a definitive RI, full principal indices or identity lookup. For a complementary task, 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.

References

Refractive Index Snell — tool.io

Similar or alternative tools

Single Reading Refractometer Estimate
Calibrate a single curved-surface spot reading against caller instrument references with propagated reading bounds/extrapolation flag; not a definitive RI, full principal indices or identity lookup.
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.