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Snell’s Law Refraction Angle Calculator — result sheet
Calculate a refracted angle from two refractive indices and an incident angle.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: n₁sinθ₁=n₂sinθ₂; θ₂=arcsin((n₁/n₂)sinθ₁).
The result applies Snell’s law at a flat interface and makes total-internal-reflection cases explicit.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Incident-medium index n₁ — minimum 1.0E-6; maximum 1000000
- Refracting-medium index n₂ — minimum 1.0E-6; maximum 1000000
- Incident angle — degrees; minimum 0; maximum 89.999999
Worked example
| Input | Value |
|---|---|
| Incident-medium index n₁ | 1 |
| Refracting-medium index n₂ | 1.5 |
| Incident angle | 30 |
Refracted angle ≈19.471°.
Assumptions and limits
- Indices are positive and angles are measured from the normal in degrees.
- The interface is planar and media are homogeneous and isotropic.
- Polarization, dispersion, surface roughness, and transmission intensity are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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