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Critical Angle Calculator — result sheet
Calculate the critical angle for total internal reflection from a higher-index medium to a lower-index medium.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Critical angle=arcsin(n₂/n₁), valid when n₁>n₂.
The boundary angle occurs when the refracted ray reaches 90 degrees, after which total internal reflection is possible under the model.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Higher refractive index n₁ — minimum 1.0E-6; maximum 1000000
- Lower refractive index n₂ — minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Higher refractive index n₁ | 1.5 |
| Lower refractive index n₂ | 1 |
Critical angle ≈41.810°.
Assumptions and limits
- The incident medium has the higher refractive index and both indices are positive.
- The interface is planar and media are homogeneous.
- Losses, surface coatings, dispersion, and fiber acceptance details 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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