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Snell's Law — result sheet
Calculate the refracted angle from two refractive indices and an incident angle, including a total-internal-reflection result when appropriate.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Snell's law is n1 sin(theta1) = n2 sin(theta2), so sin(theta2) = n1 sin(theta1)/n2. If this ratio exceeds 1, the result is total internal reflection.
This calculator applies the ideal boundary-angle relation for refraction. It returns a refracted angle in degrees when the sine ratio is at most one and an explicit total internal reflection text result when the ratio exceeds one; waveguide and material-design advice are outside scope.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First-medium refractive index — index; Finite refractive-index value for the incident medium.; minimum 0.1; maximum 10
- Second-medium refractive index — index; Finite refractive-index value for the transmitted medium.; minimum 0.1; maximum 10
- Incident angle — degrees; Angle measured from the normal, in degrees.; minimum 0; maximum 90
Worked example
| Input | Value |
|---|---|
| First-medium refractive index | 1 |
| Second-medium refractive index | 1.5 |
| Incident angle | 30 |
Refracted angle is about 19.471 degrees.
Assumptions and limits
- Both refractive indices are finite positive dimensionless values from 0.1 through 10, and the incident angle is measured from the interface normal between 0 and 90 degrees.
- The interface is ideal, the indices are treated as fixed for the entered condition, and the ordinary ray relation is used without polarization, dispersion, or surface-roughness corrections.
- This is an ideal refraction relation only. Total internal reflection is reported textually when no real refracted angle exists; waveguide behavior, material selection, and design advice are outside scope.
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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