Physics
Snell’s Law & Refractive Index Calculator
Solve n₁ sin θ₁ = n₂ sin θ₂ for the refracted medium or refracted angle.
Your measurements
Start with the example, or enter your own values. Use a dot for decimals and e for scientific notation.
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Result & working
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Step-by-step working
The formula
n₁ sin θ₁ = n₂ sin θ₂
n₂ = n₁ sin θ₁ / sin θ₂
θ₂ = sin⁻¹[(n₁/n₂) sin θ₁]
| Symbol | Meaning |
|---|---|
| n₁, n₂ | Refractive indices of the incident and second medium. |
| θ₁, θ₂ | Angles measured from the normal, in degrees here. |
When to use this calculator
Use this for refraction at a flat boundary between isotropic media. Angles are measured from the normal, not the surface.
If solving for θ₂, a sine argument greater than 1 indicates no transmitted ray under this simple model; total internal reflection is possible.
Worked example
The calculator opens with these example values. All steps below are available even with JavaScript disabled.
- n₂ = n₁ sinθ₁ / sinθ₂
- = 1 × sin(45°) / sin(28.1°) = 1.50125
n₂ = 1.50125
Common mistakes
- Measure angles from the normal.
- Keep calculator trigonometry mode consistent; this tool accepts degrees.
- Do not treat refractive index as having units.