Snell's Law Calculator
Find the angle of refraction from the refractive indices and the angle of incidence.
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Angle of refraction (°)
Angle of refraction (°)
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Critical angle (°)
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Speed in medium 2 (% of c)
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Snell's Law Calculator by TheCalcTools
How the Snell's Law Calculator works
Enter the refractive index on each side of the boundary and the angle of the incoming ray, measured from the normal.
Snell’s law relates the sines of the angles.
If light goes from a denser to a rarer medium past the critical angle it is totally reflected.
The formula
n₁ sin θ₁ = n₂ sin θ₂θc = arcsin(n₂ ÷ n₁), for n₁ > n₂
Worked example
Using the default values shown in the calculator:
| Refractive index n₁ | 1 |
|---|---|
| Refractive index n₂ | 1.5 |
| Angle of incidence (°) | 30 |
- sin θ₂ = 1.0 × sin 30° ÷ 1.5 = 0.3333.
- θ₂ = 19.471°.
- In glass, light travels at 66.7% of its vacuum speed.
Result:
| Angle of refraction (°) | 19.471 |
|---|---|
| Critical angle (°) | None (n₁ ≤ n₂) |
| Speed in medium 2 (% of c) | 66.7% |
Frequently asked questions
What are typical refractive indices?
Air ≈ 1.0003, water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42.
Where is total internal reflection used?
In optical fibres, prisms in binoculars and diamond sparkle.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.