Snell's law calculator (refraction angle)
Enter the first index, the incidence angle and the second index to get the refraction angle. Past the critical angle it tells you total internal reflection occurs.
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How to use it
- Enter refractive index of medium 1, angle of incidence and refractive index of medium 2.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
n₁ × sin θ₁ = n₂ × sin θ₂, and the critical angle θc = arcsin(n₂ / n₁) when n₁ > n₂. Angles are measured from the normal.
Example
Inputs: Refractive index of medium 1 = 1, Angle of incidence = 30 °, Refractive index of medium 2 = 1.5. Result: Refraction angle: 19.4712 °; Critical angle: None, because n₁ ≤ n₂; Speed of light in medium 2: 199,861,639 m/s.
Limits and caveats
- Refractive index varies slightly with color, so common values such as 1.33 for water and 1.5 for glass are approximate for visible light.
Questions about this tool
What are common refractive indices?
Air about 1.0003, water 1.33, ordinary glass about 1.5 and diamond about 2.42.
When does total internal reflection happen?
When light goes from a higher to a lower index at an angle beyond the critical angle; optical fiber relies on it.
Why measure from the normal, not the surface?
Snell's law uses angles from the normal. If your angle is from the surface, subtract it from 90.