Snell's Law Calculator (Refraction)
Snell's law calculator: angle of refraction, angle of incidence or refractive index, plus the critical angle.
n1 sin θ1 = n2 sin θ2
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
Light bends when it changes medium: n₁ sin θ₁ = n₂ sin θ₂. Typical indices: air 1.000, water 1.333, glass ≈ 1.5.
Going from a denser to a lighter medium, angles beyond the critical angle give total internal reflection.
Formula
n1 sin θ1 = n2 sin θ2
| Symbol | Quantity | Units |
|---|---|---|
| n1 | Refractive index 1 | — |
| θ1 | Angle of incidence | °, rad, gon, turn, ′, ″, mrad |
| n2 | Refractive index 2 | — |
| θ2 | Angle of refraction | °, rad, gon, turn, ′, ″, mrad |
Worked example
Given: n1 = 1 · θ1 = 30 ° · n2 = 1.5
θ2 = arcsin(n1 sin θ1 / n2)
Result: θ2 = 19.4712 °
Frequently asked questions
Air to glass (n = 1.5) at 30°?
The ray refracts to about 19.47°.