Snell’s law refraction calculator
Find the refraction angle, critical angle, Brewster angle and reflectance at an interface.
A clear answer. Here’s how.
Snell’s law n₁ sin θ₁ = n₂ sin θ₂ gives the refracted angle, or total internal reflection when the sine would exceed 1. The critical angle is asin(n₂ ÷ n₁) when n₁ > n₂ and the Brewster angle is atan(n₂ ÷ n₁). Reflectance comes from the Fresnel equations for s- and p-polarised light, averaged for unpolarised light, at a smooth lossless interface. Coatings, absorption and rough surfaces change real results.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Refractive index of the first medium
- 1
- Refractive index of the second medium
- 1.5
- Angle of incidence (degrees from the normal)
- 30
Example result
- Refracted angle
- 19.4712°
- Deviation from the straight path
- 10.5288°
- Reflectance, s-polarised
- 5.780%
- Reflectance, p-polarised
- 2.525%
- Reflectance, unpolarised
- 4.152%
- Transmittance, unpolarised
- 95.848%
- Critical angle
- None (light is entering a denser medium)
- Brewster angle
- 56.3099°
- Reflectance at normal incidence
- 4.000%
Snell’s law: n₁ sin θ₁ = n₂ sin θ₂, with angles measured from the surface normal. Reflectance uses the Fresnel equations for a smooth, lossless, non-magnetic interface; coatings, absorption and rough surfaces differ. Typical indices near 589 nm: air 1.0003, water 1.333, window glass about 1.52, diamond 2.417.