Snell's law calculator
With this Snell's law calculator you find the refraction angle of a light ray crossing between two media, and whether total internal reflection occurs and how much light is reflected.
Example: First medium (incident): Air · Second medium: Water · Angle of incidence θ₁ (from the normal) 45 ° → Result: The ray bends from 45° (n₁ = 1.0003) to 32.05° (n₂ = 1.333). Source: Wikipedia – Brechungsgesetz (Snellius): n₁·sin α₁ = n₂·sin α₂, Totalreflexion, Brewster-Winkel. Updated: .
How it is calculated
Snell's law is n₁·sin θ₁ = n₂·sin θ₂. A ray of light hitting water from air at 45° bends to about 32.0° from the normal.
How it is calculated
Angles are always measured from the normal (the perpendicular to the surface). θ₂ = arcsin(n₁·sin θ₁ / n₂) gives the refraction angle. If n₁ > n₂ and the angle of incidence exceeds the critical angle arcsin(n₂/n₁), there is no refracted ray any more (total internal reflection). The Fresnel equations give the reflectance, here as the mean of s and p polarisation; at Brewster's angle arctan(n₂/n₁) p-polarised light is not reflected at all.
Good to know
- Normal incidence (0°) is not bent, yet some light (about 4 % for air to glass) is still reflected.
- The refractive index depends on wavelength (dispersion); the values are for yellow light at 589 nm.
- Optical fibres and prism binoculars use total internal reflection; it is only possible when going into a less dense medium.
Frequently asked questions
What is Snell's law?
n₁ · sin θ₁ = n₂ · sin θ₂. Angles are measured from the normal, n is the refractive index of each medium.
When does total internal reflection occur?
When light goes from a denser to a less dense medium (n₁ > n₂) and the angle of incidence exceeds arcsin(n₂/n₁). From water to air the critical angle is about 48.6°.
What is Brewster's angle?
The angle of incidence arctan(n₂/n₁) at which the reflected light is completely linearly polarised. From air to water it is about 53.1°.
How fast is light in water?
c/n, so about 299,792 km/s divided by 1.333, roughly 224,900 km/s.
Sources and legal basis
- Wikipedia – Brechungsgesetz (Snellius): n₁·sin α₁ = n₂·sin α₂, Totalreflexion, Brewster-Winkel
- Wikipedia – Fresnelsche Formeln (Fresnel equations): reflectance for s and p polarization
- Wikipedia – Brechungsindex: refractive indices at 589 nm (reference values)
- NIST – Lichtgeschwindigkeit im Vakuum c = 299 792 458 m/s (exakt)
As of: · Editorial policy
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