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Snell's Law Calculator (Refraction Angle)

Solve for the angle of incidence, angle of refraction, or refractive index of either medium using Snell's law, and detect total internal reflection.

n1 (incidence medium)
1
n2 (refraction medium)
1.5
Angle of incidence (θ1)
45°
Angle of refraction (θ2)
28.126°

How it works

Snell's law relates how a light ray bends when it crosses the boundary between two media: n1·sin(θ1) = n2·sin(θ2), where n1 and n2 are the two media's refractive indices and θ1, θ2 are the angles the ray makes with the normal (a line perpendicular to the boundary), not with the surface itself.

Pick which quantity to solve for; the calculator rearranges the same identity to find it from the other three, ignoring whatever placeholder value is in the field you're solving for. The defaults (air, n=1, into glass, n=1.5, at a 45° angle of incidence) solve to a 28.13° angle of refraction.

Going from a denser medium into a less dense one (n1 > n2) at a steep enough angle, there's no real angle of refraction — all the light reflects back instead, a phenomenon called total internal reflection. This calculator detects that case (when solving for either angle) and reports it rather than an invalid number.

FAQ

What does total internal reflection actually mean?

It happens when light traveling in a denser medium (higher refractive index) hits the boundary with a less dense medium at an angle steeper than the 'critical angle' for that pair of materials. Instead of refracting through, 100% of the light reflects back into the denser medium — it's the principle fiber-optic cables use to keep light traveling down the fiber with no loss at the walls.

What are typical refractive index values?

A vacuum is exactly 1 by definition, air is very close to 1 (about 1.0003), water is about 1.33, and common glass is around 1.5. Denser optical materials like diamond reach about 2.4. This calculator doesn't hardcode any of these — enter whatever index applies to your two materials.

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