Snell's Law Calculator
Refraction angle, with the critical angle and TIR.
Work out Snell's Law. Refraction angle, with the critical angle and TIR. Shows the working, not just the answer.
Vacuum 1, air 1.0003, water 1.333, glass 1.5, diamond 2.417.
Measured from the normal, not from the surface.
Angle of refraction
22.03°
Towards the normal — entering a denser medium
n₁sin θ₁ = n₂sin θ₂, with angles measured from the normal rather than from the surface — measuring from the surface is the commonest setup error and gives the complement of the right answer. Light bends towards the normal entering a denser medium and away from it on the way out. That is why a straw looks broken at the waterline and why a pool is always shallower than it looks. Total internal reflection is possible only going from dense to less dense, which is why the critical angle is reported as none in the other direction.
How the Snell's Law Calculator works
Enter two refractive indices and an angle of incidence for the refracted angle. Where the geometry makes refraction impossible the page says so and gives the critical angle instead of returning a broken number.
Also known as: refraction calculator · critical angle calculator · total internal reflection calculator · index of refraction calculator
Frequently asked questions
What is Snell's law?
n₁sin θ₁ = n₂sin θ₂, with both angles measured from the normal — the perpendicular to the surface, not the surface itself.
What is the critical angle?
The angle of incidence beyond which no light escapes into the second medium. It exists only going from dense to less dense: water to air is 48.8°, and diamond to air only 24.4°.
How does total internal reflection make fibre optics work?
Light entering a fibre at a shallow enough angle reflects perfectly off the core boundary, over and over, losing almost nothing. No mirror is that efficient.
Why does a straw look broken at the waterline?
Light from the submerged part bends away from the normal as it leaves the water, so it reaches your eye from a different direction than it started. Your brain assumes straight lines and puts the straw in the wrong place.
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