Snell's Law Refraction Calculator
Compute refraction angles, the critical angle, and see a ray diagram.
Formula
n₁ · sin θ₁ = n₂ · sin θ₂
Critical angle (from medium 1 into medium 2, only valid when n₁ > n₂):
θc = arcsin(n₂ / n₁)
Critical angle (from medium 1 into medium 2, only valid when n₁ > n₂):
θc = arcsin(n₂ / n₁)
Physics behind refraction
When light crosses the boundary between two transparent materials, its speed changes. If it enters the new medium at an angle, the wavefront bends — toward the normal when entering a denser medium, away from the normal when entering a less dense one. Snell's law quantifies this bending. Beyond the critical angle in the denser-to-lighter case, no refracted ray exists and the light reflects internally, the principle behind optical fibres and diamond sparkle.
Worked example
n₁ = 1.0003 (air), n₂ = 1.333 (water), θ₁ = 30°
sin θ₂ = (1.0003/1.333)·sin 30° = 0.3752 θ₂ = arcsin(0.3752) ≈ 22.03°
Related tools
FAQs
What is Snell's law?
n₁ sin θ₁ = n₂ sin θ₂, the rule for how light bends when crossing a boundary.
What is total internal reflection?
Complete reflection from a boundary when the incidence angle exceeds the critical angle.