Snell’s Law Calculator

How it works

1. 1Choose whether to solve for the refracted angle θ₂ or the second refractive index n₂.
2. 2Enter the known refractive indices and/or angles; the calculator applies n₁·sinθ₁ = n₂·sinθ₂ instantly.
3. 3The live diagram shows the incident and refracted rays at the interface.

Use cases

• Optics students verifying refraction problems — light from air into water or glass.
• Lens and prism designers calculating how light bends at material boundaries.
• Checking whether total internal reflection occurs from a denser to a less-dense medium.

Frequently asked questions

What is Snell’s law?

Snell’s law states n₁·sinθ₁ = n₂·sinθ₂, where n₁ and n₂ are the refractive indices and θ₁, θ₂ are the angles of incidence and refraction from the normal. It describes how light bends crossing a boundary between transparent materials.

What does the refractive index mean?

The refractive index n is the ratio of the speed of light in a vacuum to its speed in the medium: n = c ÷ v. Vacuum is 1, air ≈ 1.0003, water ≈ 1.33, glass ≈ 1.5. A higher index means light slows and bends more.

Worked example — air into water at 30°?

With n₁ = 1.0, n₂ = 1.33, θ₁ = 30°: sinθ₂ = (1.0 × sin30°) ÷ 1.33 ≈ 0.376, so θ₂ = arcsin(0.376) ≈ 22.1°. The ray bends toward the normal entering the denser medium.