Refraction Calculator

How it works

1. 1Enter the refractive index of the first medium (n₁) — air ≈ 1.0, water ≈ 1.33, glass ≈ 1.5.
2. 2Enter the refractive index of the second medium (n₂) and the angle of incidence from the normal.
3. 3Snell’s law (n₁ sinθ₁ = n₂ sinθ₂) is applied instantly, with the refracted angle, critical angle, and a live ray diagram.

Use cases

• Optical engineering — designing lenses, prisms, and fibre-optic waveguides.
• Physics education — verifying Snell’s law and visualising how light bends at an interface.
• Photography — understanding how glass lens elements redirect light.

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. Air (1.0) into glass (1.5) at 30° refracts to arcsin(1.0 × sin30° ÷ 1.5) ≈ 19.5°.

What are typical refractive indices?

Air ≈ 1.0003 (treated as 1.0), water ≈ 1.33, crown glass ≈ 1.52, diamond ≈ 2.42. A higher index means light travels more slowly and bends more strongly toward the normal.

What is total internal reflection?

It occurs when light goes from a denser to a less dense medium (n₁ > n₂) and the incidence angle exceeds the critical angle θc = arcsin(n₂ ÷ n₁). For glass-to-air, θc ≈ 41.8°; above it, all light reflects back — the basis of fibre optics.