Solve Snell’s law n₁ sin θ₁ = n₂ sin θ₂ for the angle of refraction, angle of incidence or either refractive index. This free refraction calculator also gives the critical angle, flags total internal reflection and shows the speed of light in each medium.
Snell’s law and refraction formulas
Worked example
Light passes from air (n = 1.00) into glass (n = 1.50) at 40° to the normal. sin θ₂ = 1.00 × sin 40° ÷ 1.50 = 0.4285, so θ₂ = 25.4°: the ray bends towards the normal as it slows down. Going the other way, from glass into air, the critical angle is sin⁻¹(1/1.5) = 41.8°. Above that, all the light reflects back inside, which is how optical fibres carry signals.
Refractive indices
| Medium | n | Medium | n |
|---|---|---|---|
| Vacuum / air | 1.000 / 1.0003 | Crown glass | 1.52 |
| Water | 1.333 | Flint glass | 1.62 |
| Ice | 1.31 | Diamond | 2.42 |
Frequently asked questions
What is Snell’s law?
It relates the angles a light ray makes with the normal when it crosses between two materials: n₁ sin θ₁ = n₂ sin θ₂, where n is each material’s refractive index.
How do I find the angle of refraction?
Enter both refractive indices and the angle of incidence, and leave θ₂ empty. The calculator uses θ₂ = sin⁻¹(n₁ sin θ₁ / n₂).
What is the critical angle?
The angle of incidence above which light going into a less dense medium is totally internally reflected: sin θc = n₂/n₁. Glass to air is about 42°.
Why does light bend?
Light travels at different speeds in different materials (v = c/n). When one side of a wavefront slows down first, the wave changes direction.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.