Snell's Law Calculator (Refraction and Critical Angle)
By Santaji GadepatilinUpdated October 27, 2026
Light bends when it passes from one material into another because its speed changes. Snell's law predicts the angle of bending — and the critical angle beyond which light is totally reflected, as in optical fibres.
How to use the Snell’s law calculator
Enter the refractive indices of the two materials and the angle of incidence (measured from the normal — the line perpendicular to the surface). The calculator finds the angle of refraction. Fill any three values to solve for the fourth.
Snell’s law formula
n₁ sin θ₁ = n₂ sin θ₂
Refractive indices (visible light)
| Material | n |
|---|---|
| Vacuum | 1 (exactly) |
| Air | 1.0003 |
| Water | 1.333 |
| Ethanol | 1.36 |
| Acrylic (PMMA) | 1.49 |
| Crown glass | 1.52 |
| Flint glass | 1.62 |
| Diamond | 2.42 |
Critical angles
| From → to air | Critical angle |
|---|---|
| Water (n = 1.333) | 48.6° |
| Acrylic (n = 1.49) | 42.2° |
| Crown glass (n = 1.52) | 41.2° |
| Flint glass (n = 1.62) | 38.1° |
| Diamond (n = 2.42) | 24.4° |
Diamond’s small critical angle traps light inside, making it sparkle.
Example
Light from air into water at 30°: sin θ₂ = 1.0003 × sin 30° ÷ 1.333 = 0.3752, so θ₂ = 22.0°.
Applications
- Optical fibres carry light by total internal reflection.
- Lenses in glasses, cameras and microscopes bend light to focus it.
- Prisms split white light because n varies slightly with wavelength (dispersion).
- Mirages form when air layers of different temperature bend light.
Frequently asked questions
What is Snell's law?
n₁ sin θ₁ = n₂ sin θ₂. Light bends towards the normal when it enters a denser medium (higher n) and away from it when it leaves.
What is the critical angle?
The angle of incidence beyond which light cannot leave a denser medium and is totally reflected. sin θc = n₂ ÷ n₁. For glass to air (n 1.5), θc ≈ 41.8°.
Why does the calculator show no solution?
When going from a denser to a less dense medium above the critical angle, no refracted ray exists — this is total internal reflection.
What is the refractive index of water?
About 1.333 for visible light at 20 °C.