Snell’s Law Calculator
Enter the refractive index of both materials and the angle of the incoming ray.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- sin θ₂ = n₁ × sin θ₁ ÷ n₂
- If the result would be above 1, the ray is totally reflected
- Critical angle = arcsin(n₂ ÷ n₁), when n₁ is larger than n₂
For related angle work, see the trigonometric functions calculator.
Worked example
Light going from air (1.0) into glass (1.5) at 30°:
- sin θ₂ = 0.5 ÷ 1.5 = 0.3333
- θ₂ = 19.47°, bending towards the normal
Why your number may differ
Refractive index depends on the wavelength, so different colours bend slightly differently. The values you enter are treated as exact.
Frequently asked questions
What is Snell’s law?
n₁ × sin θ₁ = n₂ × sin θ₂. It describes how a light ray bends when moving between two materials with different refractive indices.
What is total internal reflection?
Going from a denser to a less dense material, beyond a certain angle the light cannot leave and reflects fully back. That angle is the critical angle.
What refractive index should I use?
Air is about 1.0003, water 1.33, ordinary glass about 1.5 and diamond about 2.42. Values vary a little with the colour of light.