Snell’s Law Calculator
Calculate the refraction angle at a boundary, and find the critical angle.
Please note: Results come from idealised models that assume clean, standard conditions. Real measurements deviate, and published constants carry their own tolerances. Use these for study and estimation, not for engineering sign-off.
What the Snell’s Law Calculator does
Snell’s law describes how light bends when it crosses between media of different optical density. The refractive index measures how much a medium slows light, and the ratio of the two indices fixes exactly how much the ray turns at the boundary.
Formula
n₁ × sin(θ₁) = n₂ × sin(θ₂)θ₂ = arcsin(n₁ × sin(θ₁) ÷ n₂)Critical angle θc = arcsin(n₂ ÷ n₁), when n₁ > n₂v = c ÷ n
Inputs explained
| Input | Unit | Required | Notes |
|---|---|---|---|
| First medium (light comes from) | one of 10 options | Yes | — |
| Refractive index of the first medium | number | In some modes | Accepts 1 or more. Shown in no standard mode. |
| Second medium (light enters) | one of 10 options | Yes | — |
| Refractive index of the second medium | number | In some modes | Accepts 1 or more. Shown in 6 of the 64 modes. |
| Angle of incidence | ° | Yes | Measured from the normal — the line perpendicular to the surface. Accepts 0 or more, up to 90. |
How to use it
- Choose First medium (light comes from) and Second medium (light enters).
- Enter Angle of incidence.
- Fill in the remaining inputs the form shows for your choice.
- Select Calculate.
Worked example
Light passing from air into water at 45° from the normal.
- First medium
- Air (n = 1.000293)
- Second medium
- Water (n = 1.333)
- Angle
- 45°
sin θ₂ = 1.000293 × sin(45°) ÷ 1.333 = 0.5306, so θ₂ = 32.05°. The ray bends 12.95° towards the normal.
Frequently asked questions
Why does a straw look bent in a glass of water?
Light from the submerged part refracts as it leaves the water, arriving at your eye from a different apparent direction than the part above.
What is total internal reflection?
When light travels from a denser to a less dense medium beyond the critical angle, none of it escapes — it all reflects back. Optical fibres and diamond sparkle both rely on it.