Physics

Snell’s law

Use Snell’s law to calculate refraction.

Your measurements

Number formats & units

Use decimal dots in datasets. Single values also accept decimal commas and scientific notation such as 1.2e-3 or 1.2 × 10⁻³.

Snell’s Law & Refractive Index Calculator inputs

Calculated locally. No account or uploads.

Result & working

Example

The calculator is loading. You can read the worked example below.

Copy & export

Formula & example

The relationship

n1sin⁡θ1=n2sin⁡θ2n_1\sin\theta_1=n_2\sin\theta_2
n2=n1sin⁡θ1sin⁡θ2n_2=\frac{n_1\sin\theta_1}{\sin\theta_2}
θ2=arcsin⁡ ⁣(n1n2sin⁡θ1)\theta_2=\arcsin\!\left(\frac{n_1}{n_2}\sin\theta_1\right)
What the variables mean
SymbolMeaning
n1,  n2n_{1},\;n_{2}Refractive indices of the incident and second medium.
θ1,  θ2\theta_{1},\;\theta_{2}Angles measured from the normal, in degrees here.

Worked example

Solve for
Refractive index n₂
Incident refractive index n₁
1.000
Incident angle θ₁ (°)
45
Refracted angle θ₂ (°)
28.1

n₂ = 1.50125

Follow the example steps
  1. n₂ = n₁ sinθ₁ / sinθ₂
  2. = 1 × sin(45°) / sin(28.1°) = 1.50125

Common mistakes

Measure the angle from the normal to the surface.

Incorrect approach

A ray at 30° to the surface: θ = 30°

Correct approach

θ = 90° − 30° = 60° from the normal.

More checks before you submit
  • Measure angles from the normal.
  • Keep calculator trigonometry mode consistent; this tool accepts degrees.
  • Do not treat refractive index as having units.
Method notes

Use this for refraction at a flat boundary between isotropic media. Angles are measured from the normal, not the surface.

If solving for θ₂, a sine argument greater than 1 indicates no transmitted ray under this simple model; total internal reflection is possible.