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Snell's Law Refraction Calculator

Find the refraction angle at a boundary between two media.

Inputs

Results

Refraction angle25.01696°
Critical angleNone (light enters a denser medium)

Chart

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How to use the snell's law refraction calculator

Find the refraction angle at a boundary between two media. Enter index of medium 1, index of medium 2, incident angle in the fields above; the refraction angle, critical angle are computed instantly and plotted on the chart so you can see how the answer changes.

Formula

Refraction angle (°) = asin(n1 × sin(a1) / n2)
Critical angle = n2<n1?fmt(asin(n2 / n1))+" °":"None (light enters a denser medium)"

Variables

  • n1 — Index of medium 1
  • n2 — Index of medium 2
  • a1 — Incident angle (°)

Worked example

With index of medium 1 = Vacuum, index of medium 2 = Glass, incident angle = 40 °, the calculator gives refraction angle ≈ 25.01696 °; critical angle ≈ None (light enters a denser medium).

Frequently asked questions

What is the formula for the snell's law refraction calculation?

Refraction angle (°) = asin(n1 × sin(a1) / n2). Critical angle = n2<n1?fmt(asin(n2 / n1))+" °":"None (light enters a denser medium)". Here n1 is index of medium 1, n2 is index of medium 2, a1 is incident angle (°).

What inputs do I need for the snell's law refraction calculator?

You need index of medium 1, index of medium 2, incident angle in °. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.

How do I use this calculator?

Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.

Is the result exact?

Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.

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