Snell’s Law Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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A calculator can remove arithmetic without removing judgment. For snell’s law, optical formulas are compact, but their sign conventions and geometric assumptions deserve as much attention as the arithmetic. Use the result as a transparent model of the fields on this page, not as a substitute for knowing what those fields mean.

What this calculator does

The Snell’s Law Calculator is a focused solver for angle of refraction using Medium 1, Refractive index 1 (n₁), Medium 2. Its job is to make the active equation and the quantities feeding it easy to inspect rather than model every possible real-world effect.

How to use it

Begin with Refractive index 1 (n₁), Refractive index 2 (n₂), Angle of incidence (θ₁). Do not strip the units from those values when copying them from a datasheet or measurement. Choose Medium 1, Medium 2 so the calculation path matches your case. Once calculated, vary the most influential input slightly and confirm that the response agrees with the equation before using the number elsewhere.

How the calculation works

The refraction angle follows n₁sinθ₁ = n₂sinθ₂, so θ₂ = asin[(n₁/n₂)sinθ₁]. Air, water, and glass presets replace the custom refractive-index values. If the sine argument exceeds 1, the page flags total internal reflection instead of inventing an angle.

Example

Using the default example on the page (Medium 1 = Custom; Refractive index 1 (n₁) = 1; Medium 2 = Glass; Refractive index 2 (n₂) = 1.5), the calculator returns angle of refraction of 19.471221 deg. Use the default result as a hand-check point, then test one input at a time so an inverted ratio or unit mistake becomes obvious.

How to interpret the result

Use the angle of refraction for comparisons made under the same optical assumptions. The displayed unit matters, and so does whether the page is describing power, intensity, focal geometry, angular field, or transmission—quantities that should not be treated as interchangeable.

Limitations and notes

Real optical systems can add aberration, alignment error, finite bandwidth, diffraction, scattering, detector response, and component tolerances beyond the ideal relationship shown here. The first values to recheck are Refractive index 1 (n₁), Refractive index 2 (n₂), because they directly set the scale of this result. Treat the calculator as a model of the visible inputs, and independently verify any number used for safety, certification, or final component selection.