By Zencalcy Editorial TeamLast reviewed About us
A prism bends light by an amount that depends on its apex angle, its refractive index and the angle at which the light enters. The bend is smallest when the ray passes symmetrically, and that minimum deviation is how prism glass is characterised.
Ray deviation through a triangular prism.
δ = i₁ + i₂ − A δ_min = 2 arcsin(n sin(A/2)) − A
A is the apex angle, i₁ and i₂ the angles at entry and exit, and n the refractive index. The minimum-deviation form applies to a symmetric ray path.
| Symbol | Meaning |
|---|---|
| δ | Total deviation of the ray. |
| A | Apex angle of the prism. |
| i₁, i₂ | Angles at the first and second surfaces. |
| n | Refractive index of the prism material. |
δ = 45° + 45° − 60° = 30°. For n = 1.5 the minimum deviation is 37.18°, reached when both surface angles are 48.59°.
Continue with the Refractive Index Calculator, Single Slit Diffraction Calculator, or the Snell's Law Calculator — or browse more optics and light tools and all physics calculators.
At minimum deviation the ray crosses the prism symmetrically, which makes the geometry simple enough to measure the refractive index accurately.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026