By Zencalcy Editorial TeamLast reviewed About us
When light tries to leave a dense medium into a lighter one at a shallow enough angle, it cannot refract out and reflects entirely. The threshold is the critical angle, the basis of fibre optics, prisms and diamond sparkle.
Angle beyond which total internal reflection occurs.
θ_c = arcsin(n₂ / n₁)
θ_c is the critical angle, n₁ the index of the denser medium and n₂ the index beyond it. The relation requires n₁ > n₂.
| Symbol | Meaning |
|---|---|
| θ_c | Critical angle measured from the normal. |
| n₁ | Refractive index of the denser medium. |
| n₂ | Refractive index of the less dense medium. |
For n₁ = 1.5 and n₂ = 1.0, sin θ_c = 0.667, so θ_c = 41.81°. Any ray steeper than that reflects back into the glass.
Continue with the Depth of Field Calculator, Diffraction Grating Calculator, or the Double Slit Interference Calculator — or browse more optics and light tools and all physics calculators.
Light entering a denser medium always has a real refracted angle. Total internal reflection requires travel from high index to low index.
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