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Critical Angle for Total Internal Reflection

Also known as total internal reflection angle

sin⁡θc=n2n1\sin\theta_c = \frac{n_2}{n_1}

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Set the refracted angle in Snell's law to 90° — the ray skimming along the surface — and you get the critical angle. Hit the interface any more steeply and refraction is impossible: 100% of the light reflects back. For glass to air (n₁ = 1.5, n₂ = 1.0), θ_c = arcsin(0.667) ≈ 41.8°, which is why a 45° prism makes a perfect mirror with no silvering at all. Optical fibers exploit the same physics to pipe light for kilometers with almost no loss.

Critical Angle for Total Internal Reflection
sin⁡θc=n2n1\sin\theta_c = \frac{n_2}{n_1}
Where
  • θc\theta_c= Critical angle
  • n1n_1= Index of the denser medium
  • n2n_2= Index of the outer medium
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Part of this formula set

Refraction and total internal reflection

5 formulasSnell's law and the refractive index, with the critical angle, Brewster's angle and apparent depth that follow from bending light at a boundary.