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Critical Angle Calculator (Total Internal Reflection)

Find the critical angle above which light hitting a boundary undergoes total internal reflection, θc = arcsin(n2 / n1), from the refractive indices of the two media.

Critical angle (θc)
41.81°
Total internal reflection occurs when incidence angle is
greater than 41.81°

How it works

Total internal reflection (TIR) happens when light traveling through a denser medium hits a boundary with a less dense one at a steep enough angle that it reflects entirely back in rather than refracting out — the principle behind fiber optics, and why looking up through a calm water surface shows a bright circular window surrounded by a mirror-like underside. From Snell's law, n1·sin(θ1) = n2·sin(θ2), TIR's onset is exactly where the refracted ray would graze along the boundary itself (θ2 = 90°, so sin θ2 = 1), which solves to the closed form θc = arcsin(n2 / n1).

This only has a real solution when n1 is greater than n2 — light going from a denser medium into a less dense one. Entering a denser medium (n2 ≥ n1) always refracts through at some angle, so there's no critical angle in that direction, and this calculator requires n1 > n2 accordingly.

FAQ

Why does an optical fiber need a specific critical angle?

An optical fiber guides light down its core by total internal reflection off the boundary with its cladding (a lower-index layer surrounding the core) — any light ray hitting that boundary steeper than the critical angle keeps bouncing down the fiber instead of leaking out, which is exactly why fiber cores and claddings are manufactured to a specific refractive-index difference rather than an arbitrary one.

Does a bigger refractive-index gap give a bigger or smaller critical angle?

Smaller. A larger n1 relative to n2 (a bigger n1/n2 ratio) means n2/n1 is a smaller fraction, and arcsin of a smaller fraction is a smaller angle — so light trapped in a much denser medium, like diamond (n ≈ 2.42) surrounded by air, totally internally reflects starting from a shallower angle (about 24.4°) than light in ordinary glass (n ≈ 1.5) surrounded by air (about 41.8°).

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