Critical Angle Calculator
Find the critical angle for total internal reflection between two media from their refractive indices.
How it works
θ_c = arcsin(n₂ / n₁) with n₁ > n₂
When light travels from a denser medium into a rarer one it bends away from the normal, and past a certain angle of incidence it cannot escape at all — it reflects entirely back inside. That threshold is the critical angle, set by the ratio of the two refractive indices. Total internal reflection above it is what makes optical fibres guide light and diamonds sparkle.
Worked example
From glass (n₁ = 1.5) into air (n₂ = 1.0): θ_c = arcsin(1.0 ÷ 1.5) = arcsin(0.667) ≈ 41.8°. Light hitting the glass–air surface more steeply than this is trapped inside.
Frequently asked questions
Why must n₁ be larger than n₂?
Total internal reflection only happens going from a denser (slower-light, higher-index) medium into a rarer one. If n₂ is equal to or larger than n₁ the ratio exceeds one, the arcsine is undefined, and no critical angle exists — light always refracts through.
What happens exactly at the critical angle?
The refracted ray bends to 90°, skimming right along the boundary. Below the critical angle light refracts and escapes; above it, none does — you get total internal reflection.
How is this used in optical fibres?
Fibres have a high-index core surrounded by a lower-index cladding. Light entering shallowly always strikes the core–cladding boundary above the critical angle, so it reflects internally over and over and travels the length of the fibre with very little loss.
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Educational estimate. Check the formula and units for your exact case.