Total Internal Reflection Angle Calculator

About this calculator

Total internal reflection occurs when light traveling from a denser medium into a less dense one strikes the boundary at an angle steeper than a threshold called the critical angle, at which point all the light reflects back instead of refracting through. The critical angle is found with θc = arcsin(n₂ ÷ n₁), where n₁ is the refractive index of the denser medium the light starts in and n₂ is the refractive index of the medium it would otherwise enter — this only has a solution when n₁ is greater than n₂.

Optical and fiber-optic engineers rely on total internal reflection to keep light confined inside a fiber core as it travels long distances with minimal loss, which is why the critical angle between the core and cladding materials is a key design parameter. The same principle explains everyday optical effects — like the shimmering underwater "mirror" seen when looking up at a steep angle through a water surface, or how prisms and binoculars redirect light without a reflective coating.