In geometric optics, at a refractive boundary, the critical angle is the smallest angle of incidence at which total internal reflection occurs.

The angle of incidence is measured with respect to the normal at the refractive boundary. It is given by:

<math>\theta_c = \arcsin \left( \frac{n_2}{n_1} \right) <math>,

where θ_c is the critical angle, n₂ is the refractive index of the less dense medium, and n₁ is the refractive index of the denser medium.

Note: it's assumed that the incident ray is in the denser medium.

If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence.

For visible light travelling from glass into air (or vacuum), the critical angle is approximately 41°.

Source: from Federal Standard 1037C and from MIL-STD-188