Critical angle

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

Note 1: The angle of incidence is measured with respect to the normal at the refractive boundary.

Note 2: The critical angle is given by sin^-1(n₂/n₁) where θ_c is the critical angle, n ₂ is the refractive index of the less dense medium, and n ₁ is the refractive index of the denser medium.

Note 3: The incident ray is in the denser medium.

Note 4: If the incident ray is precisely at the critical angle, the refracted ray is tangent to the boundary at the point of incidence.

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