At a Material Discontinuity between two different media, the wave vector is reinitialized using Snell’s law. First, the angle of incidence
θi is computed:
where ni is a unit vector in the direction of the incident ray and
ns is a unit vector normal to the material discontinuity.
where the ray propagates from the medium with refractive index n1 into the medium with refractive index
n2. Because the two media are nonabsorbing, the quantities
n1,
n2,
θi, and
θt are real-valued. If the media are weakly absorbing, the real parts of
n1 and
n2, are used. If the media are strongly absorbing, several corrections to Snell’s law and the Fresnel equations must be made, as discussed in
Refraction in Strongly Absorbing Media.