The paraxial approximation of Snell’s Law is a first order approximation that reduces the full form of Snell’s Law from
n sin(θ) = n’ sin(θ’)
to the linear relationship
n θ = n’ θ’
(where the primed quantities denote values after refraction), and is valid for very small angles (and thus rays that travel close to the optical axis).
OpticStudio uses these paraxial rays in the computation of paraxial data such as the EFL, F/#, and entrance pupil diameter. However, OpticStudio uses the full form of Snell’s Law in most calculations and analyses because not all surfaces can be properly defined by the power of the surface at the vertex, and to account for aberrations, which are deviations from this ideal ray. While the first order approximations might have been crucial to expediting calculations done by hand, the speed of modern computers makes the difference in calculation time inconsequential when compared to the benefits of using the full calculation for more accurate results.
Check out the knowledge base article Understanding Paraxial Ray Tracing for a more in-depth discussion on how paraxial and parabasal rays are defined and how they are used in OpticStudio.