Ray tracing (physics) in the context of "Snell's law"

In optics, a ray is an idealized geometrical model of light or other electromagnetic radiation, obtained by choosing a curve that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very complex optical systems to be analyzed mathematically or simulated by computer. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. Ray optics or geometrical optics does not describe phenomena such as diffraction, which require wave optics theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model.

An Amici prism, named for the astronomer Giovanni Battista Amici, is a type of compound dispersive prism used in spectrometers. The Amici prism consists of two triangular prisms in contact, with the first typically being made from a medium-dispersion crown glass, and the second from a higher-dispersion flint glass. Light entering the first prism is refracted at the first air–glass interface, refracted again at the interface between the two prisms, and then exits the second prism at near-normal incidence. The prism angles and materials are chosen such that one wavelength (colour) of light, the centre wavelength, exits the prism parallel to (but offset from) the entrance beam. The prism assembly is thus a direct-vision prism and is commonly used as such in hand-held spectroscopes. Other wavelengths are deflected at angles depending on the glass dispersion of the materials. Looking at a light source through the prism thus shows the optical spectrum of the source.

By 1860, Amici realized that one can join this type of prism back-to-back with a reflected copy of itself, producing a three-prism arrangement known as a double Amici prism. This doubling of the original prism increases the angular dispersion of the assembly and also has the useful property that the centre wavelength is refracted back into the direct line of the entrance beam. The exiting ray of the center wavelength is thus not only undeviated from the incident ray, but also experiences no translation (i.e. transverse displacement or offset) away from the incident ray's path.

An off-axis optical system is an optical system in which the optical axis of the aperture is not coincident with the mechanical center of the aperture. The principal applications of off-axis optical systems are to avoid obstruction of the primary aperture by secondary optical elements, instrument packages, or sensors, and to provide ready access to instrument packages or sensors at the focus. The engineering tradeoff of an off-axis optical system is an increase in image aberrations.

There are various theoretical models for aberration in off-axis optical systems. This involves various techniques including different types of equations for ray-tracing, and a goal can be optimizing the design.

In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens).

A paraxial ray is a ray that makes a small angle (θ) to the optical axis of the system, and lies close to the axis throughout the system. Generally, this allows three important approximations (for θ in radians) for calculation of the ray's path, namely:

In optics, optical path length (OPL, denoted Λ in equations), also known as optical length or optical distance, is the length that light needs to travel through a vacuum to create the same phase difference as it would have when traveling through a given medium. For a homogeneous medium through which the light ray propagates, it is calculated as taking the product of the geometric length of the optical path followed by light and the refractive index of the medium. For inhomogeneous optical media, the product above is generalized as a path integral as part of the ray tracing procedure. A difference in OPL between two paths is often called the optical path difference (OPD). OPL and OPD are important because they determine the phase of the light and govern interference and diffraction of light as it propagates.

In a medium of constant refractive index, n, the OPL for a path of geometrical length s is just