When applied to problems of electromagnetic radiation, ray tracing often relies on 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 theory does not describe phenomena such as interference and diffraction, which require wave theory (involving the phase of the wave).
Ray tracing works by assuming that the particle or wave can be modeled as a large number of very narrow beams (rays), and that there exists some distance, possibly very small, over which such a ray is locally straight. The ray tracer will advance the ray over his distance, and then use a local derivative of the medium to calculate the ray's new direction. From this location, a new ray is sent out and the process is repeated until a complete path is generated. If the simulation includes solid objects, the ray may be tested for intersection with them at each step, making adjustments to the ray's direction if a collision is found. Other properties of the ray may be altered as the simulation advances as well, such as intensity, wavelength, or polarization. The process is repeated with as many rays as are necessary to understand the behavior of the system.
One particular form of ray tracing is radio signal ray tracing, which traces radio signals, modeled as rays, through the ionosphere where they are refracted and/or reflected back to the Earth. This form of ray tracing involves the integration of differential equations that describe the propagation of electromagnetic waves through dispersive and anisotropic media such as the ionosphere. An example of physics-based radio signal ray tracing is shown to the right. Radio communicators use ray tracing to help determine the precise behavior of radio signals as they propagate through the ionosphere.
The image at the right illustrates the complexity of the situation. Unlike optical ray tracing where the medium between objects typically has a constant refractive index, signal ray tracing must deal with the complexities of a spatially varying refractive index, where changes in ionospheric electron densities influence the refractive index and hence, ray trajectories. Two sets of signals are broadcast at two different elevation angles. When the main signal penetrates into the ionosphere, the magnetic field splits the signal into two component waves which are separately ray traced through the ionosphere. The ordinary wave (red) component follows a path completely independent of the extraordinary wave (green) component.
Sound velocity in the ocean varies with depth due to changes in density and temperature, reaching a local minimum near a depth of 800–1000 meters. This local minimum, called the SOFAR channel, acts as a waveguide, as sound tends to bend towards it. Ray tracing may be used to calculate the path of sound through the ocean up to very large distances, incorporating the effects of the SOFAR channel, as well as reflections and refractions off the ocean surface and bottom. From this, locations of high and low signal intensity may be computed, which are useful in the fields of ocean acoustics, underwater acoustic communication, and acoustic thermometry.