When a ray hits an interface between two different transparent media, a portion is reflected, and another portion is transmitted; for the latter one, which is refracted, the propagation direction is generally modified according to the Snellius law of refraction. Figure 2 shows an example case for a ball lens, where only the refracted rays (which are usually stronger) have been drawn.

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To some extent, the deficits of geometrical optics can be amended by adding additional properties to rays. For example, one may attribute some optical power to each ray in a ray tracing simulation, taking into account power losses by absorption, incomplete reflection, etc. Similarly, one may add polarization properties and optical phases, for example for calculations on an interferometer setup. A simpler example is the calculation of different ray paths for different polarization directions, for example when analyzing a polarizing prism.

The main limitation of geometrical optics is that it ignores the wave properties of light, as described in wave optics. In particular, that means that the phenomena of diffraction, interference and polarization are not taken into account. This is not a substantial problem in many practical cases, where such effects may be negligible or can be taken into account separately. For example, one can study the optical aberrations of an imaging system with geometrical optics, being aware that even for perfect compensation of aberrations one will not obtain perfectly sharp images due to the diffraction limit. Anyway, aberrations often remain a more severe limitation than diffraction, which can thus often be safely ignored.

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Many useful relations can be derived based on such paraxial optics, which would otherwise be far more complicated or not analytically solvable at all.

On the surface of a flat mirror, a light ray is assumed to be reflected such that the output angle equals the input angle (both measured against the normal direction). For a curved mirror, one does that calculation based on a tangential flat plane. Figure 1 shows an example with reflection on a curved mirror.

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One may not only need to know the paths of multiple rays, but also derive various results from them. For example, ray tracing software may locate focal planes, calculate image magnification or estimates resulting optical intensities and colors.

Attempts for physical interpretations of light rays can be successful only to a quite limited extent. For example, rays were interpreted as the paths of some rapidly moving light particles, but this picture is not consistent with various observations. There are some similarities between geometrical light rays and real light beams, in particular with laser beams; for example, a laser beam can at least be relatively narrow and propagate along a straight line in a homogeneous medium. However, real light beams always have a finite transverse extension and exhibit the phenomenon of diffraction. Therefore, geometrical rays are only a rather abstract representation of actual light rays. Their behavior can be derived from wave optics in the limiting case of vanishing optical wavelength.

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Modified laws can be applied in the case of diffraction gratings, where additional diffracted rays emerge at different angles.

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Similarly, light propagation in multilayer coatings cannot be realistically analyzed with ray optics because interference effects are essential.

Ignoring diffraction becomes a serious problem when treating the propagation of light under conditions where it experiences tight confinement. For example, light propagation in single-mode fibers can not be realistically described at all with geometrical optics. One may still define the numerical aperture of a fiber, for example, based on geometrical optics, but such a quantity then has only a limited meaning for the actual propagation of light in the fiber. Even for multimode fibers with many modes, geometrical optics is only of quite limited utility. It can be completely misleading, for example, concerning optical phase delays of fiber modes [1].

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Ray tracing can be used for many purposes, for example for studying the detailed properties of imaging systems including their optical aberrations and effects of misalignment and imperfections from optical fabrication, or for the design of illumination systems.

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The propagation of light rays, as shown in the figures above, is calculated based on purely geometrical considerations. The used technique is called ray tracing and is usually applied with specialized optics software. The calculations can be geometrically exact, i.e., valid even for large incidence angles. Curved surface may have any geometrical shapes. Depending on the initial direction of a light ray, it may or may not hit a certain optical component.

In optically inhomogeneous media, light beams may propagate along curves instead of straight lines. In geometrical optics, one may correspondingly assume curved ray paths. An example is shown in Figure 3, showing the focusing of light in a gradient-index lens. The rays get deflected in the lens and may exactly meet in a focal point if the lens is optimized.

In many situations, one can use simplified equations which describe the approximate propagation of rays which stay close to the optical axis in terms of lateral offset and direction. Any terms of second or higher order are ignored; for example, one may consider the deflection of a ray at a curved lens surface as occurring in the plane touching the surface, ignoring a longitudinal position error of second order in the lateral offset.

Figure 4 shows how the beam radius, calculated with wave optics, evolves. Here, one can see that the beam radius in the focal point has a finite value related to diffraction.

Geometrical optics is a widely used concept in optics, where the propagation of light is described with geometric light rays. An equivalent term is ray optics.

Rays may be split up into multiple rays, e.g. due to partial reflection and transmission that interfaces, or due to multiple diffraction orders at gratings. In the context of diffuse optical scattering, one may employ stochastic methods for representing the scattered light with some limited number of rays. For multiple diffuse reflections, this may of course result in a very large number of rays to be treated.