Ray (optics)

In optics, a ray is a simplified geometric representation of light or other electromagnetic radiation. It is defined as a curve that runs perpendicular to the actual light's wavefronts and indicates the direction in which energy travels. By breaking a real light field into separate rays, these can be traced through an optical system using ray tracing techniques. This approach makes it possible to analyze or simulate even highly complex optical systems mathematically. Ray tracing relies on approximate solutions to Maxwell's equations, which work as long as the light waves move through or around objects much larger than the light's wavelength. Ray optics, also called geometrical optics, cannot explain phenomena like diffraction, which require wave optics. However, some wave effects, such as interference, can be partially modeled by adding phase information to the ray model.

A light ray is a line—either straight or curved—that is perpendicular to the light's wavefronts, with its tangent aligning with the wave vector. In uniform media, light rays travel in straight lines. They bend when crossing the boundary between two different media and may curve in a medium where the refractive index changes. Geometrical optics explains how rays move through an optical system. Objects being imaged are treated as collections of independent point sources, each producing spherical wavefronts and corresponding outward rays. Rays from each object point can be mathematically traced to find the matching point on the image. A more precise definition comes from Fermat's principle, which states that the path a light ray takes between two points is the one that can be traveled in the least time.

Several special rays are used in optical modeling to analyze systems. These are grouped by the type of system they model.

When a ray interacts with a surface, an incident ray is one that strikes the surface. The angle between this ray and the surface's normal is the angle of incidence. The reflected ray is the light bounced off the surface, and the angle between the surface normal and this ray is the angle of reflection. The Law of Reflection states that for a smooth, non-scattering surface, the angle of reflection always equals the angle of incidence. The refracted or transmitted ray is the light that passes through the surface. The angle between this ray and the normal is the angle of refraction, given by Snell's law. Energy conservation requires that the power in the incident ray equals the sum of the power in the refracted ray, the reflected ray, and any power absorbed at the surface. If the material is birefringent, the refracted ray can split into ordinary and extraordinary rays, each experiencing a different refractive index within the material.

In optical systems, a meridional or tangential ray stays within a plane that contains the system's optical axis. Such planes are called meridional or tangential planes. Some authors distinguish the tangential plane as a meridional plane that includes a specific object point. A skew or oblique ray does not travel in a meridional plane; it never crosses the optical axis and is not parallel to it. An axial ray is a meridional ray that starts from an on-axis object point. The marginal ray, sometimes called an a ray or marginal axial ray, begins from an on-axis object point and touches the edge of the system's aperture stop. This ray is useful because it crosses the optical axis again where a real image forms, or its backward extension crosses the axis where a virtual image forms. Since the entrance and exit pupils are images of the aperture stop, for a real image pupil, the lateral distance of the marginal ray from the optical axis at the pupil defines the pupil size. For a virtual image pupil, an extended line forward along the marginal ray before the first optical element or backward after the last element determines the size of the entrance or exit pupil. The principal or chief ray, sometimes called the b ray, is a meridional ray that starts at an off-axis object point and passes through the center of the aperture stop. The distance between the chief ray (or its extension for a virtual image) and the optical axis at an image location defines the image size. This ray (or its forward and backward extensions for virtual image pupils) crosses the optical axis at the entrance and exit pupils. The marginal and chief rays together define the Lagrange invariant, which characterizes the throughput or etendue of the system. Some authors define a principal ray for each object point, in which case the principal ray from an edge point of the object may be called the marginal principal ray. A sagittal or transverse ray from an off-axis object point is a skew ray that travels in the plane containing the principal ray from that point and perpendicular to the meridional plane that includes that point. This plane is called the sagittal plane. Because the principal ray changes angle as it is refracted or reflected by each optical interface, the sagittal plane changes after each interface.