In
optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
a ray is an idealized geometrical model of
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
, obtained by choosing a
curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line (geometry), line, but that does not have to be Linearity, straight.
Intuitively, a curve may be thought of as the trace left by a moving point (ge ...
that is perpendicular to the ''
wavefront
In physics, the wavefront of a time-varying ''wave field'' is the set (locus) of all points having the same ''phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal freque ...
s'' of the actual light, and that points in the direction of
energy flow.
Rays are used to model the
propagation of light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 ter ...
through an optical system, by dividing the real
light field
The light field is a vector function that describes the amount of light flowing in every direction through every point in space. The space of all possible '' light rays'' is given by the five-dimensional plenoptic function, and the magnitude of ea ...
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
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
...
that are valid as long as the
light wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ligh ...
s propagate through and around objects whose dimensions are much greater than the light's
wavelength
In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
. ''
Ray optics
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of ''rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstanc ...
'' or ''
geometrical optics
Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of ''rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstan ...
'' does not describe phenomena such as
diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
, which require
wave optics
In physics, physical optics, or wave optics, is the branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid. This usage tends not to include effec ...
theory. Some wave phenomena such as
interference
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extr ...
can be modeled in limited circumstances by adding
phase
Phase or phases may refer to:
Science
*State of matter, or phase, one of the distinct forms in which matter can exist
*Phase (matter), a region of space throughout which all physical properties are essentially uniform
* Phase space, a mathematic ...
to the ray model.
Definition
A light ray is a line (
straight
Straight may refer to:
Slang
* Straight, slang for heterosexual
** Straight-acting, an LGBT person who does not exhibit the appearance or mannerisms of the gay stereotype
* Straight, a member of the straight edge subculture
Sport and games
* Str ...
or
curved
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.
Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that a ...
) that is
perpendicular
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...
to the light's
wavefront
In physics, the wavefront of a time-varying ''wave field'' is the set (locus) of all points having the same ''phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal freque ...
s; its
tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More ...
is
collinear
In geometry, collinearity of a set of points is the property of their lying on a single line. A set of points with this property is said to be collinear (sometimes spelled as colinear). In greater generality, the term has been used for aligned ...
with the
wave vector
In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction. Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength), ...
. Light rays in
homogeneous media are straight. They bend at the
interface
Interface or interfacing may refer to:
Academic journals
* ''Interface'' (journal), by the Electrochemical Society
* ''Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Linguistics''
* '' Inte ...
between two dissimilar
media
Media may refer to:
Communication
* Media (communication), tools used to deliver information or data
** Advertising media, various media, content, buying and placement for advertising
** Broadcast media, communications delivered over mass el ...
and may be curved in a medium in which the
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
changes.
Geometric optics
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
describes how rays propagate through an optical system. Objects to be 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 propagated to locate the corresponding point on the image.
A slightly more rigorous definition of a light ray follows from
Fermat's principle
Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. In its original "strong" form, Fermat's principle states that the path taken by a ray between two given points is the pat ...
, which states that the path taken between two points by a ray of light is the path that can be traversed in the least time.
Special rays
There are many special rays that are used in optical modelling to analyze an optical system. These are defined and described below, grouped by the type of system they are used to model.
Interaction with surfaces
![Ray optics diagram incidence reflection and refraction](https://upload.wikimedia.org/wikipedia/commons/b/b2/Ray_optics_diagram_incidence_reflection_and_refraction.svg)
*An is a ray of light that strikes a
surface
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is t ...
. The angle between this ray and the perpendicular or
normal Normal(s) or The Normal(s) may refer to:
Film and television
* ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson
* ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie
* ''Norma ...
to the surface is the
angle of incidence.
*The corresponding to a given incident ray, is the ray that represents the light reflected by the surface. The angle between the surface normal and the reflected ray is known as the
angle of reflection
Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The ' ...
. The Law of Reflection says that for a
specular
Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface.
The law of reflection states that a reflected ray of light emerges from the reflecting surface at the same angle to the surfac ...
(non-scattering) surface, the angle of reflection is always equal to the angle of incidence.
*The or transmitted ray corresponding to a given incident ray represents the light that is transmitted through the surface. The angle between this ray and the normal is known as the
angle of refraction
In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the ''vertex'' of the angle.
Angles formed by two rays lie in the plane that contains the rays. Angles are ...
, and it is given by
Snell's Law
Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
.
Conservation of energy
In physics and chemistry, the law of conservation of energy states that the total energy of an isolated system remains constant; it is said to be ''conserved'' over time. This law, first proposed and tested by Émilie du Châtelet, means th ...
requires that the power in the incident ray must equal the sum of the power in the refracted ray, the power in the reflected ray, and any power absorbed at the surface.
* If the material is
birefringent
Birefringence is the optics, optical property of a material having a refractive index that depends on the Polarization (waves), polarization and propagation direction of light. These optically anisotropic materials are said to be birefringent (or ...
, the refracted ray may split into ordinary and extraordinary rays, which experience different
indexes of refraction when passing through the birefringent material.
Optical systems
![marginal_vs_chief_ray](https://upload.wikimedia.org/wikipedia/commons/4/4c/Marginal_vs_chief_ray.svg)
*A meridional ray or tangential ray is a ray that is confined to the plane containing the system's
optical axis
An optical axis is a line along which there is some degree of rotational symmetry in an optical system such as a camera lens, microscope or telescopic sight.
The optical axis is an imaginary line that defines the path along which light propagat ...
and the object point from which the ray originated.
*A skew ray is a ray that does not propagate in a plane that contains both the object point and the optical axis. Such rays do not cross the optical axis anywhere, and are not parallel to it.
[
*The marginal ray (sometimes known as an ''a ray'' or a ''marginal axial ray'') in an optical system is the meridional ray that starts at the point where the object crosses the optical axis, and touches the edge of the ]aperture stop
In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane.
An opt ...
of the system.[, p. 2]
This ray is useful, because it crosses the optical axis again at the locations where an image will be formed. The distance of the marginal ray from the optical axis at the locations of the entrance pupil
In an optical system, the entrance pupil is the optical image of the physical aperture stop, as 'seen' through the front (the object side) of the lens system. The corresponding image of the aperture as seen through the back of the lens system is ...
and exit pupil
In optics, the exit pupil is a virtual aperture in an optical system. Only rays which pass through this virtual aperture can exit the system. The exit pupil is the image of the aperture stop in the optics that follow it. In a telescope or compoun ...
defines the sizes of each pupil (since the pupils are image
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
s of the aperture stop).
*The principal ray or chief ray (sometimes known as the ''b ray'') in an optical system is the meridional ray that starts at the edge of the object, and passes through the center of the aperture stop.[ This ray crosses the optical axis at the locations of the pupils. As such chief rays are equivalent to the rays in a pinhole camera. The distance between the chief ray and the optical axis at an image location defines the size of the image. The marginal and chief rays together define the ]Lagrange invariant
In optics the Lagrange invariant is a measure of the light propagating through an optical system. It is defined by
:H = n\overliney - nu\overline,
where and are the marginal ray height and angle respectively, and and are the chief ray height ...
, which characterizes the throughput or etendue
Etendue or étendue (; ) is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue include a ...
of the optical system.[Greivenkamp (2004), p. 2]
Some authors define a "principal ray" for ''each'' object point. The principal ray starting at a point on the edge of the object may then be called the ''marginal principal ray''.[
*A sagittal ray or transverse ray from an off-axis object point is a ray that propagates in the plane that is perpendicular to the meridional plane and contains the principal ray.][ Sagittal rays intersect the pupil along a line that is perpendicular to the meridional plane for the ray's object point and passes through the optical axis. If the axis direction is defined to be the ''z'' axis, and the meridional plane is the ''y''-''z'' plane, sagittal rays intersect the pupil at ''yp''=0. The principal ray is both sagittal and meridional.][ All other sagittal rays are skew rays.
*A paraxial ray is a ray that makes a small angle to the optical axis of the system, and lies close to the axis throughout the system. Such rays can be modeled reasonably well by using the ]paraxial approximation
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 which makes a small angle (''θ'') to the optica ...
. When discussing ray tracing this definition is often reversed: a "paraxial ray" is then a ray that is modeled using the paraxial approximation, not necessarily a ray that remains close to the axis.
*A finite ray or real ray is a ray that is traced without making the paraxial approximation.[
* A parabasal ray is a ray that propagates close to some defined "base ray" rather than the optical axis. This is more appropriate than the paraxial model in systems that lack symmetry about the optical axis. In computer modeling, parabasal rays are "real rays", that is rays that are treated without making the paraxial approximation. Parabasal rays about the optical axis are sometimes used to calculate first-order properties of optical systems.]
Fiber optics
* A meridional ray is a ray that passes through the axis
An axis (plural ''axes'') is an imaginary line around which an object rotates or is symmetrical. Axis may also refer to:
Mathematics
* Axis of rotation: see rotation around a fixed axis
*Axis (mathematics), a designator for a Cartesian-coordinate ...
of an optical fiber
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to ...
.
* A skew ray is a ray that travels in a non-planar zig-zag path and never crosses the axis
An axis (plural ''axes'') is an imaginary line around which an object rotates or is symmetrical. Axis may also refer to:
Mathematics
* Axis of rotation: see rotation around a fixed axis
*Axis (mathematics), a designator for a Cartesian-coordinate ...
of an optical fiber
An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to ...
.
* A guided ray A guided ray (also bound ray or trapped ray) is a ray of light in a multi-mode optical fiber, which is confined by the core.
For step index fiber, light entering the fiber will be guided if it falls within the acceptance cone of the fiber, that i ...
, bound ray, or trapped ray is a ray in a multi-mode optical fiber
Multi-mode optical fiber is a type of optical fiber mostly used for communication over short distances, such as within a building or on a campus. Multi-mode links can be used for data rates up to 100 Gbit/s. Multi-mode fiber has a fairly large ...
, which is confined by the core
Core or cores may refer to:
Science and technology
* Core (anatomy), everything except the appendages
* Core (manufacturing), used in casting and molding
* Core (optical fiber), the signal-carrying portion of an optical fiber
* Core, the central ...
. For step index fiber, light entering the fiber will be guided if it makes an angle with the fiber axis that is less than the fiber's acceptance angle.
* A leaky ray or tunneling ray is a ray in an optical fiber that geometric optics predicts would totally reflect at the boundary between the core
Core or cores may refer to:
Science and technology
* Core (anatomy), everything except the appendages
* Core (manufacturing), used in casting and molding
* Core (optical fiber), the signal-carrying portion of an optical fiber
* Core, the central ...
and the cladding
Cladding is an outer layer of material covering another. It may refer to the following:
*Cladding (boiler), the layer of insulation and outer wrapping around a boiler shell
*Cladding (construction), materials applied to the exterior of buildings
...
, but which suffers loss due to the curved core boundary.
Geometrical optics
Ray tracing
See also
*Collimated beam
A collimated beam of light or other electromagnetic radiation has parallel rays, and therefore will spread minimally as it propagates. A perfectly collimated light beam, with no divergence, would not disperse with distance. However, diffraction pr ...
*Optical path
Optical path (OP) is the trajectory that a light ray follows as it propagates through an optical medium.
The geometrical optical-path length or simply geometrical path length (GPD) is the length of a segment in a given OP, i.e., the Euclidean dis ...
*Optical path length In optics, optical path length (OPL, denoted ''Λ'' in equations), also known as optical length or optical distance, is the product of the geometric length of the optical path followed by light and the refractive index of homogeneous medium through ...
*Paraxial approximation
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 which makes a small angle (''θ'') to the optica ...
*Pencil beam
In optics, a pencil or pencil of rays is a geometric construct used to describe a beam or portion of a beam of electromagnetic radiation or charged particles, typically in the form of a narrow beam ( conical or cylindrical).
Antennas which stro ...
*Ray transfer matrix analysis
Ray transfer matrix analysis (also known as ABCD matrix analysis) is a mathematical form for performing ray tracing calculations in sufficiently simple problems which can be solved considering only paraxial rays. Each optical element (surface, in ...
References
{{reflist, 30em
Geometrical optics
Fiber optics