Ray (optics)

Diagram of rays at a surface, where is the angle of refraction.
Simple ray diagram showing typical chief and marginal rays
Rays and wavefronts

Idealized geometrical model of light, obtained by choosing a curve that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow.

- Ray (optics)
Diagram of rays at a surface, where is the angle of refraction.

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As light travels through space, it oscillates in amplitude. In this image, each maximum amplitude crest is marked with a plane to illustrate the wavefront. The ray is the arrow perpendicular to these parallel surfaces.

Geometrical optics

As light travels through space, it oscillates in amplitude. In this image, each maximum amplitude crest is marked with a plane to illustrate the wavefront. The ray is the arrow perpendicular to these parallel surfaces.
Diagram of specular reflection
Illustration of Snell's Law

Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays.

Different apertures of a lens

Aperture

Aperture is a hole or an opening through which light travels.

Aperture is a hole or an opening through which light travels.

Different apertures of a lens
Definitions of Aperture in the 1707 Glossographia Anglicana Nova
Alvin Clark polishes the big Yerkes Observatory Great Refractor objective lens, with 40 inches 102 cm across, in 1896.
Diagram of decreasing aperture sizes (increasing f-numbers) for "full stop" increments (factor of two aperture area per stop)
The aperture range of a 50mm Minolta lens, f/1.4–f/16
Aperture mechanism of Canon 50mm f/1.8 II lens, with five blades
{{f/|32}} – small aperture and slow shutter
{{f/|5.6}} – large aperture and fast shutter
{{f/|22}} – small aperture and slower shutter (Exposure time: 1/80)
{{f/|3.5}} – large aperture and faster shutter (Exposure time: 1/2500)
Changing a camera's aperture value in half-stops, beginning with {{f/|256}} and ending with {{f/|1}}
Changing a camera's aperture diameter from zero to infinity

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.

Radiance L along a ray can be thought of as the amount of light traveling along all possible straight lines through a tube whose size is determined by its solid angle and cross-sectional area.

Light field

Vector function that describes the amount of light flowing in every direction through every point in space.

Vector function that describes the amount of light flowing in every direction through every point in space.

Radiance L along a ray can be thought of as the amount of light traveling along all possible straight lines through a tube whose size is determined by its solid angle and cross-sectional area.
Parameterizing a ray in 3D space by position (x, y, z) and direction (θ, ϕ).
Summing the irradiance vectors D1 and D2 arising from two light sources I1 and I2 produces a resultant vector D having the magnitude and direction shown
Radiance along a ray remains constant if there are no blockers.
Some alternative parameterizations of the 4D light field, which represents the flow of light through an empty region of three-dimensional space. Left: points on a plane or curved surface and directions leaving each point. Center: pairs of points on the surface of a sphere. Right: pairs of points on two planes in general (meaning any) position.
A downward-facing light source (F-F') induces a light field whose irradiance vectors curve outwards. Using calculus, Gershun could compute the irradiance falling on points (P1, P2) on a surface. )

The space of all possible light rays is given by the five-dimensional plenoptic function, and the magnitude of each ray is given by its radiance.

Coplanar condition of specular reflection, in which.

Specular reflection

Mirror-like reflection of waves, such as light, from a surface.

Mirror-like reflection of waves, such as light, from a surface.

Coplanar condition of specular reflection, in which.
Reflections on still water are an example of specular reflection.
Specular reflection from a wet metal sphere
Diffuse reflection from a marble ball
Esplanade of the Trocadero in Paris after rain. The layer of water exhibits specular reflection, reflecting an image of the Eiffel Tower and other objects.

The law of reflection states that a reflected ray of light emerges from the reflecting surface at the same angle to the surface normal as the incident ray, but on the opposing side of the surface normal in the plane formed by the incident and reflected rays.

A calcite crystal laid upon a graph paper with blue lines showing the double refraction

Birefringence

Optical property of a material having a refractive index that depends on the polarization and propagation direction of light.

Optical property of a material having a refractive index that depends on the polarization and propagation direction of light.

A calcite crystal laid upon a graph paper with blue lines showing the double refraction
In this example, optic axis along the surface is shown perpendicular to plane of incidence. Incoming light in the s polarization (which means perpendicular to plane of incidence - and so in this example becomes "parallel polarisation" to optic axis, thus is called extraordinary ray) sees a greater refractive index than light in the p polarization (which becomes ordinary ray because "perpendicular polarisation" to optic axis) and so s polarization ray is undergoing greater refraction on entering and exiting the crystal.
Doubly refracted image as seen through a calcite crystal, seen through a rotating polarizing filter illustrating the opposite polarization states of the two images.
Comparison of positive and negative birefringence : In positive birefringence (figure 1), the ordinary ray (p-polarisation in this case w.r.t. magenta-coloured plane of incidence), perpendicular to optic axis A is the fast ray (F) while the extraordinary ray (s-polarisation in this case and parallel to optic axis A) is the slow ray (S). In negative birefringence (figure 2), it is the reverse.
View from under the Sky Pool, London with coloured fringes due to stress birefringence of partially polarised skylight through a circular polariser
Sandwiched in between crossed polarizers, clear polystyrene cutlery exhibits wavelength-dependent birefringence
Reflective twisted-nematic liquid-crystal display. Light reflected by the surface (6) (or coming from a backlight) is horizontally polarized (5) and passes through the liquid-crystal modulator (3) sandwiched in between transparent layers (2, 4) containing electrodes. Horizontally polarized light is blocked by the vertically oriented polarizer (1), except where its polarization has been rotated by the liquid crystal (3), appearing bright to the viewer.
Color pattern of a plastic box with "frozen in" mechanical stress placed between two crossed polarizers
Birefringent rutile observed in different polarizations using a rotating polarizer (or analyzer)
Surface of the allowed k vectors for a fixed frequency for a biaxial crystal (see ).

Birefringence is responsible for the phenomenon of double refraction whereby a ray of light, when incident upon a birefringent material, is split by polarization into two rays taking slightly different paths.

Refraction of light at the interface between two media.

Angle of incidence (optics)

Refraction of light at the interface between two media.
Focusing X-rays with glancing reflection

In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal.

Ray tracing of a beam of light passing through a medium with changing refractive index. The ray is advanced by a small amount, and then the direction is re-calculated.

Ray tracing (physics)

Method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces.

Method for calculating the path of waves or particles through a system with regions of varying propagation velocity, absorption characteristics, and reflecting surfaces.

Ray tracing of a beam of light passing through a medium with changing refractive index. The ray is advanced by a small amount, and then the direction is re-calculated.
Radio signals traced from the transmitter at the left to the receiver at the right (triangles on the base of the 3D grid).
A ray tracing of acoustic wavefronts propagating through the varying density of the ocean. The path can be seen to oscillate about the SOFAR channel.
This ray tracing of seismic waves through the interior of the Earth shows that paths can be quite complicated, and reveals telling information about the structure of our planet.

Ray tracing solves the problem by repeatedly advancing idealized narrow beams called rays through the medium by discrete amounts.

The wavefronts of a plane wave are planes.

Wavefront

Set of all points having the same phase.

Set of all points having the same phase.

The wavefronts of a plane wave are planes.
Wavefronts change shape after going through a lens.
Rays and wavefronts

Such directions of energy flow, which are always perpendicular to the wavefront, are called rays creating multiple wavefronts.

Physical optics is used to explain effects such as diffraction

Physical optics

Branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid.

Branch of optics that studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid.

Physical optics is used to explain effects such as diffraction

The word "physical" means that it is more physical than geometric or ray optics and not that it is an exact physical theory.

Fig.1:Underwater plants in a fish tank, and their inverted images (top) formed by total internal reflection in the water-air surface.

Total internal reflection

Optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected back into the first ("internal") medium.

Optical phenomenon in which waves arriving at the interface (boundary) from one medium to another (e.g., from water to air) are not refracted into the second ("external") medium, but completely reflected back into the first ("internal") medium.

Fig.1:Underwater plants in a fish tank, and their inverted images (top) formed by total internal reflection in the water-air surface.
Fig.2:Repeated total internal reflection of a 405nm laser beam between the front and back surfaces of a glass pane. The color of the laser light itself is deep violet; but its wavelength is short enough to cause fluorescence in the glass, which re-radiates greenish light in all directions, rendering the zigzag beam visible.
Fig.3:Total internal reflection of light in a semicircular acrylic block.
Fig.7:Total internal reflection by the water's surface at the shallow end of a swimming pool. The broad bubble-like apparition between the swimmer and her reflection is merely a disturbance of the reflecting surface. Some of the space above the water level can be seen through "Snell's window" at the top of the frame.
Fig.8:A round "brilliant"-cut diamond.
Fig.9:Depiction of an incident sinusoidal plane wave (bottom) and the associated evanescent wave (top), under conditions of total internal reflection. The reflected wave is not shown.
Fig.10:Disembodied fingerprints visible from the inside of a glass of water, due to frustrated total internal reflection. The observed fingerprints are surrounded by white areas where total internal reflection occurs.
Fig.14:Porro prisms (labeled 2 & 3) in a pair of binoculars.
Johannes Kepler (1571–1630).
Christiaan Huygens (1629–1695).
Isaac Newton (1642/3–1726/7).
Pierre-Simon Laplace (1749–1827).
Étienne-Louis Malus (1775–1812).
Augustin-Jean Fresnel (1788–1827).
An Indian triggerfish and its total reflection in the water's surface.
Total reflection of a paintbrush by the water-air surface in a glass.
Total internal reflection of a green laser in the stem of a wine glass.

If the waves are capable of forming a narrow beam (Fig.2), the reflection tends to be described in terms of "rays" rather than waves; in a medium whose properties are independent of direction, such as air, water or glass, the "rays" are perpendicular to the associated wavefronts.