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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Optics

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.

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.

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The Nimrud lens
Alhazen (Ibn al-Haytham), "the father of Optics"
Reproduction of a page of Ibn Sahl's manuscript showing his knowledge of the law of refraction.
The first treatise about optics by Johannes Kepler, Ad Vitellionem paralipomena quibus astronomiae pars optica traditur (1604)
Cover of the first edition of Newton's Opticks (1704)
Geometry of reflection and refraction of light rays
Diagram of specular reflection
Illustration of Snell's Law for the case n1 < n2, such as air/water interface
A ray tracing diagram for a converging lens.
Images of black letters in a thin convex lens of focal length f are shown in red. Selected rays are shown for letters E, I and K in blue, green and orange, respectively. Note that E (at 2f) has an equal-size, real and inverted image; I (at f) has its image at infinity; and K (at f/2) has a double-size, virtual and upright image.
When oil or fuel is spilled, colourful patterns are formed by thin-film interference.
Conceptual animation of light dispersion through a prism. High frequency (blue) light is deflected the most, and low frequency (red) the least.
Dispersion: two sinusoids propagating at different speeds make a moving interference pattern. The red dot moves with the phase velocity, and the green dots propagate with the group velocity. In this case, the phase velocity is twice the group velocity. The red dot overtakes two green dots, when moving from the left to the right of the figure. In effect, the individual waves (which travel with the phase velocity) escape from the wave packet (which travels with the group velocity).
Linear polarization diagram
Circular polarization diagram
Elliptical polarization diagram
A polariser changing the orientation of linearly polarised light. In this picture, θ1 – θ0 = θi.
The effects of a polarising filter on the sky in a photograph. Left picture is taken without polariser. For the right picture, filter was adjusted to eliminate certain polarizations of the scattered blue light from the sky.
Experiments such as this one with high-power lasers are part of the modern optics research.
VLT's laser guide star
Model of a human eye. Features mentioned in this article are 1. vitreous humour 3. ciliary muscle, 6. pupil, 7. anterior chamber, 8. cornea, 10. lens cortex, 22. optic nerve, 26. fovea, 30. retina
The Ponzo Illusion relies on the fact that parallel lines appear to converge as they approach infinity.
Illustrations of various optical instruments from the 1728 Cyclopaedia
Photograph taken with aperture 32
Photograph taken with aperture 5
A colourful sky is often due to scattering of light off particulates and pollution, as in this photograph of a sunset during the October 2007 California wildfires.

The most common of these, geometric optics, treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces.

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.

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.

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.

A bundle of optical fibers

Optical fiber

Flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair.

Flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair.

A bundle of optical fibers
Fiber crew installing a 432-count fiber cable underneath the streets of Midtown Manhattan, New York City
A TOSLINK fiber optic audio cable with red light being shone in one end transmits the light to the other end
A wall-mount cabinet containing optical fiber interconnects. The yellow cables are single mode fibers; the orange and aqua cables are multi-mode fibers: 50/125 µm OM2 and 50/125 µm OM3 fibers respectively.
Daniel Colladon first described this "light fountain" or "light pipe" in an 1842 article titled "On the reflections of a ray of light inside a parabolic liquid stream". This particular illustration comes from a later article by Colladon, in 1884.
A frisbee illuminated by fiber optics
Light reflected from optical fiber illuminates exhibited model
Use of optical fiber in a decorative lamp or nightlight
Optical fiber types
The propagation of light through a multi-mode optical fiber.
A laser bouncing down an acrylic rod, illustrating the total internal reflection of light in a multi-mode optical fiber.
Experimental attenuation curve of low loss multimode silica and ZBLAN fiber. Black triangle points and gray arrows illustrate a four order of magnitude reduction in the attenuation of silica optical fibers over four decades from ~1000 dB/km in 1965 to ~0.17 dB/km in 2005.
Theoretical loss spectra (attenuation, dB/km) for Silica optical fiber (dashed blue line) and typical ZBLAN optical fiber (solid gray line) as function of wavelength (microns).
Specular reflection
Diffuse reflection
The P4O10 cagelike structure—the basic building block for phosphate glass
Illustration of the modified chemical vapor deposition (inside) process
Cross-section of a fiber drawn from a D-shaped preform
An optical fiber cable
ST connectors on multi-mode fiber
An aerial optical fiber splice enclosure lowered during installation. The individual fibers are fused together and stored within the enclosure for protection from damage

In a step-index multi-mode fiber, rays of light are guided along the fiber core by total internal reflection.

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.

The image side of the lens of an SLR camera; the exit pupil is the light area in the middle of the lens.

Exit pupil

Virtual aperture in an optical system.

Virtual aperture in an optical system.

The image side of the lens of an SLR camera; the exit pupil is the light area in the middle of the lens.
The aperture of this system is the edge of the objective lens. The exit pupil is an image of it.
The small exit pupil of a 25×30 telescope and large exit pupils of 9×63 binoculars suitable for use in low light
The exit pupil appears as a white disc on the eyepiece lens of these 8×30 binoculars. Its diameter is 30 ÷ 8 = 3.75 mm.

Only rays which pass through this virtual aperture can exit the system.

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.

The error associated with the paraxial approximation. In this plot the cosine is approximated by 1 - θ2/2.

Paraxial approximation

Small-angle approximation used in Gaussian optics and ray tracing of light through an optical system .

Small-angle approximation used in Gaussian optics and ray tracing of light through an optical system .

The error associated with the paraxial approximation. In this plot the cosine is approximated by 1 - θ2/2.

A paraxial ray is a ray which makes a small angle (θ) to the optical axis of the system, and lies close to the axis throughout the system.

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.