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

Model of optics that describes light propagation in terms of rays.

- Geometrical optics

105 related topics


Focus (optics)

Eye focusing ideally collects all light rays from a point on an object into a corresponding point on the retina.
A demonstration of camera focus on different distances, showing a bamboo rooftop
Text on a page that is partially in focus, but mostly not in varying degrees

In geometrical optics, a focus, also called an image point, is a point where light rays originating from a point on the object converge.

Refractive index

Optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.

A ray of light being refracted in a plastic block
Refraction of a light ray
Thomas Young coined the term index of refraction.
Diamonds have a very high refractive index of 2.417.
A split-ring resonator array arranged to produce a negative index of refraction for microwaves
In optical mineralogy, thin sections are used to study rocks. The method is based on the distinct refractive indices of different minerals.
Light of different colors has slightly different refractive indices in water and therefore shows up at different positions in the rainbow.
In a prism, dispersion causes different colors to refract at different angles, splitting white light into a rainbow of colors.
The variation of refractive index with wavelength for various glasses. The shaded zone indicates the range of visible light.
The colors of a soap bubble are determined by the optical path length through the thin soap film in a phenomenon called thin-film interference.
Refraction of light at the interface between two media of different refractive indices, with n2 > n1. Since the phase velocity is lower in the second medium (v2 < v1), the angle of refraction θ2 is less than the angle of incidence θ1; that is, the ray in the higher-index medium is closer to the normal.
Total internal reflection can be seen at the air-water boundary.
The power of a magnifying glass is determined by the shape and refractive index of the lens.
The relation between the refractive index and the density of silicate and borosilicate glasses
A calcite crystal laid upon a paper with some letters showing double refraction
Birefringent materials can give rise to colors when placed between crossed polarizers. This is the basis for photoelasticity.
A gradient-index lens with a parabolic variation of refractive index (n) with radial distance (x). The lens focuses light in the same way as a conventional lens.
The principle of many refractometers
A handheld refractometer used to measure the sugar content of fruits
A differential interference contrast microscopy image of yeast cells

Since the refractive index of the ionosphere (a plasma), is less than unity, electromagnetic waves propagating through the plasma are bent "away from the normal" (see Geometric optics) allowing the radio wave to be refracted back toward earth, thus enabling long-distance radio communications.

Mirror image

Reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface.

Mount Hood reflected in Mirror Lake water.
A symmetrical urn and its mirror image
The word "FIRE" and its mirror image are displayed on the front of this fire engine

In physics, mirror images are investigated in the subject called geometrical 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.

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.

Optical aberration

Property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point.

Reflection from a spherical mirror. Incident rays (red) away from the center of the mirror produce reflected rays (green) that miss the focal point, F. This is due to spherical aberration.
Figure 1
Figure 2
Fig. 3a: Barrel distortion
Fig. 3b: Pincushion distortion
Figure 4
Image plane of a flat-top beam under the effect of the first 21 Zernike polynomials. The beam goes through an aperture of the same size, which is imaged onto this plane by an ideal lens.
Figure 5
Laser guide stars assist in the elimination of atmospheric distortion.

Aberration can be analyzed with the techniques of geometrical optics.

Ray (optics)

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.

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

Ray optics or geometrical optics does not describe phenomena such as diffraction, which require wave optics theory.

Fermat's principle

Fig.1:Fermat's principle in the case of refraction of light at a flat surface between (say) air and water. Given an object-point A in the air, and an observation point B in the water, the refraction point P is that which minimizes the time taken by the light to travel the path APB. If we seek the required value of x, we find that the angles α and β satisfy Snell's law.
Fig.2:Two points P and P&prime; on a path from A to B. For the purposes of Fermat's principle, the propagation time from P to P&prime; is taken as for a point-source at P, not (e.g.) for an arbitrary wavefront W passing through P. The surface &Sigma; (with unit normal n̂ at P&prime;) is the locus of points that a disturbance at P can reach in the same time that it takes to reach P&prime;; in other words, &Sigma; is the secondary wavefront with radius PP&prime;. (The medium is not assumed to be homogeneous or isotropic.)
Fig.3:An experiment demonstrating refraction (and partial reflection) of rays &mdash; approximated by, or contained in, narrow beams
Fig.4:Two iterations of Huygens' construction. In the first iteration, the later wavefront W&prime; is derived from the earlier wavefront W by taking the envelope of all the secondary wavefronts (gray arcs) expanding in a given time from all the points (e.g., P) on W. The arrows show the ray directions.
Pierre de Fermat (1607–1665)
Christiaan Huygens (1629–1695)
Pierre-Simon Laplace (1749–1827)
Thomas Young (1773–1829)
Augustin-Jean Fresnel (1788–1827)

Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics.

Paraxial approximation

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

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).

Gaussian 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.

Gaussian optics is a technique in geometrical optics that describes the behaviour of light rays in optical systems by using the paraxial approximation, in which only rays which make small angles with the optical axis of the system are considered.

Paradigm shift

Fundamental change in the basic concepts and experimental practices of a.

Kuhn used the duck-rabbit optical illusion, made famous by Wittgenstein, to demonstrate the way in which a paradigm shift could cause one to see the same information in an entirely different way.

The transition in optics from geometrical optics to physical optics with Augustin-Jean Fresnel's wave theory.