In mathematics, Fresnel's wave surface, found by Augustin-Jean Fresnel in 1822, is a quartic surface describing the propagation of light in an optically biaxial crystal. Wave surfaces are special cases of tetrahedroids which are in turn special cases of Kummer surfaces.
In projective coordinates (w:x:y:z) the wave surface is given by
They are used in the treatment of conical refractions.
Augustin-Jean Fresnel was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theory, from the late 1830s until the end of the 19th century. He is perhaps better known for inventing the catadioptric (reflective/refractive) Fresnel lens and for pioneering the use of "stepped" lenses to extend the visibility of lighthouses, saving countless lives at sea. The simpler dioptric stepped lens, first proposed by Count Buffon and independently reinvented by Fresnel, is used in screen magnifiers and in condenser lenses for overhead projectors.
Diffraction is 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 secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.
The Fresnel equations describe the reflection and transmission of light when incident on an interface between different optical media. They were deduced by French engineer and physicist Augustin-Jean Fresnel who was the first to understand that light is a transverse wave, when no one realized that the waves were electric and magnetic fields. For the first time, polarization could be understood quantitatively, as Fresnel's equations correctly predicted the differing behaviour of waves of the s and p polarizations incident upon a material interface.
In optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
In physics, total internal reflection (TIR) is the phenomenon in which waves arriving at the interface (boundary) from one medium to another are not refracted into the second ("external") medium, but completely reflected back into the first ("internal") medium. It occurs when the second medium has a higher wave speed than the first, and the waves are incident at a sufficiently oblique angle on the interface. For example, the water-to-air surface in a typical fish tank, when viewed obliquely from below, reflects the underwater scene like a mirror with no loss of brightness (Fig. 1).
Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. Fermat's principle states that the path taken by a ray between two given points is the path that can be traveled in the least time.
In electrodynamics, elliptical polarization is the polarization of electromagnetic radiation such that the tip of the electric field vector describes an ellipse in any fixed plane intersecting, and normal to, the direction of propagation. An elliptically polarized wave may be resolved into two linearly polarized waves in phase quadrature, with their polarization planes at right angles to each other. Since the electric field can rotate clockwise or counterclockwise as it propagates, elliptically polarized waves exhibit chirality.
In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. The term linear polarization was coined by Augustin-Jean Fresnel in 1822. See polarization and plane of polarization for more information.
Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air. In optics, the law is used in ray tracing to compute the angles of incidence or refraction, and in experimental optics to find the refractive index of a material. The law is also satisfied in meta-materials, which allow light to be bent "backward" at a negative angle of refraction with a negative refractive index.
Baron Siméon Denis Poisson FRS FRSE was a French mathematician and physicist who worked on statistics, complex analysis, partial differential equations, the calculus of variations, analytical mechanics, electricity and magnetism, thermodynamics, elasticity, and fluid mechanics. Moreover, he predicted the Arago spot in his attempt to disprove the wave theory of Augustin-Jean Fresnel.
Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are described as birefringent or birefractive. The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with non-cubic crystal structures are often birefringent, as are plastics under mechanical stress.
In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with а trivial canonical bundle and irregularity zero. An (algebraic) K3 surface over any field means a smooth proper geometrically connected algebraic surface that satisfies the same conditions. In the Enriques–Kodaira classification of surfaces, K3 surfaces form one of the four classes of minimal surfaces of Kodaira dimension zero. A simple example is the Fermat quartic surface
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 circumstances.
In crystal optics, the index ellipsoid is a geometric construction which concisely represents the refractive indices and associated polarizations of light, as functions of the orientation of the wavefront, in a doubly-refractive crystal. When this ellipsoid is cut through its center by a plane parallel to the wavefront, the resulting intersection is an ellipse whose major and minor semiaxes have lengths equal to the two refractive indices for that orientation of the wavefront, and have the directions of the respective polarizations as expressed by the electric displacement vector D. The principal semiaxes of the index ellipsoid are called the principal refractive indices.
In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation.
In algebraic geometry, a tetrahedroid is a special kind of Kummer surface studied by Cayley, with the property that the intersections with the faces of a fixed tetrahedron are given by two conics intersecting in four nodes. Tetrahedroids generalize Fresnel's wave surface.
In fluid dynamics, the mild-slope equation describes the combined effects of diffraction and refraction for water waves propagating over bathymetry and due to lateral boundaries—like breakwaters and coastlines. It is an approximate model, deriving its name from being originally developed for wave propagation over mild slopes of the sea floor. The mild-slope equation is often used in coastal engineering to compute the wave-field changes near harbours and coasts.
In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4.
In projective geometry, a desmic system is a set of three tetrahedra in 3-dimensional projective space, such that any two are desmic. It was introduced by Stephanos. The three tetrahedra of a desmic system are contained in a pencil of quartic surfaces.
Conical refraction is an optical phenomenon in which a ray of light, passing through a biaxial crystal along certain directions, is transformed into a hollow cone of light. There are two possible conical refractions, one internal and one external. For internal refraction, there are 4 directions, and for external refraction, there are 4 other directions.
