Pierre de FermatPierre de Fermat (pjɛʁ də fɛʁma; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory.
Focal lengthThe focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly.
Problem of pointsThe problem of points, also called the problem of division of the stakes, is a classical problem in probability theory. One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value. The problem concerns a game of chance with two players who have equal chances of winning each round. The players contribute equally to a prize pot, and agree in advance that the first player to have won a certain number of rounds will collect the entire prize.
Huygens–Fresnel principleThe Huygens–Fresnel principle (named after Dutch physicist Christiaan Huygens and French physicist Augustin-Jean Fresnel) states that every point on a wavefront is itself the source of spherical wavelets, and the secondary wavelets emanating from different points mutually interfere. The sum of these spherical wavelets forms a new wavefront. As such, the Huygens-Fresnel principle is a method of analysis applied to problems of luminous wave propagation both in the far-field limit and in near-field diffraction as well as reflection.
Ray (optics)In optics, a ray is an idealized geometrical model of light or other electromagnetic radiation, obtained by choosing a curve that is perpendicular to the wavefronts of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation of light through an optical system, by dividing the real light field 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.
Fermat's principleFermat'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. First proposed by the French mathematician Pierre de Fermat in 1662, as a means of explaining the ordinary law of refraction of light (Fig. 1), Fermat's principle was initially controversial because it seemed to ascribe knowledge and intent to nature.
Point reflectionIn geometry, a point reflection (also called a point inversion or central inversion) is an transformation of affine space in which every point is reflected across a specific fixed point. A point reflection is an involution: applying it twice is the identity transformation. It is equivalent to a homothetic transformation with scale factor −1. The point of inversion is also called homothetic center. An object that is invariant under a point reflection is said to possess point symmetry; if it is invariant under point reflection through its center, it is said to possess central symmetry or to be centrally symmetric.
LensA lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (elements), usually arranged along a common axis. Lenses are made from materials such as glass or plastic and are ground, polished, or molded to the required shape. A lens can focus light to form an , unlike a prism, which refracts light without focusing.
Virtual imageIn optics, an image is defined as the collection of focus points of light rays coming from an object. A is the collection of focus points made by converging rays, while a virtual image is the collection of focus points made by extensions of diverging rays. In other words, a virtual image is found by tracing real rays that emerge from an optical device (lens, mirror, or some combination) backward to perceived or apparent origins of ray divergences.
Liquid oxygenLiquid oxygen—abbreviated LOx, LOX, LOXygen or Lox in the aerospace, submarine and gas industries—is the liquid form of molecular oxygen. It was used as the oxidizer in the first liquid-fueled rocket invented in 1926 by Robert H. Goddard, an application which has continued to the present. Liquid oxygen has a light or pale cyan color and is strongly paramagnetic: it can be suspended between the poles of a powerful horseshoe magnet. Liquid oxygen has a density of , slightly denser than liquid water, and is cryogenic with a freezing point of and a boiling point of at .
Curved mirrorA curved mirror is a mirror with a curved reflecting surface. The surface may be either convex (bulging outward) or concave (recessed inward). Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices. The most common non-spherical type are parabolic reflectors, found in optical devices such as reflecting telescopes that need to image distant objects, since spherical mirror systems, like spherical lenses, suffer from spherical aberration.
Reflection (mathematics)In mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its in the axis or plane of reflection. For example the mirror image of the small Latin letter p for a reflection with respect to a vertical axis (a vertical reflection) would look like q.
