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Optical Path Length
In optics, optical path length (OPL, denoted ''Λ'' in equations), also known as optical length or optical distance, is the product of the geometric length of the optical path followed by light and the refractive index of homogeneous medium through which a light ray propagates; for inhomogeneous optical media, the product above is generalized as a path integral as part of the ray tracing procedure. A difference in OPL between two paths is often called the optical path difference (OPD). OPL and OPD are important because they determine the phase of the light and governs interference and diffraction of light as it propagates. Formulation In a medium of constant refractive index, ''n'', the OPL for a path of geometrical length ''s'' is just :\mathrm = n s .\, If the refractive index varies along the path, the OPL is given by a line integral :\mathrm = \int_C n \mathrm d s,\quad where ''n'' is the local refractive index as a function of distance along the path ''C''. An electroma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optics
Optics is the 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. Optics usually describes the behaviour of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties. Most optical phenomena can be accounted for by using the classical electromagnetic description of light. Complete electromagnetic descriptions of light are, however, often difficult to apply in practice. Practical optics is usually done using simplified models. 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. Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Shift
In physics and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or 2\pi as the variable t completes a full period. This convention is especially appropriate for a sinusoidal function, since its value at any argument t then can be expressed as \phi(t), the sine of the phase, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.) Usually, whole turns are ignored when expressing the phase; so that \phi(t) is also a periodic function, with the same period as F, that repeatedly scans the same range of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Depth
In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to ''transmitted'' radiant power through a material. Thus, the larger the optical depth, the smaller the amount of transmitted radiant power through the material. Spectral optical depth or spectral optical thickness is the natural logarithm of the ratio of incident to transmitted spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged. In chemistry, a closely related quantity called "absorbance" or "decadic absorbance" is used instead of optical depth: the common logarithm of the ratio of incident to transmitted radiant power through a material, that is the optical depth divided by ln 10. Mathematical definitions Optical depth O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamiltonian Optics
Hamiltonian opticsH. A. Buchdahl, ''An Introduction to Hamiltonian Optics'', Dover Publications, 1993, . and Lagrangian opticsVasudevan Lakshminarayanan et al., ''Lagrangian Optics'', Springer Netherlands, 2011, . are two formulations of geometrical optics which share much of the mathematical formalism with Hamiltonian mechanics and Lagrangian mechanics. Hamilton's principle In physics, Hamilton's principle states that the evolution of a system \left(q_1,\dots,q_N\right) described by N generalized coordinates between two specified states at two specified parameters ''σ''''A'' and ''σ''''B'' is a stationary point (a point where the variation is zero) of the action functional, or \delta S= \delta\int_^ L\left(q_1,\cdots,q_N,\dot_1,\cdots,\dot_N,\sigma\right)\, d\sigma=0 where \dot_k=dq_k/d\sigma and L is the Lagrangian. Condition \delta S=0 is valid if and only if the Euler-Lagrange equations are satisfied, i.e., \frac - \frac\frac = 0 with k = 1, \dots, N. The momentum is def ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian Optics
Hamiltonian opticsH. A. Buchdahl, ''An Introduction to Hamiltonian Optics'', Dover Publications, 1993, . and Lagrangian opticsVasudevan Lakshminarayanan et al., ''Lagrangian Optics'', Springer Netherlands, 2011, . are two formulations of geometrical optics which share much of the mathematical formalism with Hamiltonian mechanics and Lagrangian mechanics. Hamilton's principle In physics, Hamilton's principle states that the evolution of a system \left(q_1,\dots,q_N\right) described by N generalized coordinates between two specified states at two specified parameters ''σ''''A'' and ''σ''''B'' is a stationary point (a point where the Calculus of variations, variation is zero) of the action (physics), action functional (mathematics), functional, or \delta S= \delta\int_^ L\left(q_1,\cdots,q_N,\dot_1,\cdots,\dot_N,\sigma\right)\, d\sigma=0 where \dot_k=dq_k/d\sigma and L is the Lagrangian. Condition \delta S=0 is valid if and only if the Euler-Lagrange equations are satisfied, i.e., ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Air Mass (astronomy)
In astronomy, air mass or airmass is a measure of the amount of air along the line of sight when observing a star or other celestial source from below Earth's atmosphere ( Green 1992). It is formulated as the integral of air density along the light ray. As it penetrates the atmosphere, light is attenuated by scattering and absorption; the thicker atmosphere through which it passes, the greater the attenuation. Consequently, celestial bodies when nearer the horizon appear less bright than when nearer the zenith. This attenuation, known as atmospheric extinction, is described quantitatively by the Beer–Lambert law. "Air mass" normally indicates ''relative air mass'', the ratio of absolute air masses (as defined above) at oblique incidence relative to that at zenith. So, by definition, the relative air mass at the zenith is 1. Air mass increases as the angle between the source and the zenith increases, reaching a value of approximately 38 at the horizon. Air mass can be less th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Optical Ray
In optics a ray is an 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. 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. Ray tracing uses approximate solutions to Maxwell's equations that are valid as long as the light waves propagate through and around objects whose dimensions are much greater than the light's wavelength. ''Ray optics'' or ''geometrical optics'' does not describe phenomena such as diffraction, which require wave optics theory. Some wave phenomena such as interference can be modeled in limited circumstances by adding phase to the ray model. Definition A li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glass
Glass is a non-crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of the molten form; some glasses such as volcanic glass are naturally occurring. The most familiar, and historically the oldest, types of manufactured glass are "silicate glasses" based on the chemical compound silica (silicon dioxide, or quartz), the primary constituent of sand. Soda–lime glass, containing around 70% silica, accounts for around 90% of manufactured glass. The term ''glass'', in popular usage, is often used to refer only to this type of material, although silica-free glasses often have desirable properties for applications in modern communications technology. Some objects, such as drinking glasses and eyeglasses, are so commonly made of silicate-based glass that they are simply called by the name of the material. Despite bei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, , where ''θ''1 and ''θ''2 are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices ''n''1 and ''n''2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity ( Fresnel's equations) and Brewster's angle. The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that medium is , where ''Π... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coherence (physics)
In physics, two wave sources are coherent if their frequency and waveform are identical. Coherence is an ideal property of waves that enables stationary (i.e., temporally or spatially constant) interference. It contains several distinct concepts, which are limiting cases that never quite occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics. More generally, coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets. Interference is the addition, in the mathematical sense, of wave functions. A single wave can interfere with itself, but this is still an addition of two waves (see Young's slits experiment). Constructive or destructive interference are limit cases, and two waves always interfere, even if the result of the addition is complicated or not remarkable. When interfering, two waves can add together to create a wave of g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Principle
Fermat's principle, also known as the principle of least time, is the link between ray optics and wave optics. In its original "strong" form, 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 order to be true in all cases, this statement must be weakened by replacing the "least" time with a time that is " stationary" with respect to variations of the path — so that a deviation in the path causes, at most, a ''second-order'' change in the traversal time. To put it loosely, a ray path is surrounded by close paths that can be traversed in ''very'' close times. It can be shown that this technical definition corresponds to more intuitive notions of a ray, such as a line of sight or the path of a narrow beam. 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 initiall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a ''traveling wave''; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a '' standing wave''. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero. Waves are often described by a ''wave equation'' (standing wave field of two opposite waves) or a one-way wave equation for single wave propagation in a defined direction. Two types of waves are most commonly studied in classical physics. In a ''mechanical wave'', stress and strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (strain) in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
