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Smith–Helmholtz Invariant
In optics the Smith–Helmholtz invariant is an invariant quantity for paraxial beams propagating through an optical system. Given an object at height \bar and an axial ray passing through the same axial position as the object with angle u, the invariant is defined by :H = n\baru, where n is the refractive index. For a given optical system and specific choice of object height and axial ray, this quantity is invariant under refraction In physics, refraction is the redirection of a wave as it passes from one transmission medium, medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commo .... Therefore, at the ith conjugate image point with height \bar_i and refracted axial ray with angle u_i in medium with index of refraction n_i we have H = n_i \bar_i u_i. Typically the two points of most interest are the object point and the final image point. The Smith–Helmholtz invariant has a close ... [...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 optical instruments, instruments that use or Photodetector, detect it. Optics usually describes the behaviour of visible light, visible, ultraviolet, and infrared light. Light is a type of electromagnetic radiation, and 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 electromagnetism, classical electromagnetic description of light, however complete electromagnetic descriptions of light are 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 Ray (optics), rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics is a more comprehensive mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paraxial Approximation
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). A paraxial ray is a ray that makes a small angle (''θ'') to the optical axis of the system, and lies close to the axis throughout the system. Generally, this allows three important approximations (for ''θ'' in radians) for calculation of the ray's path, namely: : \sin \theta \approx \theta,\quad \tan \theta \approx \theta \quad \text\quad\cos \theta \approx 1. The paraxial approximation is used in Gaussian optics and ''first-order'' ray tracing. Ray transfer matrix analysis is one method that uses the approximation. In some cases, the second-order approximation is also called "paraxial". The approximations above for sine and tangent do not change for the "second-order" paraxial approximation (the second term in their Taylor series expansion is zero), while for cosine the second order approximation is : \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electromagnetic Theory Of Propagation, Interference And Diffraction Of Light
In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interactions of atoms and molecules. Electromagnetism can be thought of as a combination of electrostatics and magnetism, which are distinct but closely intertwined phenomena. Electromagnetic forces occur between any two charged particles. Electric forces cause an attraction between particles with opposite charges and repulsion between particles with the same charge, while magnetism is an interaction that occurs between charged particles in relative motion. These two forces are described in terms of electromagnetic fields. Macroscopic charged objects are described in terms of Coulomb's law for electricity and Ampère's force law for magnetism; the Lorentz force describes microscopic charged particles. The electromagnetic force is responsible for ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refraction, refracted, when entering a material. This is described by Snell's law of refraction, , where and are the angle of incidence (optics), angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices and . The refractive indices also determine the amount of light that is reflectivity, reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity (Fresnel equations) and Brewster's angle. The refractive index, n, 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 me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refraction
In physics, refraction is the redirection of a wave as it passes from one transmission medium, medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and Wind wave, water waves also experience refraction. How much a wave is refracted is determined by the change in wave speed and the initial direction of wave propagation relative to the direction of change in speed. Optical Prism (optics), prisms and Lens (optics), lenses use refraction to redirect light, as does the human eye. The refractive index of materials varies with the wavelength of light,R. Paschotta, article ochromatic dispersion in th, accessed on 2014-09-08 and thus the angle of the refraction also varies correspondingly. This is called dispersion (optics), dispersion and causes prism (optics), prisms and rainbows to divide white light into its constituent spectral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abbe Sine Condition
In optics, the Abbe sine condition is a condition that must be fulfilled by a lens or other optical system in order for it to produce sharp images of off-axis as well as on-axis objects. It was formulated by Ernst Abbe in the context of microscopes. The Abbe sine condition says that the sine of the object-space angle \alpha_\mathrm should be proportional to the sine of the image space angle \alpha_\mathrm Furthermore, the ratio equals the magnification of the system multiplied by the ratio of refractive indices. In mathematical terms this is: \frac = \frac = \frac, M, where the variables (\alpha_\mathrm, \beta_\mathrm) are the angles (relative to the optic axis) of any two rays as they leave the object, and (\alpha_\mathrm, \beta_\mathrm) are the angles of the same rays where they reach the image plane (say, the film plane of a camera). For example, (\alpha_\mathrm, \alpha_\mathrm) might represent a paraxial ray (i.e., a ray nearly parallel with the optic axis), and (\beta_\m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrange Invariant
In optics the Lagrange invariant is a measure of the light propagating through an optical system. It is defined by :H = n\overliney - nu\overline, where and are the marginal ray height and angle respectively, and and are the chief ray height and angle. is the ambient refractive index. In order to reduce confusion with other quantities, the symbol may be used in place of . is proportional to the throughput of the optical system (related to étendue). For a given optical system, the Lagrange invariant is a constant throughout all space, that is, it is invariant upon refraction In physics, refraction is the redirection of a wave as it passes from one transmission medium, medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commo ... and transfer. The optical invariant is a generalization of the Lagrange invariant which is formed using the ray heights and angles of any two rays ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Etendue
Etendue or étendue (; ) is a property of light in an optical system, which characterizes how "spread out" the light is in area and angle. It corresponds to the beam parameter product (BPP) in Gaussian beam optics. Other names for etendue include acceptance, throughput, light grasp, light-gathering power, optical extent, and the AΩ product. ''Throughput'' and ''AΩ product'' are especially used in radiometry and radiative transfer where it is related to the view factor (or shape factor). It is a central concept in nonimaging optics. From the source point of view, etendue is the product of the area of the source and the solid angle that the system's entrance pupil subtends as seen from the source. Equivalently, from the system point of view, the etendue equals the area of the entrance pupil times the solid angle the source subtends as seen from the pupil. These definitions must be applied for infinitesimally small "elements" of area and solid angle, which must then b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
