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A prism of power 1 Δ would produce 1 unit of displacement for an object held 100 units from the prism. Thus a prism of 1 Δ would produce 1 cm visible displacement at 100 cm, or 1 meter. This can be represented mathematically as: = where is the amount of prism correction in prism dioptres, and is the angle of deviation of the light.
The formula for iseikonic lenses (without cylinder) is: = (()) where: t = center thickness (in metres); n = refractive index; P = front base curve (in 1/metres); h = vertex distance (in metres);
1 m −1. Illustration of the relationship between optical power in dioptres and focal length in metres. A dioptre ( British spelling) or diopter ( American spelling ), symbol dpt, is a unit of measurement with dimension of reciprocal length, equivalent to one reciprocal metre, 1 dpt = 1 m−1. It is normally used to express the optical power ...
Prandtl–Glauert transformation. The Prandtl–Glauert transformation is a mathematical technique which allows solving certain compressible flow problems by incompressible -flow calculation methods. It also allows applying incompressible-flow data to compressible-flow cases.
Explanation of the cosine in the first term. The force of gravity and the normal force. The resultant force acts as the required centripetal force. The mathematical derivation for the Eötvös effect for motion along the Equator explains the factor 2 in the first term of the Eötvös correction formula.
In optics, Cauchy's transmission equation is an empirical relationship between the refractive index and wavelength of light for a particular transparent material. It is named for the mathematician Augustin-Louis Cauchy, who originally defined it in 1830 in his article "The refraction and reflection of light". [1]
Eötvös rule. The Eötvös rule, named after the Hungarian physicist Loránd (Roland) Eötvös (1848–1919) enables the prediction of the surface tension of an arbitrary liquid pure substance at all temperatures. The density, molar mass and the critical temperature of the liquid have to be known. At the critical point the surface tension is zero.
where the correction due to the Eötvös effect, A, can be expressed as follows: A = − 1 g ( 2 Ω u ¯ cos ϕ + u ¯ 2 + v ¯ 2 r ) , {\displaystyle A=-{\frac {1}{g}}\left(2\Omega {\overline {u}}\cos \phi +{\frac {{\overline {u}}^{2}+{\overline {v}}^{2}}{r}}\right),}
Fine structure. Interference fringes, showing fine structure (splitting) of a cooled deuterium source, viewed through a Fabry–Pérot interferometer. In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation.
In condensed matter and atomic physics, Van Vleck paramagnetism refers to a positive and temperature -independent contribution to the magnetic susceptibility of a material, derived from second order corrections to the Zeeman interaction. The quantum mechanical theory was developed by John Hasbrouck Van Vleck between the 1920s and the 1930s to ...