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Prentice's rule, named so after the optician Charles F. Prentice, is a formula used to determine the amount of induced prism in a lens: = where: P is the amount of prism correction (in prism dioptres) c is decentration (the distance between the pupil centre and the lens's optical centre, in millimetres)
The first example is for unequal but near variances (=, =) and equal sample sizes (= =). Let A1 and A2 denote two random samples: Let A1 and A2 denote two random samples: A 1 = { 27.5 , 21.0 , 19.0 , 23.6 , 17.0 , 17.9 , 16.9 , 20.1 , 21.9 , 22.6 , 23.1 , 19.6 , 19.0 , 21.7 , 21.4 } {\displaystyle A_{1}=\{27.5,21.0,19.0,23.6,17.0,17.9,16.9,20.1 ...
The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis.
Bolometric correction is the correction made to the absolute magnitude of an object in order to convert an object's visible magnitude to its bolometric magnitude. Alternatively, the bolometric correction can be made to absolute magnitudes based on other wavelength bands beyond the visible electromagnetic spectrum. [4]
The Sellmeier equation is an empirical relationship between refractive index and wavelength for a particular transparent medium. The equation is used to determine the dispersion of light in the medium. It was first proposed in 1872 by Wolfgang Sellmeier and was a development of the work of Augustin Cauchy on Cauchy's equation for modelling ...
For example, for = 0.05 and m = 10, the Bonferroni-adjusted level is 0.005 and the Šidák-adjusted level is approximately 0.005116. One can also compute confidence intervals matching the test decision using the Šidák correction by using 100 ⋅ {\displaystyle \cdot } (1 − α) 1/ m % confidence intervals.
Sight is defined as the observation of the altitude, and sometimes also the azimuth, of a celestial body for a line of position; or the data obtained by such observation. [1] The mathematical basis of sight reduction is the circle of equal altitude. The calculation can be done by computer, or by hand via tabular methods and longhand methods.
The yellow sheet is the prism of a half-hyperbola corresponding to ν=-45°, whereas the red tube is an elliptical prism corresponding to μ=1. The blue sheet corresponds to z =1. The three surfaces intersect at the point P (shown as a black sphere) with Cartesian coordinates roughly (2.182, -1.661, 1.0).
Lorentz factor. where and v is the relative velocity between two inertial frames . For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames. As the relative velocity approaches the speed of light, γ → ∞. Time dilation (different times t and t' at the same position x in same inertial frame)
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. What remains to be explained is the cosine factor.