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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)
In geometry, an n-gonal antiprism or n-antiprism is a polyhedron composed of two parallel direct copies (not mirror images) of an n-sided polygon, connected by an alternating band of 2n triangles. They are represented by the Conway notation An . Antiprisms are a subclass of prismatoids, and are a (degenerate) type of snub polyhedron.
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 of a lens or curved mirror, which is a physical quantity equal to the reciprocal of the focal length ...
In the above formula for r s , if we put = / (Snell's law) and multiply the numerator and denominator by 1 / n 1 sin θ t , we obtain r s = − sin ( θ i − θ t ) sin ( θ i + θ t ) . {\displaystyle r_{\text{s}}=-{\frac {\sin(\theta _{\text{i}}-\theta _{\text{t}})}{\sin(\theta _{\text{i}}+\theta _{\text{t}})}}.}
For example, for decays of 132 Cs, 98.1% are ε ( electron capture) or β + ( positron) decays, and 1.9% are β − ( electron) decays. The partial decay constants can be calculated from the branching fraction and the half-life of 132 Cs (6.479 d), they are: 0.10 d −1 (ε + β +) and 0.0020 d −1 (β − ).
The application of Euler's continued fraction formula is straightforward: e x = 1 1 − x 1 + x − 1 2 x 1 + 1 2 x − 1 3 x 1 + 1 3 x − 1 4 x 1 + 1 4 x − ⋱ . {\displaystyle e^{x}={\cfrac {1}{1-{\cfrac {x}{1+x-{\cfrac {{\frac {1}{2}}x}{1+{\frac {1}{2}}x-{\cfrac {{\frac {1}{3}}x}{1+{\frac {1}{3}}x-{\cfrac {{\frac {1}{4}}x}{1+{\frac {1}{4 ...
Applications. There are many different effective medium approximations, each of them being more or less accurate in distinct conditions. Nevertheless, they all assume that the macroscopic system is homogeneous and, typical of all mean field theories, they fail to predict the properties of a multiphase medium close to the percolation threshold due to the absence of long-range correlations or ...
The formula for decay correcting is: = where is the original activity count at time zero, is the activity at time "t", "λ" is the decay constant, and "t" is the elapsed time.
A correction must also be made for fractionation. The fractionation correction converts the 14 C / 12 C ratio for the sample to the ratio it would have had if the material was wood, which has a δ 13 C value of -25‰. This is necessary because determining the age of the sample requires a comparison of the amount of 14
K correction converts measurements of astronomical objects into their respective rest frames. The correction acts on that object's observed magnitude (or equivalently, its flux ). Because astronomical observations often measure through a single filter or bandpass, observers only measure a fraction of the total spectrum , redshifted into the ...