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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 formula for vertex correction is = (), where F c is the power corrected for vertex distance, F is the original lens power, and x is the change in vertex distance in meters.
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.
Example. Consider a pair of spectacles to correct for myopia with a prescription of −1.00 m −1 in one eye and −4.00 m −1 in the other. Suppose that for both eyes the other parameters are identical, namely t = 1 mm = 0.001 m, n = 1.6, P = 5 m −1, and h = 15 mm = 0.015 m.
The De Broglie relations give the relation between them: ϕ = h f 0 {\displaystyle \phi =hf_ {0}\,\!} Photon momentum. p = momentum of photon (kg m s −1) f = frequency of photon (Hz = s −1) λ = wavelength of photon (m) The De Broglie relations give: p = h f / c = h / λ {\displaystyle p=hf/c=h/\lambda \,\!}
For example, repeated multiplication, assuming no correlation, gives f = A B C ; ( σ f f ) 2 ≈ ( σ A A ) 2 + ( σ B B ) 2 + ( σ C C ) 2 . {\displaystyle f=ABC;\qquad \left({\frac {\sigma _{f}}{f}}\right)^{2}\approx \left({\frac {\sigma _{A}}{A}}\right)^{2}+\left({\frac {\sigma _{B}}{B}}\right)^{2}+\left({\frac {\sigma _{C}}{C}}\right)^{2}.}
The free air correction is calculated from Newton's Law, as a rate of change of gravity with distance: g = G M R 2 d g d R = − 2 G M R 3 = − 2 g R {\displaystyle {\begin{aligned}g&={\frac {GM}{R^{2}}}\\{\frac {dg}{dR}}&=-{\frac {2GM}{R^{3}}}=-{\frac {2g}{R}}\end{aligned}}}
Spherical aberration of collimated light incident on a concave spherical mirror. In optics, spherical aberration ( SA) is a type of aberration found in optical systems that have elements with spherical surfaces. This phenomenon commonly affects lenses and curved mirrors, as these components are often shaped in a spherical manner for ease of ...
It can readily be seen that the formula above for motion along the equator follows from the more general equation below for any latitude where along the equator v = 0.0 and = a r = 2 Ω u cos ϕ + u 2 + v 2 R {\displaystyle a_{r}=2\Omega u\cos \phi +{\frac {u^{2}+v^{2}}{R}}}
In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution.