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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)
After simplifying the final equation is found: F F c = 1 − x F ⇒ F c = F 1 − x F = 1 1 F − x ⇒ F = 1 1 F c + x {\displaystyle {\begin{aligned}&&{\frac {F}{F_{\text{c}}}}&=1-xF\\&\Rightarrow &F_{\text{c}}&={\frac {F}{1-xF}}={\frac {1}{{\frac {1}{F}}-x}}\\&\Rightarrow &F&={\frac {1}{{\frac {1}{F_{\text{c}}}}+x}}\end{aligned}}}
Mathematically, such a calculation could be expressed: B C K = M bol − M k {\displaystyle BC_{K}=M_{\text{bol}}-M_{k}} Where M K is the absolute magnitude value and BC K is the bolometric correction value in the K-band.
Aberration (astronomy) A diagram showing how the apparent position of a star viewed from the Earth can change depending on the Earth's velocity. The effect is typically much smaller than illustrated. In astronomy, aberration (also referred to as astronomical aberration, stellar aberration, or velocity aberration) is a phenomenon where celestial ...
Continuum mechanics. In nonideal fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in an incompressible and Newtonian fluid in laminar flow flowing through a long cylindrical pipe of constant cross section.
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}}}
The K-correction can be defined as follows M = m − 5 ( log 10 D L − 1 ) − K C o r r {\displaystyle M=m-5(\log _{10}{D_{L}}-1)-K_{Corr}\!\,} I.E. the adjustment to the standard relationship between absolute and apparent magnitude required to correct for the redshift effect. [4]
Additional terms are sometimes added to make the calculation even more precise. Sometimes the Sellmeier equation is used in two-term form: [6] n 2 ( λ ) = A + B 1 λ 2 λ 2 − C 1 + B 2 λ 2 λ 2 − C 2 . {\displaystyle n^{2}(\lambda )=A+{\frac {B_{1}\lambda ^{2}}{\lambda ^{2}-C_{1}}}+{\frac {B_{2}\lambda ^{2}}{\lambda ^{2}-C_{2}}}.}
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation , it is a special case of a more general formula in spherical trigonometry , the law of haversines , that relates the sides and angles of spherical triangles.
The linear map h → J(x) ⋅ h is known as the derivative or the differential of f at x . When m = n, the Jacobian matrix is square, so its determinant is a well-defined function of x, known as the Jacobian determinant of f. It carries important information about the local behavior of f.