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Planck–Einstein equation and de Broglie wavelength relations. P = ( E/c, p) is the four-momentum, K = (ω/ c, k) is the four-wavevector, E = energy of particle. ω = 2π f is the angular frequency and frequency of the particle. ħ = h /2π are the Planck constants. c = speed of light. Schrödinger equation.
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 most general form of Cauchy's equation is. where n is the refractive index, λ is the wavelength, A, B, C, etc., are coefficients that can be determined for a material by fitting the equation to measured refractive indices at known wavelengths.
Now apply Snell's law to the ratio of sines to derive the formula for the refracted ray's direction vector: sin θ 2 = ( n 1 n 2 ) sin θ 1 = ( n 1 n 2 ) 1 − ( cos θ 1 ) 2 {\displaystyle \sin \theta _{2}=\left({\frac {n_{1}}{n_{2}}}\right)\sin \theta _{1}=\left({\frac {n_{1}}{n_{2}}}\right){\sqrt {1-\left(\cos \theta _{1}\right ...
Linearity. The Schrödinger equation is a linear differential equation, meaning that if two state vectors and are solutions, then so is any linear combination. of the two state vectors where a and b are any complex numbers. [13] : 25 Moreover, the sum can be extended for any number of state vectors.
The fine structure correction predicts that the Lyman-alpha line (emitted in a transition from n = 2 to n = 1) must split into a doublet. The total effect can also be obtained by using the Dirac equation.
Electromagnetic wave equation. The electromagnetic wave equation describes the propagation of electromagnetic waves through a medium or in a vacuum. The homogeneous form of the equation, written in terms of either the electric field E or the magnetic field B, takes the form: where c is the speed of light in the medium.
The equation for universal gravitation thus takes the form: =, where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.
The overall equation is Δ E ( r ) = E g a p + h 2 8 r 2 ( 1 / m e ∗ + 1 / m h ∗ ) . {\displaystyle \Delta E(r)=E_{\mathrm {gap} }+{\frac {h^{2}}{8r^{2}}}\left(1/m_{\mathrm {e} }^{*}+1/m_{\mathrm {h} }^{*}\right).}
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is