Annus MirabilisEinstein in 1905
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special relativity

The equation explained

ν′=ν1−vVcos⁡φ1−(vV)2.\nu' = \nu \frac{1 - \frac{v}{V} \cos \varphi}{\sqrt{1 - \left( \frac{v}{V} \right)^2}} .
In wordsThe frequency of the incident light in the mirror's system is its frequency in the stationary system times one minus the speed over the velocity of light times the cosine of the angle of incidence, divided by the square root of one minus the square of that ratio.OverviewThe frequency of the incident light in the mirror's system: Doppler's principle of § 7, applied to the light that falls on the mirror.Full explanationThis completes the description of the incident light in kk: amplitude, direction and frequency. It is § 7's Doppler principle (p. 911) for the mirror moving with kk. The amplitude and the frequency change by the same factor.Every stepν′=ν1−cos⁡φvV1−(vV)2\nu' = \nu \frac{1 - \cos \varphi \frac{v}{V}}{\sqrt{1 - \left( \frac{v}{V} \right)^2}}Doppler's principle, from § 7 (p. 911).ν′=ν1−vVcos⁡φ1−(vV)2\nu' = \nu \frac{1 - \frac{v}{V} \cos \varphi}{\sqrt{1 - \left( \frac{v}{V} \right)^2}}The same, with the factors of the numerator in the order this display prints them.Also

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