Annus MirabilisEinstein in 1905
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special relativity

The equation explained

A′=A1−vVcos⁡φ1−(vV)2,A' = A \frac{1 - \frac{v}{V} \cos \varphi}{\sqrt{1 - \left( \frac{v}{V} \right)^2}} ,
In wordsThe amplitude of the incident light in the mirror's system is its amplitude 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 first step of the moving-mirror problem: the incident light's amplitude as the mirror's own system kk measures it.Full explanationA perfectly reflecting mirror lies in the plane ξ=0\xi = 0 of the moving system, so it moves with kk. The paper solves the problem in three moves: describe the incident light in kk, reflect it there as from a mirror at rest, and describe the reflected light back in KK. This display and the next two are the first move, taken from § 7: the amplitude, the direction and the frequency of the incident light in kk. The amplitude is the square root of § 7's result for its square.Every stepA′2=A2(1−vVcos⁡φ)21−(vV)2A'^2 = A^2 \frac{\left( 1 - \frac{v}{V} \cos \varphi \right)^2}{1 - \left( \frac{v}{V} \right)^2}The squared amplitude in kk, from § 7 (p. 912).A′=A1−vVcos⁡φ1−(vV)2A' = A \frac{1 - \frac{v}{V} \cos \varphi}{\sqrt{1 - \left( \frac{v}{V} \right)^2}}Take the square root; both sides are positive, since vV\frac{v}{V} is less than 1.Also

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