Annus MirabilisEinstein in 1905
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special relativity

The equation explained

cos⁡φ′=cos⁡φ−vV1−vVcos⁡φ,\cos \varphi' = \frac{\cos \varphi - \frac{v}{V}}{1 - \frac{v}{V} \cos \varphi} ,
In wordsThe cosine of the angle of incidence in the mirror's system is the cosine of the angle of incidence in the stationary system less the speed over the velocity of light, divided by one minus that ratio times the same cosine.OverviewThe direction of the incident light in the mirror's system: the law of aberration of § 7, applied to the light that falls on the mirror.Full explanationφ\varphi is the angle between the incident light's direction and the direction of motion, which is also the normal of the mirror, measured in KK; φ′\varphi' is the same angle measured in kk. This is § 7's law of aberration (p. 912) repeated for the mirror problem.Every stepa=cos⁡φa = \cos \varphiThe incident light's direction cosine along the motion, § 7's aa, is the cosine of the angle of incidence.cos⁡φ′=cos⁡φ−vV1−vVcos⁡φ\cos \varphi' = \frac{\cos \varphi - \frac{v}{V}}{1 - \frac{v}{V} \cos \varphi}§ 7's first direction cosine in kk, the old one less vV\frac{v}{V} over one less their product (p. 911), written with the angles as § 7 writes it on p. 912: the law of aberration.Also

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