Annus MirabilisEinstein in 1905
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special relativity

The equation explained

P=2A28πcos⁡2φ.P = 2 \frac{A^2}{8\pi} \cos^2 \varphi .
In wordsTo a first approximation, the pressure of light on the mirror is twice the energy per unit volume of the incident light, from its amplitude, times the square of the cosine of the angle of incidence.OverviewThe radiation pressure on a mirror when its speed is negligible against the velocity of light: twice the energy density of the light, times the square of the cosine of the angle of incidence.Full explanationDropping the terms in vV\frac{v}{V} leaves the pressure on a mirror at rest. The paper says that this agrees with experience and with other theories. It names neither. For light falling straight on the mirror the pressure is twice the energy per unit volume of the light. At oblique incidence it is smaller by cos⁡2φ\cos^2 \varphi, the value the exact formula takes when vV\frac{v}{V} is set to zero.Every stepP=2A28π(cos⁡φ−vV)21−(vV)2P = 2 \frac{A^2}{8\pi} \frac{\left( \cos \varphi - \frac{v}{V} \right)^2}{1 - \left( \frac{v}{V} \right)^2}The pressure on the moving mirror, the previous display.vV→0\frac{v}{V} \to 0The first approximation: the mirror's speed is small against the velocity of light, so the terms in vV\frac{v}{V} are dropped.P=2A28πcos⁡2φP = 2 \frac{A^2}{8\pi} \cos^2 \varphiThe numerator becomes cos⁡2φ\cos^2 \varphi and the denominator 1.Also

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