Page:SahaElectrodynamics.djvu/26

moving system, which are enclosed by the surfaces mentioned above, then

${\frac {E'}{E}}={\frac {{\frac {A'^{2}}{8\pi }}S'}{{\frac {A^{2}}{8\pi }}S}}={\frac {1-{\frac {v}{c}}\cos \Phi }{\sqrt {1-v^{2}/c^{2}}}}$

If $\Phi =0$, we have the simple formula :—

${\frac {E'}{E}}=\left({\frac {1-{\frac {v}{c}}}{1+{\frac {v}{c}}}}\right)^{\frac {1}{2}}$

It is to be noticed that the energy and the frequency of a light-complex vary according to the same law with the state of motion of the observer.

Let there be a perfectly reflecting mirror at the co-ordinate-plane $\xi =0$, from which the plane-wave considered in the last paragraph is reflected. Let us now ask ourselves about the light-pressure exerted on the reflecting surface and the direction, frequency, intensity of the light after reflexion.

Let the incident light be defined by the magnitudes $Acos\Phi$, v (referred to the system K). Regarded from k, we have the corresponding magnitudes :

$A'=A{\frac {1-{\frac {v}{c}}\cos \Phi }{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$ $\cos \Phi '={\frac {\cos \Phi -{\frac {v}{c}}}{1-{\frac {v}{c}}\cos \Phi }}$ $\nu '=\nu {\frac {1-{\frac {v}{c}}\cos \Phi }{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$