Page:The principle of relativity (1920).djvu/60

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

E´/E = ((A´^2/8π)S´) / ((A^2/8π)S) = (1 - (v/c)cos Φ)/[sqrt](1 - v^2/c^2)

If Φ = 0, we have the simple formula:—

E´/E = ((1 - v/c)/(1 + v/c))^{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 ξ = 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 A cos Φ, v?] (referred to the system K). Regarded from k, we have the corresponding magnitudes:

A´ = A (1 - (v/c)cos Φ)/[sqrt](1 - v^2/c^2)

cos Φ´ = (cos Φ - v/c)/(1 - (v/c)cos Φ)

ν´ = ν (1 - (v/c)cos Φ)/[sqrt](1 - v^2/c^2)