This equation can only then be satisfied for all values of and , when
These equations give us the law of reflection
(10)
and the Doppler effect
in full agreement with Abraham. Incidentally, equation (10) is also easily given from equation (12) of my earlier treatise.[1]
Now, to derive the value of the pressure from it, we have to assume that the energy density of a light wave is proportional (at equal amplitude) to the -2. power of the wave length, thus to the quantity . Thus when we denote by the density of the incident wave, by that of the reflecting one, then it is
Now, the energy falling upon the mirror in unit time, is contained in space ; the reflected energy in space . Thus the amount the incident energy per second is: