Φ′ = ω′(t - ---------------------- )
c
where
From the equation for ω′ it follows:—If an observer moves with the velocity v relative to an infinitely distant source of light emitting waves of frequency ν, in such a manner that the line joining the source of light and the observer makes an angle of Φ with the velocity of the observer referred to a system of co-ordinates which is stationary with regard to the source, then the frequency ν′ which is perceived by the observer is represented by the formula
This is Döppler’s principle for any velocity. If Φ = 0, then the equation takes the simple form
We see that—contrary to the usual conception—ν = ∞, for v = -c.
If Φ′ = angle between the wave-normal (direction of the ray) in the moving system, and the line of motion of the observer, the equation for l´ takes the form