# What property of an electromagnetic wave can change with distance?

I want to figure out if the total distance traveled by an electromagnetic wave can be calculated by change in any of its properties from source. Is there any property that changes with distance?

• yes, the amplitude; so if you know the emitted wave's amplitude and you that there are no multipath reflections then the amplitude is inversely proportional to the distance travelled ( far-field) – hyportnex Apr 11 at 15:48

Yes, several quantities vary with distance from the source. One useful quantity is the radiant flux (the amount of energy passing through a given area in a given amount of time -- basically how 'bright' it looks from your position). In fact, for a source that is spherically symmetric or far enough away that we can regard it as spherically symmetric, the radiant flux falls off nicely as $$F \propto \frac{1}{r^2}.$$ Basically, the power of the wave is being spread over larger and larger spherical shells as it spreads out away from the source, and so the 'amount of energy' passing through one spot per unit time varies inversely with the surface area of that sphere.
So if we know the flux $$F_e$$ emitted at the surface of a spherical object (say, a star), the flux at our location is simply $$F = \frac{R^2}{r^2}F_e,$$ where $$R$$ is the radius of the source and $$r$$ is the distance from the source to us. Often it's easier to work with the source's luminosity, which is all the light energy emitted by the object per unit time. The luminosity of the object is related to the flux at our location by $$L = 4\pi r^2 F.$$ So if we know the luminosity of a spherically symmetric source and if we can measure the flux at our location, we can compute the distance $$r$$ to the source.