What property of an electromagnetic wave can change with distance?

Question

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?

Answer 1

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.

This is actually one of the ways astronomers can determine how far away stars are. Astronomers will determine the effective temperature of a star from its spectral type, and employ some clever tricks to determine its mass. From there, our astronomer can guess at the star's radius from our models of stellar structure. Using this, he/she will employ Stefan-Boltzmann Law to obtain the flux or luminosity, which he/she will compare to the flux (i.e. brightness) observed here on earth to determine the distance.

The mass measurement is often difficult to do directly -- we usually need our star to be part of a sufficiently well-behaved binary system. There are other ways to get the luminosity of a star, such as in cases where the star behaves in ways that depend on its luminosity (e.g. we can obtain luminosity from the periods of variable stars), or we can get the distance to a star by recognizing that it's close to a star whose luminosity we can measure, but there is no general method that works in every case.

Answer 2

Intensity changes because energy of the wave is absorbed by the medium in which it propagates. Also the wavefront appear different. Far away from a source, waves have plane parallel wavefront, like light from the stars.