# Spherical wave in far field is a plane wave ?

1. Jun 10, 2008

### broli86

Is it true that we can consider a spherical wave in the far field (i.e. away from antenna, at a large distance) as a plane wave ? For a plane wave the electric field at a distance s is usually given as:

E(s) = E(0) * exp(-jks) ----- (1)

where k is the wave vector, s is the distance travelled and E(0) is the electric field at a reference point.

But if I'm not wrong then in case of a spherical wave, there is a 1/s decay so for spherical wave:

E(s) = E(0) * 1/s * exp(-jks) --------(2)

Now my question is: If I am trying to simulate a plane wave with a spherical wave in far field, then should I use formula (1) or (2).

2. Jun 10, 2008

### HallsofIvy

Staff Emeritus
Suppose you are look at a 2 foot long piece of a circle with radius 20000 feet. What does it look like? As an interesting calculation, you might calculate how much the ends of that arc differ from the tangent line to the circle at the center of the arc.