# Plane wave conditions

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Which conditions have to be fulfilled in order to approximate a light beam by a plane
wave (i.e. $\phi(x)\approx \phi(0)e^{ikx}$)?

I am looking for both mathematical and experimental conditions. At the moment, the only thing I can think of is to consider that the source is at a very distant point and the use of collimators.

Closed as per community consensus as the post is high-school/UG level.
asked May 27, 2015
recategorized May 27, 2015

Is this question maybe more appropriate for physics stackexchange?

I agree with @JoshBurby.

Voting to close as high-school/UG level. PO is for graduate-level+ questions.

A spherical wave has an exact expression (with $1/r$ factor). Within certain precision $\varepsilon$ the denominator can be considered constant. Thus, the plane wave approximation has the corresponding limits in the volume.

## 1 Answer

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For the intuition's sake, perhaps it would be useful to visualize the ripples produced by throwing a stone into a pond. Close to where the stone impacted the pond's surface, the wave fronts are strongly curved, and are not approximated well by a plane wave. However, at large distances from the point of impact the curvature of the wavefronts is very small, and a plane wave approximation is more accurate.

Because the wave equation for electromagnetic waves in free space is essentially identical to that governing the surface waves on a pond, the above picture generalizes to give a picture of light waves produced by, say, an oscillating dipole. When you are sufficiently far from the dipole, the radiation field will be approximately plane.

answered May 27, 2015 by (120 points)