Are plane waves actually spherical waves at large distance?

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Discussion Overview

The discussion revolves around the relationship between plane waves and spherical waves, particularly at large distances. Participants explore whether spherical waves can be considered as plane waves under certain conditions, and the validity of a mathematical proof related to this concept.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant doubts that any plane wave is generated from a spherical wave, suggesting that at large distances, the curvature becomes negligible, similar to perceiving the Earth's surface as flat.
  • Another participant asserts that at very large distances, spherical waves can be approximated as plane waves to first order.
  • A subsequent post reiterates the approximation of spherical waves as plane waves at large distances and questions the acceptability of a mathematical proof provided.
  • Another participant challenges the proof, stating it does not derive the equation for a plane wave, indicating that it only shows one characteristic of the waves.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between plane and spherical waves, with no consensus reached on the validity of the mathematical proof or the nature of the waves at large distances.

Contextual Notes

The discussion includes assumptions about the conditions under which spherical waves may be approximated as plane waves, and the proof's limitations in deriving the relevant equations.

Arup Biswas
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I am doubting that any plane wave is generated from a spherical wave. At large distance the radii of curvature becomes so large that we can think it as plane. Like we se Earth surface as plane though it is spherical. Is it true? I have a mathematical proof for my argument!
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At very large distances spherical waves are approximately plane waves (to first order)
 
Dale said:
At very large distances spherical waves are approximately plane waves (to first order)
Is the proof acceptable??
 
Arup Biswas said:
Is the proof acceptable??
I wouldn’t accept it as proof. It shows one characteristic, but doesn’t derive the equation for a plane wave.
 

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