Are plane waves actually spherical waves at large distance?

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SUMMARY

At large distances, spherical waves can be approximated as plane waves due to the increasing radii of curvature. This phenomenon is analogous to perceiving the Earth's surface as flat despite its spherical nature. However, the mathematical proof presented in the discussion is deemed insufficient, as it fails to derive the fundamental equation for a plane wave, which is essential for a complete understanding of the concept.

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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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