How does the finite size of an obstacle affect diffraction patterns?

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The discussion centers on the impact of finite obstacle size on diffraction patterns, specifically for objects significantly smaller than the wavelength of light, such as a sphere with a 1nm radius or a cube with a 2nm edge length, using a wavelength of approximately 500nm. Participants explore the limitations of Huygens-Fresnel theory, which assumes obstacles are larger than the wavelength, and question the applicability of Rayleigh scattering due to its reliance on intensity proportional to the sixth power of the characteristic length. The consensus indicates that while the shape may not drastically alter the diffraction pattern, it remains a critical factor in accurately predicting interference outcomes.

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Hi,

I'm considering the case of diffraction by an object, with dimensions far smaller than the wavelength of the light source. If I consider for example an sphere with radius 1nm, or a cube with edge length a≈2nm , and the usual λ≈500nm, how will the finite shape of the obstacle be of significance to the interference pattern?

I thought about using Hyugens-Fresnel theory, but it implies that the size of the obstacle is far greater than the λ, so I'm not sure as to how to approach this situation.

Thanks
 
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Rayleigh scattering describes this.
I would expect that the precise shape is not relevant, as long as the amount of material does not change it should be similar to a sphere.
 
I considered Rayleigh scattering, but the fact that the intensity is proportional to d^6 without taking into account the shape of the obstacle makes this approach questionable. The factor d^6 would imply that a tiny change in the characteristic length of the obstacle would increase the intensity way too much. And directly not considering the shape of the obstacle even if it's small is just not good enough.
 

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