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

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In summary, the conversation discusses the significance of the finite shape of an object, with dimensions much smaller than the wavelength of the light source, on the interference pattern in diffraction. The use of Hyugens-Fresnel theory is considered, but it may not be applicable in this situation. Rayleigh scattering is also mentioned, but the fact that the intensity is proportional to d^6 without considering the shape of the obstacle raises questions about its accuracy. Therefore, a more precise approach is needed to understand the impact of the finite shape on the interference pattern.
  • #1
Talker1500
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Hi,

I'm considering the case of diffraction by an object, with dimensions far smaller than the wavelenght 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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  • #2
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.
 
  • #3
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.
 

1. What is diffraction by small obstacle?

Diffraction by small obstacle is a phenomenon that occurs when a wave encounters a small obstacle or aperture in its path. The wave bends or spreads out as it passes through the obstacle, resulting in changes to the intensity and direction of the wave.

2. How does the size of the obstacle affect diffraction?

The size of the obstacle plays a crucial role in diffraction. Smaller obstacles cause greater diffraction, as the wave has to bend more to pass through the obstacle. Larger obstacles result in less diffraction, as the wave can easily pass over or around them.

3. What types of waves exhibit diffraction by small obstacle?

Diffraction can occur with any type of wave, including light, sound, and water waves. However, the amount of diffraction may vary depending on the wavelength of the wave and the size of the obstacle.

4. What is the difference between diffraction and interference?

Diffraction and interference are both phenomena that occur when a wave encounters an obstacle. However, diffraction is the bending or spreading of a wave as it passes through an obstacle, while interference is the result of two or more waves overlapping and interacting with each other.

5. How is diffraction by small obstacle useful in real-world applications?

Diffraction by small obstacle has many practical applications, such as in the design of diffraction gratings for use in spectrometers and in radio antennas that use diffraction to focus and direct radio waves. It is also a crucial concept in understanding the behavior of waves in various fields such as optics, acoustics, and fluid dynamics.

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