# Defraction properties

• Nerd

#### Nerd

I know this may sound like a homework question but it is not.
I am having an argument with my science teacher and I was hoping you guys could help me prove her wrong.
The argument goes as follows:
My teacher says diffraction cannot take place if the opening is bigger than the wavelength of the wave. I say that diffraction can take place regardless whether the split is bigger or smaller than the wavelength, but diffraction cannot take place if the distance between the source of the wave and the split is smaller than the split.
Please tell me if I am right and if you have any links to proof it, I would really appreciate it (the link is so that I can print proof from a reliable source to show my teacher).

## Answers and Replies

I would say your teacher is more or less correct. Yes, you will get a miniscule amount of diffraction on slits larger than the wavelength but it generally isn't anything to write home about. I don't see why the distance between the slit and source matters. The diffracted wave is pretty independent of how the wave looks when it is incident upon the slit.

Hmmm... looks like I still have my Yee code. I could make up some pretty pictures tomorrow.

I used to teach an optics lab in which students studied diffraction using slits with a typical width of 0.04 mm, which is about 80 times a typical wavelength of visible light (500 nm). We got diffraction patterns which could be viewed and measured easily on a screen about 2 m away from the slits.

I believe that the useful minimum aperture of a camera lens is about f22, because with smaller apertures (e.g., f32) the photo becomes fuzzy due to difraction. Here is a photography website discussing diffraction in lenses:
http://www.cambridgeincolour.com/tutorials/diffraction-photography.htm
Use the visual examples of diffraction on fuzzyness.

I know this may sound like a homework question but it is not.
I am having an argument with my science teacher and I was hoping you guys could help me prove her wrong.
The argument goes as follows:
My teacher says diffraction cannot take place if the opening is bigger than the wavelength of the wave. I say that diffraction can take place regardless whether the split is bigger or smaller than the wavelength, but diffraction cannot take place if the distance between the source of the wave and the split is smaller than the split.
Please tell me if I am right and if you have any links to proof it, I would really appreciate it (the link is so that I can print proof from a reliable source to show my teacher).

What do you mean by 'split'? Is it supposed to be 'slit'?

Look up 'small angle scattering'.

Ok, I dug up my old code and made some movies in Matlab. Take a look at them on Youtube. The proximity to the slit is not a factor. The size of the slit does affect the diffraction. When it is larger than th wavelength, the diffracted wave no longer behaves like it was created by a point source at the slit. Instead, only diffraction at the edges of the slit occurs. If you look at the wave that passes through the middle of the slit it is obvious that the wave front was produced back at the location of the original source and not at the slit.

So the diffraction by large slits will depend on where you observe it, the size of the slit, and the extent that you are illuminating the slit. There is still diffraction, mostly edge diffraction, but it will be less pronounced than with sub-wavelength slits.

http://www.youtube.com/watch?v=7-VPLF6eRtk&feature=PlayList&p=A1964E692ECF7A4E&index=0&playnext=1

There are seven videos in all.

https://www.youtube.com/watch?v=<object width="425" height="344"><param name="movie" value="http://www.youtube.com/v/7-VPLF6eRtk&hl=en&fs=1"></param><param [Broken] name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/7-VPLF6eRtk&hl=en&fs=1" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="425" height="344"></embed></object>

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I used to teach an optics lab in which students studied diffraction using slits with a typical width of 0.04 mm, which is about 80 times a typical wavelength of visible light (500 nm). We got diffraction patterns which could be viewed and measured easily on a screen about 2 m away from the slits.

This gave me an excuse to play around with my new version of Excel to generate a graph of the intensity pattern for these numbers.

#### Attachments

• SingleSlit.pdf
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Look up 'small angle scattering'.
The term small angle scattering has been applied to the propagation of charged particles through matter, and the development of multiple scattering theory, based on the probability distribution of small angle Coulomb scattering of incoming charged particles on nuclei. This leads to the concept of radiation length and the Gaussian-like growth of charged particle beam divergences. How does this apply to the subject of this thread?

Thank you all for your input.
I realize that diffraction reduces greatly when the slit is much larger than the wavelength. I am still wondering, however, if diffraction would occur if the source is closer to the slit than the length of a wave.
I did a experiment with a piece of rope, to try and figure out whether a wave could be reflected if the reflector is closer to the source of the wave than 1 wavelenth. With the rope that I used it was not possible, but I realize that my apparatus may have been at fault. I figure that if a wave cannot be reflected from less than a wavelength it would also not be able to be difracted. Right?
So, can anyone prove with results from a reliable experiment that a wave can infact be reflected from a reflector closer to the source than 1 wavelength?

Placing a sub-wavelength sized aperture in close proximity to a source is the basis of near-field imaging methods.

Loosely, the aperture becomes the source. far-field diffraction effect will still occur.

Thank you all for your input.
I realize that diffraction reduces greatly when the slit is much larger than the wavelength. I am still wondering, however, if diffraction would occur if the source is closer to the slit than the length of a wave.
I did a experiment with a piece of rope, to try and figure out whether a wave could be reflected if the reflector is closer to the source of the wave than 1 wavelenth. With the rope that I used it was not possible, but I realize that my apparatus may have been at fault. I figure that if a wave cannot be reflected from less than a wavelength it would also not be able to be difracted. Right?
So, can anyone prove with results from a reliable experiment that a wave can infact be reflected from a reflector closer to the source than 1 wavelength?

Nobody ever reads my posts. :(

I did a few simulations under those conditions and the diffraction was the same with the exception of the magnitudes. A wave can be reflected at sub-wavelength distances from a source. I think you were trying to set up a standing wave which does require specific conditions for it to occur for a given wavelength.

The term small angle scattering has been applied to the propagation of charged particles through matter, and the development of multiple scattering theory, based on the probability distribution of small angle Coulomb scattering of incoming charged particles on nuclei. This leads to the concept of radiation length and the Gaussian-like growth of charged particle beam divergences. How does this apply to the subject of this thread?

Ah, I didn't know people used it in that meaning. For me, small angle scattering is the scattering of X-rays or thermal neutrons with wavelengths of the order of a few angstrom to large scale structures (correlations in density in fluids, macromolecules and so on) and hence have diffraction angles which are small (hence small angle...).

See for instance http://www.isis.rl.ac.uk/largescale/loq/documents/sans.htm [Broken]

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Ah, I didn't know people used it in that meaning. For me, small angle scattering is the scattering of X-rays or thermal neutrons with wavelengths of the order of a few angstrom to large scale structures (correlations in density in fluids, macromolecules and so on) and hence have diffraction angles which are small (hence small angle...)
See for example
Small Angle Scattering of Polarized Protons
Nov 5, 2002 ... Title: Small Angle Scattering of Polarized Protons. Authors: B.Z. Kopeliovich. (Submitted on 5 Nov 2002). Abstract: Experiment E950 at Brookhaven Alternating Gradient Synchrotron ...
arxiv.org/abs/hep-ph/0211061 - Similar pages
by BZ Kopeliovich -