Why can't diffraction happen if wavelength>slit size

[BriO111]

I get that diffraction takes place when wavelength is smaller than slit size due to interference. I am confused though, if every point on the slit is taken as a new source when a wave passes through a slit, then surely, if the wave had a longer wavelength than the slit, then the let's say passing through coherent light would spread out without destructive interference but some partial construive intereference would still take place, causing diffraction?

 

[Orodruin]

What happens as you decrease the slit size (for fixed wavelength) is that the diffraction minima start moving to larger angles. Once you reach a wavelength, the first minima will go to 90 degrees. As you decrease slit size from there, all interference becomes more and more constructive everywhere.

 

[tech99]

What happens as you decrease the slit size (for fixed wavelength) is that the diffraction minima start moving to larger angles. Once you reach a wavelength, the first minima will go to 90 degrees. As you decrease slit size from there, all interference becomes more and more constructive everywhere.

It looks to me as if the slit might act as a slot antenna. If so, it now becomes sensitive to polarization of the wave, so that only the polarization at right angles to the slit can go through. Even if the slit is very narrow, waves can still pass through unhindered. The energy passing through falls off as we move off axis, as a result of the pattern of a Huygens' Source. Maybe the energy passing might be considered as being radiated by currents flowing in the sheet in which the slit is cut.

 

[my2cts]

The diffraction can be understood by considering the Fourier transform of the slit.
Google for Fourier optics.
In the case of a narrow slit the incoming wave is diffracted into a sum of waves in all outgoing directions.
The result is a hemispherical wave.
Diffraction always occurs. Only if the wave length is small enough, that is the opposite limit of what you are considering, it can be neglected and ray tracing applies.
Interference however disappears in the long wavelength limit, since only a single (spherical) wave remains.

 

[BriO111]

Yeah so It should diffract right? So how come here https://en.wikipedia.org/wiki/Diffraction it says that diffraction only occurs when wavelength is around slit size, when clearly it also happens if wavelength is bigger?

 

[Drakkith]

Yeah so It should diffract right? So how come here https://en.wikipedia.org/wiki/Diffraction it says that diffraction only occurs when wavelength is around slit size, when clearly it also happens if wavelength is bigger?

From that same article: While diffraction occurs whenever propagating waves encounter such changes, its effects are generally most pronounced for waves whose wavelength is roughly comparable to the dimensions of the diffracting object or slit.

Diffraction happens any time a wave encounters an obstacle or slit. The larger the wavelength compared to the obstacle, the less pronounced the effects are, but there is no hard cutoff.

 

[Orodruin]

If so, it now becomes sensitive to polarization of the wave, so that only the polarization at right angles to the slit can go through.

Polarisation is not what diffraction is about. Not all type of waves have a property of polarisation, but they all experience diffraction effects.

 

[tech99]

Polarisation is not what diffraction is about. Not all type of waves have a property of polarisation, but they all experience diffraction effects.

I agree with that, but for a very narrow slit, one polarization cannot get through. For instance, I tried today using 3cm waves, and with the slit a wavelength wide, both polarizations get through equally, but when it is only an eight of a wavelength wide, I could detect only one polarization.
I also confirmed what you say about the diffraction pattern, which became cylindrical for the narrow spacing mentioned.
Regarding transmission of energy through a narrow slit, I found that the width of the slit altered the amount of energy getting through. This is contrary to experience with the slot antenna, where slit width has little effect. I then realized that for the antenna case the slit is resonant, and when I tried diffraction through resonant slits half a wave long, the width made almost no difference.

 

[Orodruin]

I agree with that, but for a very narrow slit, one polarization cannot get through. For instance, I tried today using 3cm waves, and with the slit a wavelength wide, both polarizations get through equally, but when it is only an eight of a wavelength wide, I could detect only one polarization.

You still do not get it. Polarisation is not something all waves have. Diffraction is. Try the same thing with sound waves.

 

[tech99]

You still do not get it. Polarisation is not something all waves have. Diffraction is. Try the same thing with sound waves.

Yes I agree with that.

 

[blue_leaf77]

For instance, I tried today using 3cm waves, and with the slit a wavelength wide, both polarizations get through equally, but when it is only an eight of a wavelength wide, I could detect only one polarization.

I believe this is antenna stuff you are playing with, and the slit is cut out from a sheet of metal, am I wrong? The response of metal to long wave is just different from the very short wave such as visible light. When a sheet of metal is exposed to long EM wave, some current density might come to existence. But if this metal were illuminated by visible light or any shorter wave, I don't think the free electrons there can oscillate by following the wave's oscillation. Therefore, EM wave diffraction due to metallic material is a completely different story between long wave and visible wave.

but when it is only an eight of a wavelength wide, I could detect only one polarization.

I think the disappearance of the other polarization is caused by a destructive interference between the original wave and the wave emitted by the induced current. Again I don't think the same phenomena can be observed if you use visible wave instead.

 

[tech99]

I believe this is antenna stuff you are playing with, and the slit is cut out from a sheet of metal, am I wrong? The response of metal to long wave is just different from the very short wave such as visible light. When a sheet of metal is exposed to long EM wave, some current density might come to existence. But if this metal were illuminated by visible light or any shorter wave, I don't think the free electrons there can oscillate by following the wave's oscillation. Therefore, EM wave diffraction due to metallic material is a completely different story between long wave and visible wave.I think the disappearance of the other polarization is caused by a destructive interference between the original wave and the wave emitted by the induced current. Again I don't think the same phenomena can be observed if you use visible wave instead.

I think the shiny appearance of metals possibly arises because they are conductors, so that free electrons might be moving in response to light.
If electrons do not move in the sheet of material, how does the EM wave know it is there?

 

[blue_leaf77]

I think the shiny appearance of metals possibly arises because they are conductors

This is true, to be precise this is caused by the imaginary nature of the refractive index of most metals at optical wavelengths, however for wavelength around the onset of X-ray, most metals begin losing its reflective property - XUV and shorter wavelengths is transmitted in most metals. It's also true that electrons must response in certain movement to an incoming EM field regardless of its wavelength, but the response is not the same throughout the spectrum. This may be not very accurate to address the problem here, but at least according to the classical Drude-Lorentz model, the conductivity of ordinary metals reads
$$\sigma (\omega) = \frac{\sigma_0}{1-i\omega \tau}$$
which decreases as frequency increases. In other words, the induced current will be smaller when induced by higher frequency.

 

[bcrowell]

This is the subject of a classic 1944 paper by Bethe. For a sketch of how the calculation works, see this stackexchange question that I asked http://physics.stackexchange.com/questions/141562/diffraction-by-small-holes/141713 and my own answer to it, which I wrote after realizing that it was discussed in Jackson. It is certainly not true that diffraction doesn't happen if the wavelength is greater than the size of the slit. When the slit is small compared to the wavelength, you get a *lot* of diffraction in the sense that the radiation pattern is very broad, as opposed to the geometrical shadow that you'd expect according to the ray model of light. However, the fraction of the energy transmitted through the slit gets smaller and smaller as the slit gets smaller compared to the wavelength, so in this sense there is *less* diffraction.

 

[tech99]

This is the subject of a classic 1944 paper by Bethe. For a sketch of how the calculation works, see this stackexchange question that I asked http://physics.stackexchange.com/questions/141562/diffraction-by-small-holes/141713 and my own answer to it, which I wrote after realizing that it was discussed in Jackson. It is certainly not true that diffraction doesn't happen if the wavelength is greater than the size of the slit. When the slit is small compared to the wavelength, you get a *lot* of diffraction in the sense that the radiation pattern is very broad, as opposed to the geometrical shadow that you'd expect according to the ray model of light. However, the fraction of the energy transmitted through the slit gets smaller and smaller as the slit gets smaller compared to the wavelength, so in this sense there is *less* diffraction.

This is very interesting, thank you. It does seem, however, that if the small slit is brought to resonance, it can extract energy from an area greater than its own physical size.

 

[Drakkith]

This is very interesting, thank you. It does seem, however, that if the small slit is brought to resonance, it can extract energy from an area greater than its own physical size.

I believe antennas work this way. An incoming EM wave of the correct frequency would 'see' a dipole antenna as being much larger than its physical size. In contrast, an EM wave with a frequency much too low for the antenna would essentially not 'see' the antenna at all.

The shielding in your microwave's door also does this. Its physical surface area is much less than a solid piece of metal would be for the same size, but the microwaves act as if the shielding is a single, solid object without holes.

 

[Joe Ciancimino]

I believe antennas work this way. An incoming EM wave of the correct frequency would 'see' a dipole antenna as being much larger than its physical size. In contrast, an EM wave with a frequency much too low for the antenna would essentially not 'see' the antenna at all.

The shielding in your microwave's door also does this. Its physical surface area is much less than a solid piece of metal would be for the same size, but the microwaves act as if the shielding is a single, solid object without holes.

Dipole and waveguide theory, the passage must be of harmonic size to the wavelength, 1/2, 1/4, 18, ect. Makes me wonder if anyone has played with this concept in the double slit experiment just to see if there were any variations due to harmonic resonance.

 

[Gaz]

Must be of harmonic size to the wavelength ? you mean like a aerial on your radio ? well that isn't true if your radio aerial breaks you can simply stick a screw in it to fix it and attaching longer wire makes it work better to. You mean it works better if its the right length. And em waves don't "see" antenna's wether the antenna simply picks up all frequencies and your radio separates out the correct frequency. I see where your both coming from but using must and see's is just wrong.