Single slit diffraction concept issue

[hunty]

The standard explanation for diffraction patterns from a single slit employs Huygens Principle and the production of secondary wavelets to form a new 'front'. These fronts reinforce constructively and destructively to produce the pattern.

But...if you consider an infinite number of points along the single slit, each generating its own wavelet, why don't you simply get the same result as a wave traveling through a wider gap - that is, a single, spherical, propagated front and no diffraction bars?

 

[mgb_phys]

Good question, in simple terms - you can't fit many photons in a narrow slit, this is why the effect only works for slits which are similair in size to a wavelength. As you make the slits much larger you can fit more photons across them and the diffraction pattern disapears.

 

[hunty]

yeh...but...(I have a few 'yeh, buts') I thought that Huygens Principle was supposed to prove the wave nature of light and not the particle nature. Also, I get the maths which shows how the slight difference in distance traveled by wave fronts to points either side of the midline, results in them arriving out of phase and destructively interacting to produce a dark band...but...the initial assumption is that the distance to the receptor from the slit is such that you assume parallel light rays!?

I'm missing something here.

 

[cesiumfrog]

As you make the slits much larger you can fit more photons across them and the diffraction pattern disapears.

That is just wrong (photons do not have a transverse size).

Hunty, if you don't mind then how about we stop talking about light (which often provokes the kind of confusion seen above) and restrict the discussion for now to an unambiguously classical wave, like on the surface of a pond? If we set up a plane wave to be incident (perpendicularly) on a slit aperture: the shape of the wave on the other side will vary from spherical, when the aperture is small compared to the wavelength, to straight (but still with curved edges) when the the aperture is much wider than many wavelengths. (Incidentally, the strength of the transmitted wave will also vary in different directions.) Now, was your question how Huygen's principle gives these different shapes? (Hint: application of the principle requires knowing the wavelength.)

 

[Claude Bile]

Good question, in simple terms - you can't fit many photons in a narrow slit, this is why the effect only works for slits which are similair in size to a wavelength. As you make the slits much larger you can fit more photons across them and the diffraction pattern disapears.

I have to disagree with this, first and foremost because the particulate nature of light never enters the picture when it comes to diffraction and also because the phrase "fitting photons across a slit" is quite misleading.

(Mgb_phys, your contributions on this forum are usually well thought out, which is why I get a feeling something was lost in translation in this instance!)

Hunty; A slit generates a diffraction pattern because it "cuts-off" or truncates the wavefront. This causes the wavefront to change shape as it propagates, Huygens' principle tells us this.

The next question is - Why do we get a sinc^2 interference pattern when a wave passes through a single slit? Well, you can use Huygens' principle to show that the field diffraction pattern is the Fourier transform of the aperture transmission function. The aperture transmission function of a slit, is a rectangular function, whose FT is a sinc function. Since diffraction patterns are Irradiance patterns, what we see is the ^2 of the field pattern, thus we get the familiar sinc^2 diffraction pattern from a single slit.

Claude.

 

[mgb_phys]

I was trying to say that the slit being a similair size to the wavelength prevents an infinite number of waves adding in-coherently from one slit.

 

[hunty]

Thanks all, but not convinced. Some want to use particle theory, some want to use wave theory. I thought wave theory was supposed to be demonstrated by this experiment. Never mind that taking single 'points' seems to imply particle theory. Can anyone actually answer the question I put, which was why do we observe the diffraction bands? How does cesiumfrog's wavefronts interfere in such a way as to produce them. Claude, is maths the only way to explain this, or is there a graphical/spacial description that can be grasped by nongs like me?

 

[jtbell]

Mathematics is the language of physics.

You can find a graphical construction for single slit diffraction at

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinint.html#c1

and the setup for a straight mathematical calculation (using integral calculus) at

http://scienceworld.wolfram.com/physics/FraunhoferDiffractionSingleSlit.html

You can find details in most any intermediate-level optics textbook, e.g. Hecht, Pedrotti, Meyer-Arendt, Jenkins/White, et al.

 

[hunty]

thankyou to all. Got it. :)