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When Thomas Young first conducted his double slit experiment to prove the wave nature of light, he shone light through two slits, creating an interference pattern. Apparently he then covered up one slit, and the interference pattern disappeared, proving that the interference was due to interaction between each slit.

My question however, is why did the interference pattern disappear? Won't light shining through a single slit also produce a pattern with light/dark bands? (similar to this)

How did the fact that dark/light bands appeared when light was shone through a single slit not prove the fact that light was a wave?

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When the slit is smaller than the wavelength, the single slit diffraction pattern is not visible in the range of angles $-\pi/2$ to $\pi/2$. The diffraction pattern is the Fourier transform of the transmission function, and when the slit is much narrower than the wavelength, the diffraction pattern turns into the Fourier transform of a delta function, a constant. The two-slit pattern turns into a nearly constant intensity, with only a little bit of decrease in intensity of size $1/k^2$ when the two slits are closer than the wavelength divided by k.

Addition as requested

single slit diffraction also works to demonstrate that light is a wave, it is just a little trickier to analyze mathematically because it requires doing an integral, while double slit is trivial, so Young focuses on double slit. Newton had a weird pulsating-particle model for light which could reproduce interference fringes, by assuming that light pulsates regularly between different states, and only some of the states could get through a material. Newton wanted this to be true because he believed matter was particulate, and that the particles interact through the third law, explaining the conservation laws. He couldn't bear the idea that this scheme only worked for matter, and not light, so he tried to shoehorn light into a particle model.

The final proof that light is an actual wave, not a Newtonian pulsating particle, came from the observation of the completely-counterintuitive constructive-interference bright spot at the center of perfect circular disk shadow. At the center of a disk, you get a spot of constructive interference called the "Poisson spot". Wikipedia says that Poisson, who believed in the Newton theory, demonstrated this as a paradoxical consequence of the Fresnel theory of diffraction, but Arago experimentally observed the spot almost immediately afterwards, vindicating the wave theory. No pulsating-particle model can explain how particles at different sides of the disk can conspire to join up exactly at the center--- that must be a wave diffracting around the whole disk.

Of course, we now know quantum mechanics and photons, so Newton wasn't so terribly off. But his pulsations need to be spatially extended so that they make a full diffracting wavefunction, not just a temporal oscillation along the particle path.

Fresnel's paper is here:

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When would a physical slit ever be smaller than the wavelength of light though? It seems highly unlikely the slits would have been <500-700nm. – Parachuting Panda Sep 7 '11 at 5:12
It's not that hard to do--- you just slit a long solid and squeeze it so it just barely admits light. Even if you don't get it much smaller than the wavelength, you will only see single-slit fringes at much large angles as compared to the double slit fringes--- diffraction turns length scales inside out like Fourier transforms always do. – Ron Maimon Sep 7 '11 at 5:49
Also, you help yourself to a factor of $2\pi$, which makes all the difference. – genneth Sep 7 '11 at 9:17
@Ron you have not addressed the part of the question that asks that since one can see a one slit interference pattern, that should also be attributed to the wave nature of light. – anna v Sep 7 '11 at 11:52
@Ron - it's even easier. Take 2 mechanical pencil leads, hold them parallel and very close to each other in one hand. With the other hand, shine a red laser pointer at the leads. Look beyond the leads, at the laser light falling on the wall - that's your single-slit diffraction. Then hold 3 leads instead of 2 and you get double-slit interference. – Florin Andrei Sep 7 '11 at 18:19

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