# Diffraction through one slit?

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.

Also, you help yourself to a factor of $2\pi$, which makes all the difference. – genneth Sep 7 '11 at 9:17