How far apart can the slits be in a double-slit experiment using direct sunlight? In a normal double slit experiment, I'm told that sunlight doesn't produce a visible interference pattern because there is no stable phase relationship between the two slits.
However, sunlight bouncing off a CD does produce interference-based rainbows, so sunlight can interfere if the slits are close enough.
How close do the slits need to be to see interference when direct sunlight falls on them?
 A: The visibility of interference fringes from a double slit depends on the how correlated the fields from the source at the two slits are. The typical slit-distance for which the fringes are manifestly visible is called the transverse coherence length $d_{\rm coh}$ of the source. For a spatially extended source, this quantity primarily depends on two parameters, namely the size $S$ of the source and the distance $R$ of the double-slit from the source. The quantitative relation is, (please see "Optical Coherence and Quantum Optics" by L. Mandel and E. Wolf for the derivation)
$d_{\rm coh}\approx\frac{R\bar{\lambda}}{S}$
where $\bar{\lambda}$ is the mean wavelength of the source. The inverse dependence on $S$ can be intuitively understood from the fact that a spatially extended source is a collection of many uncorrelated point sources, each of which produces its own double-slit pattern. The pattern due to the full source is the incoherent sum of these intensity fringes. Since the individual point sources were uncorrelated, these fringes add up in an uncorrelated manner and have the effect of washing out. As a result, the larger the source, the lesser the coherence length and consequently more difficult for interference to manifest. Upon plugging in the numbers in the above formula, you will find that $d_{\rm coh}$ for the sun for a double-slit placed on earth is of the order of tens of microns. Thus, the distance between the two slits must be less than this transverse coherence length of sunlight, i.e less than few tens of microns to observe interference. Regarding your example, since the surface topography of a compact disc varies on those scales, the interference effects are manifestly visible to the naked eye. 
P.S: To address the point raised by one of the comments, when you focus the sunlight using a lens and do a double slit experiment, the slit distance can indeed be larger. This is due to the fact that you have now prepared a secondary source (tiny point source) from the primary source (sun), and the interference effects will now be governed by the coherence of the secondary source. The transverse coherence length according to the above formula (taking the limit $S\to0$) is indeed large. 
