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can this be done with any optical disk (DVD//DVD-R/W//CD//CD-R/W,etc.)?
Yes, I believe any of those will work. The key here is that the regular spacing of groves on an optical disk acts as a high quality diffraction grating.
I've long known of this effect (it's rather hard to miss), but did not realize that it could resolve a spectrum this well (and it's even more distinct by eye than I was able to capture on camera due to imperfect focus). Also, just like how most spectrometers limit the light through a tiny slit so that you can distinguish individual spectral 'lines', it's helpful if the light source you want to see a spectrum of is either a point source or very narrow, in this case a thin plasma filament. Otherwise an extended source will make a smeared out overlapping spectrum, and the unique spectral features may be harder to see.