I have a camera with an APS-C sized sensor. Should my flash zoom match my lens's actual focal length or its 35mm equivalent?
I am hoping that someone can shed some scientific light to this matter.
The traditional flash head zoom steps really mean "covers the field of view of a full-frame lens at this focal length". That's because flashes don't really have focal length of their own — they just have a reflector which can move to deliver a wider or narrower beam, and for convenience, the angle of that beam is specified by the lens focal length that it's wide enough to cover.
Generally, for flashes made for 35mm-film cameras, focal lengths in that format are what's used.* For example, if a flash has a beam wide enough to cover 40º horizontally, that'll be called "50mm", or if it's narrower at 24º, that'll be labelled "85mm". But there's not really any focal length involved at all, and in APS-C terms, those same angles correspond to 33mm and 57mm.
So, for manual zoom flashes and for many automatic flashes, use the equivalent. I personally find it easier to do the conversion "backwards", and divide the flash's stated zoom number by the crop factor. That way, I'm still working with the real focal length of my lenses.
Except, some modern flashes automatically adjust for the format. You'll need to check the flash manual to know if this is so.
For Pentax P-TTL-compatible flashes, there's more on this on my Pentax flash guide, under Camera Format Conversion — in short, higher end Metz and Pentax flashes do the conversion, but the lower end models from those companies and all flashes Sigma, Promaster, and Tumax do not. (For Metz, you have the option of turning this off if you prefer — that might be handy if you have a mix of flashes with and without the feature.) To make this even more confusing, Sigma flashes zoom to the correct setting for crop-factor cameras, but display the equivalent focal length (at least on Pentax and with current Sigma firmware).
For Nikon, the SB-700 appears to automatically detect DX or FX sensor format and adjust accordingly, but I remember seeing complaints that earlier Nikon flashes don't — I'm not sure exactly where the change is.
Canon has a nice document about this, and they note that the 580EX and 430EX (and presumably newer) have a sensor-format detection feature and will do the right thing, but that older auto-zoom flashes will actually use unconverted field of view (and therefore be needlessly wide-angle).
As one might expect, the Four Thirds / Micro Four Thirds system flashes are designed for the format and use the native focal length (Panasonic flashes will say "four thirds" in the display) — but if you're using a third-party flash, it could go either way.