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I agree a formula would be useful, but I don't know of one. A mag zero star produces ~1 million photons/cm2/s in the visual-band. So that's 10,000 for mag 5, 100 for mag 10, 1 for mag 15 and 0.1 photons/cm2/s for mag 20. Would that be detectable by your camera chip vs sky signal?
You could do it by trial-and-error, perhaps? You'd need a chart that goes deep (mag 16+) and could then cross-check your image (with different exposures) against known-magnitude stars.
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