Your underlying concept is easy enough to understand, but where you're going with it is a little esoteric. This is going to be one of those questions that needs a point by point breakdown.
Assume the traditional analog-type film using an emulsion made of silver halide crystals,
I suppose we'll have to, given that there aren't really any other types in commercial production. So, film, not a digital camera. OK.
specifically Kodachrome II with speed rating ASA 25
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How 'bout that. You saved some. Paul Simon should be proud. Anyway, film, ASA rating 25, with the proprietary composition for vivid color reproduction. We realize some obstacles right away, the specifics are proprietary. You will never find some of the information on this topic, on a chemistry forum. You should be able to realize that on your own. Why you've decided to use a vivid color film formulation to catch a white flash of light also mystifies me.
When you make a picture of burning white phosphorus (WP), does the emitted light expose the film much faster?
As compared to ...?
For example, assume that the recommended time to expose the film is 25 milliseconds, given the light conditions in the background
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Most definitely. Wouldn't a flash bulb, or any light source do the same? You've selected an exposure for say, a darkened room, and maybe let a flash of daylight in ... wouldn't that overexpose a spot?
Does a light emitted by WP leave a white spot on the film even though the light appears only for a few milliseconds during the first 10 milliseconds, and then disappears.
I'm missing the point about duration here. The film reaction is pretty fast, be definition.
Is there something unique in the light emitted by burning WP? It burns up to 5000 F
It might be richer in UV wavelengths, that an exposure photometer you used to determine exposure might have missed. But you never claimed to have determined the exposure first, so I don't know how we can use the information.
And be careful of the burning phosphorous fumes. Google for "phossy jaw" so that you're aware of the risks.