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I've taken a series of photos as a bracketed HDR, starting at 1/4000th of a second going up to 1 second. How many stops are there between those? How would you be able to tell?

The aperture and ISO do not change

4

Each stop is double the amount of light - so:

doubling 1/4000 goes to 1/2000, then 1/1000, and 1/500, 1/250, 1/125, 1/60 (not exactly double but close enough), 1/30, 1/15, 1/8 (another "close enough"), 1/4, 1/2 and finally 1.

So we need to double the value 12 times - 12 stops

6

Algebraically, we want to to solve the following equation:

    2n = 1 / (1 / 4000)

Taking log2 of both sides, we get

    n = log2(1 / (1 / 4000))

    n ≈ 12

Indeed, shutter speeds are supposed to be powers of two, so 1/4000 should actually be 1/4096 (that is, 1/212); they're just rounded to make them more human-friendly.

0

According to the table on this page, it's 12 stops.

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