I have been reading the B&H Speedlight Buyer's Guide. I am confused specifically about the guide number calculation. I understand the principle and how the inverse square law is used. Here is the example from the article that I am basing my calculation on:
Simplifying this a bit, a realistic example would be if you have a flash with a guide number of 100—photographing a subject 25' away will require the use of f/4 for proper exposure. Likewise, a subject 50' away requires f/2 or a subject 5' away requires approximately f/22.
My confusion lies with the case when the subject is 5' away. The f/stop required here is in fact exactly f/20 (since using the guide number equation: 20*5=100). f/20 is 4 2/3 (4.66) stops away from f/4. I have no problem with this at all.
My confusion comes when I try to compare this value to what I get when I try to calculate using the amount of light needed. If the subject is 5' away then it is 5x closer than when it is 25' away. Using the inverse square law this means that we would need the flash to be 5^2=25 times less bright to get proper exposure (correct me if I'm wrong?).
I want to compare this value to how many stops of light this would be. Each time the lens is stopped down one f/stop, half the amount of light is allowed through. So in the case of this example if we stop down from f/4 to f/16, this is reducing the exposure by 4 stops (or 16x less light). If we stop down once more to f/22 we now reduce the exposure by 5 stops (or 32x less light). But in this case we want 25x less light to get a proper exposure at 5'. Here's the dealbreaker: f/20 is 2/3 of a stop past f/16. However, 25 is NOT 2/3 of the way between 16 and 32. It's actually 9/16 (0.5625). Meaning that 25x less light is actually 4.5625 stops less bright, rather than 4.66 stops. As far as I can tell these two values should be exactly the same. What am I doing wrong? I must me missing something here, but I can't work out what.
I hope you understand what I'm trying to say here. As far as I can tell there shouldn't be a discrepancy between the two values. Any help shedding some light on this would be greatly appreciated.