This may belong here in LENSES, or maybe somewhere else. Whatever. Anyway, the algebra portion of my brain seems to have rusted away. Here's my perplexity:
I use a couple spreadsheets to track my lenses. On one, I compare the widest aperture of various primes at common focal lengths with the widest aperture for my most-used zooms at those focal lengths. I'd like to simply calculate the difference in f-stops. Don't ask why.
Here, row 12 is for 55mm. D12 shows f/5.6 for the 18-55. E12 shows f/4.5 for the 18-250. F12 shows f/3.3 for a crappy 40-80. And K12 shows f/1.8 for a Super-Tak prime.
I can look at those numbers and judge that the Tak is 3.33 stops faster than the 18-55, is 2.66 stops faster than the 18-250, and is 1.66 stops faster than the 40-80. Fine.
But I want to automate the calculation. So, my problem: what is a simple formula that I can plug into the spreadsheet, that computes the difference in f-stops between two different apertures? Yes, I know that the
"f-stop scale... is an approximately geometric sequence of numbers that corresponds to the sequence of the powers of the square root of 2." But I just can't wrap my poor brain around an algorithm for finding the difference in f-stops between steps in that sequence. Duh.
Is there an algebraist in the house?