Relation (Math) question with roots and squares..

[foxi]

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Statement from passage: "Each f-value in the table is greater than the preceding one by a factor of √2, and this corresponds to a factor of 2 decrease in light intensity."

The question asked this: "Which of the following best describes the relationship between the f-stop value and the intensity of the light reaching the film?"
a) intensity is inversely-related to square root of f-value
b) intensity is inversely-related to square of f-value

Which one is it and how did you mathematically determine so?
I chose a)... Got it wrong.

 

[NextStepTutor_3]

Let's say our first f-value is 1, and our next one is √2 (greater than the first by a factor of √2). Then, let's also say that our first intensity value is 1 (corresponding with our original f-value of 1). According to the passage, our next intensity value must be 1/2, as it's decreased from the first value by a factor of 2. To sum up, we now have f values of 1 and √2 and intensity values of 1 and 1/2.

Now, what's happening here? "f" is increasing by a factor of √2, while "i" is decreasing by a factor of 2. 2 is the square - not the square root - of √2. So, intensity relates to the square of the f-value (choice B). If intensity were related to the square ROOT of the f-value, it would change by a relatively smaller amount than f does, which is not the case. (In other words, if our first "f" values were 1 and √2, and our first intensity value was 1, our next intensity value would be [1/√(√2)] - it would be varying inversely with the square root of f).