How does the f-number of camera lenses affect image area?

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The discussion centers on the relationship between the f-number of camera lenses and image area. It clarifies that the area of the image is proportional to the square of the image distance (q²), which contrasts with the initial assumption that it is proportional to q. Participants note that while the f-number affects image brightness, it does not influence the field of view. The distinction between image area and brightness in relation to the f-number is emphasized. Understanding these relationships is crucial for photographers when considering lens selection and image composition.
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I was reading on the f-number of lenses for cameras...somewhere in the text, they stated that the area of the image is proportional to q2, in which q is image distance. I figured the area to be proportional to q, but I don't really see it as q2...so how does this work out?
 
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The f/# doesn't affect the field of view, so I'm not sure what you mean, exactly. The image *brightness* goes as the square of the f/#, but that's different.
 

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