Olaf, now I'm confused.
I'd say that's only because you don't read my postings carefully enough.
You said it is wrong that if the focal lenght doubles, the FOV halfes, because that is only an aproximation for long focal lenghts, right?
Yeah, right.
I understood your simple formula as a proportion wich I assumed to be linear.
Yes, it
is linear ... at long focus distance, that is.
But since you said the underlying relationship is not linear but depends on some circle functions, I assumed that the first formula would not hold true for short focal lenghts (wide FOV's). Where is my error?
Your error is that you're confusing two different things.
You asked
two questions, remember? The first question was: How do I compute the equivalent focal length for a cropped area in my photograph? The second question essentially was: Is the relationship between focal length and angle of view a linear one?
And the equivalent focal length
is linearly proportional to the width of the crop (question #1), but focal length is
not linearly proportional to the angle of view (question #2). Field of view is not the same as angle of view.
I am an engineer, I enjoy deriving formulae.
I have read and understood Merklinger's books "The ins and out of Focus" and "Focusing the view camera".
So have I.
Focal length was defined as the extension (film to lens distance) at which an object at infinity would be in focus ...
Actually, it's the lens-to-film distance (or more generally speaking, the lens-to-image distance) at infinity focus. As an engineer, you'll understand the (subtle) difference---in optical imaging systems, distances are always measured in subject-to-image orientation.
... but this only applies to normal, rather than tele-photo retro-focus lenses.
Actually, it applies to all kinds of lenses, be them regular, telephoto, or retro-focus. The difference between the three is where exactly 'the lens' formally is located, in relation to the mass of the glass.
In the English language, as far as I am aware, there is no technical phrase "focus distance" ...
There isn't!? Oops! I thought so. In fact I often saw that term ... but maybe that's just layman's talk, as opposed to a technical term.
So please tell me: what is the technical term for the distance between subject and image? That's the sum of the subject-to-lens distance plus the lens-to-image distance (plus, if we are scrupulous, the distance between the lens' principal planes). It's the distance engraved on the lenses' distance scales. I always thought the technical term for this was 'focus distance' ... no?
... what is the focal length of a 180° lens?
It's 0 mm. Except when it's a fish-eye lens.
-- Olaf