Bokeh and depth of field are two different concepts. Any lens only focuses on one plane, a thin flat field, but depending on the size of the aperture, the areas in front of and behind this thin plane will look more or less sharp. In olden times, the longish lenses used for portraits had large apertures because they used the existing light, but this made a very thin depth of field--the eyes were sharp, but the nose and ears--not so much. Since this effect was common with the great portraits of old, everybody tried to duplicate it, even though we had enough light for smaller apertures and good sharpness throughout. So that is the style issue, of expecting backgrounds (especially for people) to be out of focus.
Recently (a few years--not decades) ago, the Japanese applied their word, "bokeh" to describe a certain preferred look for the out of focus background (foreground too, if appropriate)--not all lenses gave the same look, even at the same settings and distances (and focal length). The word "bokeh" is not a scientific or descriptive term in any strict sense--it is an artistic interpretation, and so as far as I know, it is the result of one scientific factor--the shape and thickness of the aperture blades when the exposure is taken. Old lenses uses so many blades that the circle was nearly a perfect circle, without noticeable corners between them; but by the 1950's, even large format lenses were using apertures with only 5 blades, making a hole the shape of a pentaprism; or sometimes a few blades more. This had no noticeable effect unless you shot into the light--in that case, the point of light took on the aperture shape, so you got pentaprisms or other patterns of light within the photo, where the light was or reflected to other places by each of the elements of glass in the lens. Some people like this, but most people consider it something to avoid--coated lenses helped a lot, and the use of a shade or hood around the lens also helped.
But more recently (I don't know just when), the above mentioned Japanese saw that even in good light (above and behind the photograher, for instance) there was a different sort of look, or quality, to out-of-focus backgrounds when the lens was set to larger apertures (or anything that is well outside the place of good focus), which was related to how many blades were in the aperture. Round apertures of old, they said, looked better in the out of focus areas--they rendered a better "bokeh." What is better or worse in this regard is not a scientific question, and even in regard to artistic states, it is not entirely clear what people mean by good bokeh--maybe, today, many people just mean the bokeh is the out of focus stuff, and the more out of focus it is, the better the bokeh.
If being out of focus is the real issue, then the factors that will give you the most out of focus backgrounds are:
1. size of relative aperture (the f-stop) (smaller numbers are larger apertures--thinner depth of field)
2. focal length of lens (the longer the lens, the thiner the depth of field at any given aperture) [Note--you said the longer lens gets out of focus background only zoomed in--which is to say, longest focal length]
3. distance of camera to subject (the closer the subject, the more out of focus the background)
4. distance of subject to background (the farther, the less focused)
5. size of film or sensor (camera format--the bigger the sensor, the less depth of field at given settings)
6. degree of enlargement of the photo and the distance for viewing it (billboards may look sharp in the background from a distance)
For softest background, use longer lens, close to subject, with distant background, using the largest aperture. (But there are other things to consider for artistic purposes.)
But note--the shape of the aperture neither increases nor decreases the severity of the out-of-focus background; rather (some say) it somehow enhances the quality of such backgrounds in a way that only the word "bokeh" is meant to capture. If someone says a certain lens or lens series had good bokeh, it is not clear what they mean, but they probably just mean it had a round aperture with many blades, and they (somehow) see this in the pictures. To me, it is significant that nobody could see this until the word "bokeh" was picked up from the Japanese, not even experts. Some people still can't see it. I don't think Ansel Adams mentioned it in his 5-volume textbook series, maybe because he did not speak Japanese.
Bokeh and depth of field are two different concept... (
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