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More a confirmation then a question.

Going off of what Keith said, the closer your subject is to your background, the less shallow your DOF is? If your subject is further away from the background you have a better DOF.

I really hope I got that right.

I think you're miss using the word DOF. DOF stands for depth of field and refers to the parts of the photo that are considered to be in focus and sharp to the eye. It has no direct connection to the background as such. Further the distance of your subject from the background won't affect the depth of field - the depth of field will remain the exact same. However think of the depth of field like a sheet of paper parallel to the front of your lens. If your paper is thin (ie small depth) then the background will be further away from the paper and so more blurred - if the paper is thicker (eg book) then the depth of field is greater and thus the background will be closer or even inside the book and thus be less blurred.

However that also tells you that if you move the subject and the background further apart then even with a larger depth of field you can get the background to be far enough away that it retains its blurred nature.

edit - to summarise - if you want more blur on the background then yes moving the subject and the background further away from each other will give more blur to the background.
 
I just found this thread...wow...there's so much confusion with terms and concepts. Here's what I would keep in mind. I think what you want is "shallower" depth of field, as opposed to greater depth of field. The technique you want to employ is called "selective focus", which is where the main subject is rendered sharply and the background is rendered distinctly out of focus. At the short focal lengths of an 18-55mm kit lens with apertures ranging from f/3.5 at 18mm to f/5.6 at 55mm, selective focus shots are not always easy to achieve. In fact, on a full-length human figure shot with the wider-angle lengths of 18-35mm, it's almost impossible to throw the background totally out of focus, due to the amount of depth of field those focal lengths have at the apertures available on the kit zooms.

To keep the backgrounds well out of focus, the easiest thing to do is to keep the subject close to the camera, and to keep the backgrounds as far behind the subject as is possible. Depth of field increases RAPIDLY with DISTANCE, no matter what the lens's focal length is--short,medium,telephoto--as the camera-to-subject distance gets longer, the depth of field grows, rapidly, and then by incredibly huge leaps and bounds.

You can also use longer focal length settings, and larger aperture settings; so, the 55-200 VR's slightly wider aperture at 55mm as opposed to the kit 18-55's f/5.6 aperture will mean that the longer zoom, the 55-200 VR, will produce somewhat more-blurred backgrounds at 55mm than will the slower lens.

I read your earlier post; what Ashley wanted was a bunch of shallow depth of field images. You can achieve your shallowest DOF images by using the 55-200, keeping her as close as possible to the camera, and as FAR away from the backgrounds as possible. The issue of getting shallow DOF comes when you want to show Ashley full-length, because then you need to back the camera away from her quite far--and even with a 55 to 200mm zoom range, the camera is far enough away from her that there's still reasonably deep depth of field at the f/stop range that lens provides you. This is where a wider-aperture lens like a 70-200/2.8, 300/2.8 ,or 200/2 is useful--to throw the backgrounds out of focus more than is possible with consumer gear.
 
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Well then... Looks like I wasn't so close after all. I think I do understand it though. Thank you Derrel for putting it simply and explaining it. I do believe next time i'm on location I will pull out the bigger lens, and see what I can get with that.
 
You can buy a 50mm f1.8 manual lens for only around $35usd on bay. You should consider it
 

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