What Nikon lens is good for a great depth of field?

I own a Nikon D3100 and I'm looking for blurry backgrounds, so I'm looking for a lens with a very good depth of field to make backgrounds blurry. I prefer closeups, but it doesn't really matter. Also, not too expensive!

Added (1). Yeah I realized that I mixed up the two meanings, I meant a small depth of field.

Any lens can produce blurry backgrounds if you understand the idea behind it. However, some do it more easily than others. It's not just minimum aperture, there's more to it than that.

On a D3100, a 50mm or 35mm 1.8 lens (neither of which is expensive) could be one option. Shoot it at 1.8 and set up the shot correctly, and you'll have a nice blurry background.

I don't know how you're defining "expensive", but Nikon have two lenses which were designed for bokeh (the blurry backgrounds you speak of). They are a) rare and b) somewhat expensive (although not compared to things like the Leica Noctiluxes). They're the 105 and 135 F2 DC lenses. And they are spectacularly good. I've added a shot that I took with one of them just to show what they are capable of.

However, I imagine they might be outside your range, so the 50mm 1.8 I mentioned initially will do the job nicely. I have to stress again, though, you have to know how to set up a shot to get the background that way.

Depth of field is the sharp part of the photo… So if you need LESS deep of field you have to search a very "fast" lens ( f:2,8 o less ) that can give you a blurry b.ground… If you use it properly… Something like the 50/1,8G or 40/2,8macro

focal lenght is important too, but long lenses are ( too ) expensive

You can find a tutorial about understanding depth of field here: http://www.cambridgeincolour.com/...-field.htm" class='ext_link'>http://www.cambridgeincolour.com/...-field.htm

Your terminology is totally backwards. "A great depth of field" and "a very good depth of field" means that you have all the scene in focus, … NOT a blurry background. For a blurry background you are wanting a SHALLOW depth of field. The other answers have already given you lens and technique advice.

There are only three factors that affect your Depth of Field (DOF):

1) The focal length of the lens.
2) The aperture used.
3) The subject distance.

By learning about DOF you'll discover that the 18-55mm zoom lens you have is capable of producing the out of focus background you desire - at all its marked focal lengths (18, 24, 35, 45, 55).

http://www.luminous-landscape.com/tutorials/understanding-series/dof.shtml

http://www.cambridgeincolour.com/tutorials/depth-of-field.htm

At http://www.dofmaster.com/dofjs.html you can use the DOF Calculator to compute your DOF for any combination of the three factors imaginable.

Here is a comparison of the DOF using 18mm and 55mm with a subject at 5'-0''.

18mm @ f/3.5 focused on a subject at 5'-0'' DOF will be from 3'-10'' to 7'-6''. Anything from 1'-2'' in front of your subject to anything 2'-6'' behind your subject will be in focus. Anything 3'-0'' or more behind your subject will be nicely out of focus.

55mm @ f/5.6 focused on a subject at 5'-0'' DOF will be from 4'-9'' to 5'-4''. Anything from 0'-3'' in front of your subject to anything 0'-4'' behind your subject will be in focus. Anything 1'-0'' or more behind your subject will be nicely out of focus.

Knowledge trumps buying new gear about 99% of the time.