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The Nikon D40 does not have an autofocus motor, relying on the lens having one. This Sigma lens does not have such a motor, relying on the camera having one. Nikon designates lenses with an autofocus motor AF-S, Sigma calls theirs HSM.
The Sigma 70-300mm f/4-5.6 DG will not autofocus with the D40 since the lens does not feature an internal focusing motor (HSM). The D40 does not have an AF motor in the body and hence it can autofocus only with lenses featuring an integrated motor (eg. Nikon AF-S lenses, Sigma HSM lenses, Tokina DX II series etc). Unfortunately you can use the said lens only in MF mode.
Here is Nikon's specs of lens compatibility for the D40X:
Compatible Lenses*: Nikon F mount with AF coupling and AF contacts Type G or D AF Nikkor: 1) AF-S, AF-I: All functions supported; 2) Other Type G or D AF Nikkor: All functions supported except autofocus 3) PC Micro-Nikkor 85mm f/2.8D: Can only be used in mode M; all other functions supported except autofocus 4) Other AF Nikkor*â¹/AI-P Nikkor: All functions supported except autofocus and 3D Color Matrix Metering II 5)
Non-CPU: Can be used in mode M, but exposure meter does not function;
electronic range finder can be used if maximum aperture is f/5.6 or
faster 6) IX Nikkor lenses cannot be used *â¹ Excluding lenses for F3AF
Unfortunately, this lens is not supported by the D40 due to Nikon's unfortunate decision to leave out the autofocus motor from this camera. This is why I tell folks not to waste their money on the D40 - access to the many, many, many lenses that Nikon has made over the years, many of which are available used for a substantial savings, is lost on this camera. The only Nikon lenses that work are AF-S lenses, and some third party lenses that have their own internal motors. I got a list of Sigma lenses that are compatible with the D40 for you:
The list of compatible Sigma lenses for the Nikon D40 as of the current date is as follows:
10-20mm F4-5.6 EX DC
17-35mm F2.8-4 DG
50-500mm F4-6.3 DG
APO 50-150mm F2.8 EX DC HSM
70-200mm F2.8 DG MACRO
100-300mm F4 DG
120-300mm F2.8 DG
300-800mm F5.6 DG
14mm F2.8 EX
30mm F1.4 EX DC HSM
150mm F2.8 EX DG
180mm F3.5 EX DG
300mm EX DG
500mm EX DG
800mm f5.6 EX DG
from here: http://www.imaging-resource.com/NEWS/1177682545.html Sorry for the bad news. The cheaper thing at this point may be to sell the D40 and get a D80. I personally have a D70S, but that is no longer made.