Is the focus type sigma 500 F7.2 lens for Nikon a Autofocus or Manual? The camera which was used with this lens a Nikon F100 35mm SLR Camera.

There are three things you have to consider when getting lenses for the D3200.

First, you already know that the lens has to have the Nikon F mount.

Second, in order to autofocus, the lens must have a focus motor since the D3200 doesn't have one itself. Sigma designates lenses with the focus motor as HSM. Tamron designates theirs as USD. Lenses that don't have the focus motor will still work with the D3200, you just have to focus manually.

Third, the lens must have the electronics to communicate with the camera in order for the exposure meter to work. Any Sigma or Tamron lenses designed for digital cameras will have the electronics. Older mechanical lenses, including those from Nikon, will still work with the D3200, but you must set the exposure manually, without any help from the camera's light meter.

Yes.

No. This lens lacks an autofocus motor, relying on the camera to have one. The D5100 lacks an autofocus motor, relying on the lens to have one. Adding a battery grip does not change this situation.

The D5100 only autofocuses with lenses having an internal autofocus motor. Nikon designates such lenses AF-S, Sigma calls it HSM. Lenses without the motor will only autofocus with the larger and heavier Nikon cameras such as the D7000.

Sigma makes some lenses for Nikon cameras-- though the Nikon D40 requires a lens with its own internal focusing mechanism, since it does not have an autofocus motor. This entirely depends on what Sigma lens you have, i.e. if it were a Sigma lens made for a Canon camera, yes there would be an adapter for that-- but the likelihood of success is less with the limitation of the D40 needing an internal focus motor on the lens.

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.

You need to have a compatible lens to be able to autofocus. Some older Nikkor lenses and even more so 'generic' lenses (ie. Tamron, Sigma, Opteka etc.) do not autofocus or can be used with Nikon bodies.

Check that the lens is compatible with your camera.

That lens is not an AFS type lens. The D40x camera only uses AFS compatible lenses. You could still mount and use it in M, but it will never give you autofocus or TTL flash.

All Sigma:
50-500mm f/4-6.3 DG
50-150mm f/2.8 EX DC HSM
70-200mm f/2.8 DG MACRO
80-400mm f/4.5-5.6
100-300mm f/4 DG
120-300mm f/2.8 DG

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

They do not recommend 3rd party lenses, ever

Your camera is only compatable with AFS-type lenses because it has no screw-drive motor.  You can only use AFS Nikkors and Sigma HSM lenses (the lens actually has a motor inside).  You were misinformed.  Bring the lens back and ask for a refund. Take that money and purchase a compatable lens somewhere else.