Is a nikon 60mm macro compatible with a nikon d3000?

I want a macro, but does the 60mm fit with the nikon d3000?

Yep, no probe at all.

I was told that nikon lens are compatible with any cameras. I even bought an antique wide angel lens and fits right into my new nikon camera. You can try it out at a photo store. Just pretend that you're shopping for that lens.

If it comes with a F-mount then it will fit the D3000. The level of compatibility would depend on the exact model of the lens. The D3000 can't AF all Nikon lenses. Of course if the lens was manual, you shouldn't expect much from it anyway. Also, most manual lenses would work only at Manual mode without a lightmeter on the D3000.

The Nikon 60mm f2.8 macro is an AF-S lens so it will autofocus on your D3000 no problem.
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