Is the D3100 a crop sensor? I think it is but how crop it is?
Someone suggested a Nikon 24-70mm for a full frame. He mentioned a cropped sensor would probably be a Sigma 17-50mm f/2.8?
Would it be correct to buy a 70-200mm Nikon on a D3100 or there is an equivalent for cropped sensor?
A full frame lens will work perfectly well on this sensor, but your field of view will be approximately 75 percent of what you see on a full frame, or put another way, focal length will appear to be about 150 percent of what you're used to on full frame. So, for example, the 18-55mm kit lens that came with the D3100 would be about the same as a 28-80mm on full frame, wide but not ultra-wide, to very short telephoto.
If you want a true wide angle, you need to get down into the teens at the short end. The 24-70mm, while it will doubtless make fine pictures, will only get you to the full frame equivalent of 36mm, which is a a wide-ish but not terribly wide angle. Of course what you need will depend on what you generally prefer. On your cropped sensor, the 24-70mm will be almost exactly equivalent to a 35-105mm. Back in film days it was one of the more popular full frame zoom lengths, and very handy as a "walk-around" lens. I have one that I used for many years with a 35mm, and it's a very nice range. It really depends on how wide you think you'll need to go. Once upon a time, before zooms, a full frame user would likely have had in his arsenal, a 35mm, a 50mm, and a 135mm lens. Wide angles have gotten wider, and telephotos longer, in recent generations.
For the telephoto end of things, a 70-200mm will get you pretty nice results, I imagine, equivalent to a 300mm on full frame. If you want decent optics and don't mind it being a bit slow in both aperture and focus speed, you might consider the DX-only 55-300mm. I have this as a complement to the 18-55mm kit lens that came on my D3200, and it's a very decent performer. Its focus speed is not terrific for fast action, and its aperture is a bit small for indoor sports. A lot of bang for the buck, though, and 300mm on a DX format gets you some serious telephoto reach. It’s compact, sharp, and inexpensive.
Final edit note: see headers above for a Moose review of the 55-300mm. I basically agree with this review.
2. The 24-70mm is indeed a full frame lens which you can certainly use on the D3100. For full frame cameras, that lens is considered a fast normal zoom. It’s “fast” because of the constant f/2.8 aperture throughout the focal range. It’s “normal” because it the focal range goes from moderately wide to moderately tele.
While you can use the 24-70mm as a fast normal zoom on the D3100, there are a couple of drawbacks. This is a rather large and heavy lens. On an APS-C sensor, 24mm may not be wide enough for some folks, and it’s expensive.
There are 3 other fast normal zooms that can be used on the D3100. They are the Nikon 17-55mm f/2.8, the Sigma 17-50mm f/2.8, and the Tamron 17-50mm f/2.8.
The Nikon model is just as huge as the 24-70mm and also very expensive.
The Sigma and Tamron models are a lot less expensive and considerably smaller and lighter, and they have optical stabilization.
3. Just like the 24-70mm, the 70-200mm is a full frame lens which you can certainly use on the D3100. Nikon has 2 current 70-200mm lenses. One has a constant f/2.8 aperture throughout and the other is f/4. This lens is considered a fast tele zoom. Unfortunately, there’s no real alternatives to this other than the third party offerings (i.e., Sigma, and Tamron). The 70-200mm f/2.8 is huge, heavy, and expensive. The f/4 lens is slightly smaller.
There are no fast tele zooms made specifically for APS-C. The only options are the variable zooms such as the 55-200mm or the 55-300mm. There’s also the super zoom 18-200mm, but none of these are “fast” lenses.
If you want fast zooms and to cover a large focal range, it’s an easy choice if you shoot with a full frame camera. You just get the 24-70mm and the 70-200mm.
For us APS-C shooters, it’s a bit more tricky if you want to cover the equivalent field of view. Personally, I went with the 17-50mm and then a 70-200mm.
It’s frustrating that Nikon won’t make a fast tele zoom for their APS-C bodies. Fuji actually has an X-mount lens on their roadmap which is the 50-140mm f/2.8. It would be perfect if Nikon (or Sigma/Tamron) make an F-mount version.