I have a D3100 Nikon with a 35mm f1.8 prime lens. I want to buy a wide angle lens converter to make it more like a wide angle lens.
What is your advice on that? How do I know whether the lens converter will be compatible with my existing lens?
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Such things are indeed made, and they break down into two major categories:
relatively expensive, complex lenses that will shorten the apparent focal length of the lens only a little bit (to about 24mm) with only a small (but completely unavoidable) negative impact on every aspect of image quality (sharpness, contrast, aberrations, distortion, flare, etc.); and
cheap simple concave lenses (doublets at best) that may offer the same or slightly wider angle than the expensive bits, but will drastically reduce the quality of your pictures. Oh, and while they may be "cheap", they won't necessarily be disposable-level inexpensive.
If you need a lens you can occasionally use to shoot something at a wider angle (where a fast aperture won't buy you much, photographically speaking), you'd probably be a lot better off with the 18-55mm kit lens. If yyou already have it, there's no need to spend money making your 35mm worse, and if you don't have one, the non-VR "II" version will be about the same price as a mid-range conversion lens (just over $100 new and cheaper used), will be more versatile, and has very reasonable image quality, all things considered.