Basically, you're correct. In general, wider angle lenses provide greater depth of field. I used to laugh at the autofocusing 20mm lenses- they would hardly move at all when focusing.
If you're using your camera manually, just remember that for each stop you open the lens, you have to cut the shutter speed in half to maintain the same level of exposure. The confusion sets in because most cameras are calibrated in 1/3 stops. For example, f/3.5 is 2 1/3 stops faster than f/8, and the shutter would have to be adjusted accordingly. With the new digital cameras, I fear folks just aren't going to bother to learn how photography really works, as the camera does all the work for you.
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