how deep must a range hood be to effectively clear cooking vapor?
The deeper the better; ideally, it should be as deep as the range. Closer to the burners is better too, as is a higher airflow, within reason. Beyond 300 CFM, you might need a makeup air system or to be diligent about opening a window when it's running.

More info: http://www.greenbuildingadvisor.com/blogs/dept/green-building-curmudgeon/why-range-hoods-don-t-work