My understanding is that fog lights have nothing to do with how powerful your main lights are. Go out in the fog and put your main beam on, you wont be able to see fark all except white! Fog lights are placed low to the floor where they can penetrate the fog on a different pane to your nomal lights so you dont get as much back scatter from them and thus can see better. They are meant for when visibility is really bad so you dont need to see far in front, just what is directly in front of you.
From Wikipedia: