To my knowledge, they are designed to illuminate the road surface and edges and to ensure other road users can see you.
When you think about it, fog is moisture and when you shine a light on it, the moisture just acts as millions of tiny reflectors and refractors, so the more light you shine on it, the more light it reflects back at you and the less you can see through it. Next time you're in fog, and it is safe to do so, pop your full beam on and see how much worse your visibility becomes.
The other problem is that with the rear fog lamps, they are red, and red is a highly unstable colour. When the red light shines through the dense, moist air, the red light scatters even more and becomes less visible. The brighter red light of a fog lamp only fares slightly better than normal ones, but it is enough to hopefully make a difference.
Suffice to say, when visibility is greatly reduced by fog or dense water spray, fog lights will have some benefit but they are useless unless the driver adjusts his or her driving technique to suit the conditions, I.E. slow down, brake earlier and if necessary, stop their journey until it is safe to carry on.
Rob
Mk.2 Marea Weekend 1.8 16v 115 ELX - Bigger IS better !