The correct reason why turning on the headlights does not help the driver see through the fog is:
Fog is a heterogeneous mixture of water and air. It scatters light in all directions, which is why it is hard to see.
When headlights illuminate the fog, the light becomes scattered by the water droplets in the fog, causing a reduction in visibility. Instead of illuminating the road ahead, the light reflects off the fog itself, creating a bright, washed-out effect that makes it difficult to see through the fog.