Applying a thin layer of soap to a bathroom mirror prevents it from fogging by reducing the surface tension of water droplets. This allows water to form a continuous film rather than individual beads, which is why the mirror stays clear. The discussion highlights that soap alters the adhesion properties between water and glass, causing water to sheet off instead of bead. Similar principles apply when washing a car; soap allows water to slide off, while wax creates beading, which can trap dirt and make cleaning difficult. Alternatives like Rain-X No Fog and natural solutions such as onion or potato juice are mentioned, though the latter may come with undesirable odors. The conversation also touches on personal experiences with anti-fogging techniques, including spitting into diving masks.