Q.Why is yellow light preferred during fog?

When sunlight enters the atmosphere, particles and molecules deflect (scatter) light out of its original direction. If the scattering particles are much smaller than the light's wavelength ($a\ll\lambda$, as with air molecules), the process is called Rayleigh scattering, whose intensity varies as $I\propto1/\lambda^4$ -- shorter wavelengths scatter far more strongly than longer ones. Violet light, having the shortest visible wavelength, is scattered the most, but because the human eye is more sensitive to blue, the daytime sky appears blue. During sunrise and sunset, sunlight travels a much longer path through the atmosphere to reach an observer, so almost all of the strongly-scattered blue (and violet) light is scattered away before arriving, leaving the weakly-scattered red and orange light to dominate, giving the reddish colour of the sky at these times; yellow light (intermediate wavelength, moderately scattered) is therefore preferred for headlights and signals in fog, since it penetrates the scattering haze better than blue/white light while still being reasonably visible. If the scattering particles are much larger than the wavelength ($a\gg\lambda$, as with the dust and water droplets in clouds), …