This explanation is flawed for more than one reason

This explanation is flawed for more than one reason. Fog droplets are, on

average, smaller than cloud droplets, but they still are huge compared with

the wavelengths of visible light. Thus scattering of such light by fog is

essentially wavelength independent. Unfortunately, many people learn

(without caveats) Rayleigh's scattering law and then assume that it applies

to everything. They did not learn that this law is limited to scatterers

small compared with the wavelength and at wavelengths far from strong

absorption.

The second flaw is that in order to get yellow light in the first place you

need a filter. Note that yellow Fog Lights were in use when the only

available headlights were incandescent lamps. If you place a filter over a

white headlight, you get less transmitted light, and there goes your

increased penetration down the drain.

There are two possible explanations for yellow fog lights. One is that the

first designers of such lights were mislead because they did not understand

the limitations of Rayleigh's scattering law and did not know the size

distribution of fog droplets. The other explanation is that someone deemed

it desirable to make fog lights yellow as a way of signalling to other

drivers that visibility is poor and thus caution is in order.

Designers of headlights have known for a long time that there is no magic

color that gives great penetration. I have an article from the Journal of

Scientific Instruments published in October 1938 (Vol. XV, pp. 317-322).

The article is by J. H. Nelson and is entitled "Optics of headlights". The

penultimate section in this paper is on "fog lamps". Nelson notes that

"there is almost complete agreement among designers of fog lamps, and this

agreement is in most cases extended to the colour of the light to be used.

Although there are still many lamps on the road using yellow light, it

seems to be becoming recognized that there is no filter, which, when placed

in front of a lamp, will improve the penetration power of that lamp."

This was written 61 years ago. Its author uses a few words ("seem",

"becoming recognized") indicating that perhaps at one time lamp designers

thought that yellow lights had greater penetrating power. And it may be

that because of this the first fog lamps were yellow. Once the practice of

making such lamps yellow began it just continued because of custom."