There is no good reason why fog lights are yellow. Here is an
excellent explanation provided by Professor Craig Bohren of Penn State
University:


"First I'll give you the wrong explanation, which you can find here and
there. It goes something like this. As everyone knows, scattering (by
anything!) is always greater at the shortwavelength end of the visible
spectrum than at the longwavelength end. Lord Rayleigh showed this, didn't
he? Thus to obtain the greatest penentration of light through fog, you
should use the longest wavelength possible. Red is obviously unsuitable
because it is used for stop lights. So you compromise and use yellow
instead.


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."


Dr. Lawrence D. Woolf
General Atomics