Why are fog lights yellow? Does it help that they are?
Does it matter if you are driving in city or countryside?

Answer: It is important for fog lights to be one color (rather than white,
which is all colors) because the different wavelengths(colors) of visible
light scatter off the fog droplets differently. This phenomenon is known
as "dispersion," because the different colors of light in an image will
separate from each other, causing the image to "disperse." If you illuminate
the road with only one wavelength (color) of light, the images of the objects
you see will still become somewhat blurry because of the scattering of
light by the fog, but at least you won't have extra problems from dispersion.

So, if we want to use just one wavelength of light, which wavelength should
we use? It turns out that light with short wavelengths scatters more than
light with long wavelengths (short to long: violet, indigo, blue, green, yellow,
orange, red). So, a long wavelength light will be best. There's another thing
to consider, too: our eyes are not equally sensitive to all colors. It turns out
that we are most sensitive to yellow and green light. So, our best compromise
between sensitivity for our eyes and a long wavelength for least scattering
is yellow light.

Now, I don't know what kind of light bulbs are used in fog lights, but another
consideration used in street lighting is cost and efficiency. You may have
seen some yellow street lighting in some places; this is "low-pressure
sodium vapor" lighting. The special thing about this light is that it is almost
entirely one (actually two very close together) wavelength of yellow light,
and that it gives the most illumination for the amount of electricity. A big
problem with this light, though, is that it throws off color perception.
Under sodium vapor light, something blue looks gray. This makes it hard
to say recognize your car in a parking lot.

There is no good reason why fog lights are yellow.
Here is an excellent explanation.

"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."

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