Just to be clear, for anyone who lives on Mars and does not know about cars, the headlights of cars today usually have two filaments.
One filament projects the beam (off the mirrors behind) straight ahead (roughly level with the road, say), and the other one projects the beam (off the mirrors) downwards (ie dipped, pointing downwards).
Thus -- when the light is on normal (that is to say, "high" beam, because the beam is pointing up high), it hits the road a long way ahead.
But in contrast, when you dip the lights, you will see the light shining on the road a fairly short distance ahead. Because they are dipped or pointing-low - the beam is pointing downwards, rather than onwards and hence in to the eyes of other drivers.
(It is surely impossible that anyone who has driven a car would not understand this -- you can either have the lights pointing a long way ahead, or dip them and you will see the two lights shining in a circle fairly close just ahead of you.)
The thing that you dip the lights with is (understandably) called a "dip switch."
(They used to - before the 60s say - typically be a small footswitch, now they are on a stalk, or automatic.)
Note that "dimming" the lights would not help, you would still dazzle the oncoming driver. You must, of course, point the beam downwards - it's how headlights work.
Note that I mention "bulbs have two filaments.." in the early days of motoring there were different systems to point the headlights downwards, when a car was oncoming..
"'Dipping' (low beam) [ie low, downwards onto the ground] headlamps were introduced in 1915 by the Guide Lamp Company, but the 1917 Cadillac system allowed the light to be dipped with a lever inside the car rather than requiring the driver to stop and get out..." etc etc.
Of course there are much more advanced things today...self levelling, lights that follow with you around a corner, morphing xenons, etc.
In the fog example, yes, naturally you have to point the beams downwards ("dip them") to avoid sparkle in the fog. Just as you have to dip your beams downwards when there is an oncoming car.
Dipping headlights, one of the basic elements of driving, along with brakes, turning indicators, etc.!
It would appear that using the word "dip" for dipping the headlights downwards, is now (always has been?) more British-usage. It seems that in the USA, the word has transformed (?) to "dim," and moreover, people in the USA tend to think of the downwards-dipped beam as the "normal" one, and you then have brights, "high" beam, etc.