This information about fog should help you to understand that it's not as big a problem as you probably think, so read on with confidence. First a tiny bit of met theory. All air contains water vapour. It stays invisible until its temperature drops to a critical level. That critical point is called the dew point. When the temperature and dew point are the same, fog forms. This happens on your bathroom tiles when you run a bath or shower.
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Pilots early in their careers learn to be cautious in fog. When landing it’s possible to fly over an airport and see the runway and buildings very clearly and then in the last part of the landing, as the plane descends into the fog layer, for the visibility to be so reduced that it’s impossible to see to land. So we learn about fog and visibility very early on, and it comes under the heading of slant visibility if a fog layer is 50 feet thick it would be more than likely you could see through it from directly above. More info from fear of flying Premium
Aviation law will state what equipment has to be available, how it is to be checked and calibrated and which aircraft can use it. Some of the requirements are listed here.
On reporting for duty a crew will be given or will get a weather briefing. According to the runway visual range (RVR) certain things will apply. First the minima which is part of the pilots operating procedure. Nothing can happen unless the RVR is above a certain amount and this is called the operating minima (or limits). These apply to take off, landing, and making an approach to land. The RVR value is part of the minima laid down.