Question

what is the formation of fog

Answer 1

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Fog may appear from different reasons. The most current one is:

Radiation fog. As the heat stored during the day radiates back into the sky as infrareds at night, it gets colder. When the temperature reaches under dew point, moisture must condense on a condensation nuclei such as the tree leaves, the grass or your car. That is called, dew. Then it condenses on tiny particles such as smoke or pollen in the air and, when dense enough, it is called fog. The thing is: since the air now is colder under than above, it forms a thermal inversion as the air doesn’t rise and the fog lingers over the land.

Convection fog. When a large body of water is warmer than the land, during an onshore wind, cold warmer air moves over the land and, as it cools down, form fog. In the USA and Canada, this is sometimes called, Lake-Effect fog.

Orographic fog. When moist air meets a mountain and rises, it forms fog as the air cools down. Mind you, if the people in the mountain calls it, fog, those in the valley call it … a cloud.

Katabatic fog. At night, when the colder air from the hills sink in the valleys, it may cause a wind called, a katabatic wind. Sometimes it also brings “rivers” of fog down the slopes of the hills. It is not very common but quite spectacular when you get a chance to observe it...
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Answer 2

Fog forms when the difference between air temperature and dew point is less than 2.5 °C (4.5 °F).

Fog begins to form when water vapor condenses into tiny liquid water droplets that are suspended in the air. Six examples of ways that water vapor is added to the air are by wind convergence into areas of upward motion; precipitation or virga falling from above; daytime heating evaporating water from the surface of oceans, water bodies, or wet land; transpiration from plants; cool or dry air moving over warmer water; and lifting air over mountains. Water vapor normally begins to condense on condensation nuclei such as dust, ice, and salt in order to form clouds.Fog, like its elevated cousin stratus, is a stable cloud deck which tends to form when a cool, stable air mass is trapped underneath a warm air mass.