Hint: Before going through the question let us have a one line answer for the given query to get an idea about the topic.One cannot see through fog because the light is scattered in every direction by the droplets of fog.
Complete answer: Fog, according to international definition, decreases visibility to less than one kilometre. The concentration of cloud condensation nuclei and the subsequent distribution of droplet sizes determine fog visibility reduction. Patchy fog may also occur, particularly when air with varying temperatures and moisture content interacts, making these concepts difficult to apply in practise. Fogs of all kinds form when the air's temperature and dewpoint are the same (or nearly so). This can happen by cooling the air to just below its dew point (causing advection fog, radiation fog, or upslope fog), or by adding moisture and raising the dew point (producing steam fog or frontal fog). When the dewpoint spread is greater than \[4^\circ F\], fog seldom forms. Fog that obscures less than \[0.6\;\] of the sky is referred to as land fog in. Simply put, shallow fog is fog that is so thin that it does not block visibility at a height of 6 feet above the horizon. Fog can be differentiated from haze by its grey colour and higher relative humidity. According to Köhler theory, haze does not contain triggered droplets larger than the critical scale. Mist is a hybrid of fog and haze in that its particles are smaller (a few metres maximum), it has a lower relative humidity than fog, and it does not block visibility as often. However, there is no clear distinction between either of these classes. Fog is often mixed with smoke near industrial areas, and this mixture is known as smog. Fog droplets, on the other hand, are normally absent in photochemical smog, which consists solely of unactivated haze droplets.
Note: Water vapour molecules combine during condensation to form tiny liquid water droplets that float in the air. Because of these tiny water droplets, fog can be seen. Fog can shape quickly and disappear just as quickly, depending on humidity and temperature. This is referred to as "flash fog."