I know that smog is generally a mixture of various chemicals, such as peroxyacetyl nitrate (PAN) and ozone. I also know that smog obscures visibility.
My question is two-fold:
There are two types of smog:
We 'need' the gaseous air pollutants to form secondary aerosol particles. The reduced visibility during winter and summer smog events is caused by these secondary aerosol particles (they scatter the light and, by this process, reduce visibility). The gaseous air pollutants might contribute to reduced visibility but their contribution is negligible compared to the aerosol impact.
The composition as well as the size distribution of the aerosol particles is important to determine the aerosol's optical properties. If you look into mass concentrations, a given mass of fine particles extincts more light than the same mass of coarse particles. If you look into composition (inorganic components), nitrate extincts more light than sea salt and sulfate. The extinction of organic aerosol depends on their composition (I have no idea which factors/species are relevant there).
If you are interested in further literature on the impact of the particle composition on the light extinction you might look into Pitchford et al. (2007). I didn't find a publication which quantifies the contribution of different particulate compositions/species to light extinction for smog. However, Pitchford et al. (2007) deals with light extinction for calculating the optical thickness from model data.
The deterioration of visibility can be divided into four parts as follows:
absorption of gases + scattering of gases + absorption of aerosol + scattering of aerosol
quote from a Ph.D dissertation link here
scattering is a process where the incident radiation is reradiated into all directions after interacting with a scattering point.
In the visible zone (400 nm - 700 nm), the cloud free atmosphere is remarkably transparent, This means that the absorption of the radiation at visible band occurs primarily at the surface and not within the atmosphere itself.
We can derive that the aerosol is the dominant reason of the visibility loss.
PS: the gases species can also impact the radiative transfer process of the earth system, but mainly in non-visible regions.
Koschmiederp came up with an equation which connect the visibility and extinction coefficient $b_{ext}$ as follows:
$$V_R = 3.91/b_{ext} $$
$V_R$ is the visibility reduction, unit in meters;
$b_{ext}$ is the total extinction coffecient in all aspects (containing the four subset which I have already noted).
In the visible band, the scattering of gases can be omitted and the absorption of gases is mainly attributed to $NO_2$. As an empirical equation, the $b_{ext}$ can be derived as follows:
$$b_{ext} = 3f(RH)*[(NH_4)_2SO_4] + 3f(RH)*[(NH_4)_2SO_4] + 4f(RH)*[Organics] + 10[EC]+[Soil] +[0.6][Coarse\ mass]+ 3.3*[NO_2]+ 10 $$
$f(RH)$ is the function of relative humidity, it will increase with atmospheric RH.
[Coarse mass] = [$PM_{10}$] - [$PM_{2.5}$]
10: the extinction of clean air
In this way, the visibility loss can be rebuilt. We can derive that the "there is a relationship between the concentrations of the chemical and the optical depth/visibility" as your second question.
A figure I clipped from Chen et al., 2016 represent the relationship between $PM_{2.5}$ concentration and visibility. We can see the visibility is decrease when $PM_{2.5}$ increasing and the decreasing curve is sharp when the concentration is below 50 ${u}g/m^3$. Besides, relative humility is a key factor here which high RH can worsen the deterioration of visibility. This is due to the hygroscopic behavior of some species (eg. $(NH_4)_2SO_4$)
Smog is Air pollution + Water Vapour(Cloud)
NO2 (Nitrogen Dioxide) : deep red-orange
H2O (Water Vapour) : White
Nitrogen oxide, Sulfur oxide, Sulfur dioxide are said to be transparent gases.
