The extinction cross section (or the total cross section) represents the total losses (or Extinction, or Attenuation) of energy from the incident beam (flux) due to both absorption and scattering, and is defined as the sum of the absorption and scattering cross sections.

Absorption cross-section (in m2) = Total power absorbed by a particle / Density of the flux power that falls on that particle

Scattering cross-section (in m2) = Total power scattered by a particle / Density of the flux power that falls on that particle

By the way, in newer literature the term "attenuantion" is preferred over "extinction"

If you consider the extinction process as a reaction between a photon and a substance, the reaction cross section of this process may be termed as extinction cross section. Similarly we have photo-emission cross section, photo-dissociation cross section and etc. Indeed this is more intuitive rather than having a physical or geometrical cross section, which is the surface area spanned by two colliding particle with diameter of 2 times the particle radius.

The extinction cross section (or the total cross section) represents the total losses (or Extinction, or Attenuation) of energy from the incident beam (flux) due to both absorption and scattering, and is defined as the sum of the absorption and scattering cross sections.

Absorption cross-section (in m2) = Total power absorbed by a particle / Density of the flux power that falls on that particle

Scattering cross-section (in m2) = Total power scattered by a particle / Density of the flux power that falls on that particle

When light falls on a particle, some fraction of it gets absorbed within the particle and the rest is scattered from the particle. The amount of light absorbed or scattered is dependent on the geometrical cross section of the particle as well as the optical properties like dielectric constant of the particle and the surrounding medium.

Combining all these things, sometimes, a particle is capable of absorbing or scattering more than the light incident on it (see this interesting paper of Carig. F. Bohren, Am. J. Phy. 51 (4) , 1983).

Therefore it is required to define the absorption and scattering cross section of a particle apart from its geometrical cross section. Now, in the context of Mie theory, simply the sum of the scattering cross section and absorption cross section defines the extinction cross section of the particle (Extinction= absorption+scattering).

The relec=vant chapter (6) of Bohren is for free o n the web

It shows why there is the cross section: irradiance is the intensity of light through unit surface area. Hence one particle removes anergy form the beam according to a parameter that has dimensions of surface: the cross section

Aparajita

Most particles do not absorb light. These only exert scattering

Roman

The father of modern scattering calls it extinction and not attenuationM.I. Mishchenko, 2013: Direct simulation of extinction in a slab of spherical particles. J. Quant. Spectrosc. Radiat. Transfer , 123, 103-112

@Harry ten Brink,

Sir, You are absolutely right. That's why in the next line I mentioned that the absorption is dependent on the geometrical cross section along with the optical properties of the material. Thanks for pointing it out .

Aparajita

I had not appreciated this as meaning that (most) materials do not absorb light in the visible region

Googled all evening and found ( a little to my surprise, but then he is the best teacher of physics) Feynman lectures vol 1 chapter 32 section 5. OK it is for Rayleigh scattering but it is crystal clear about the meaning and even calculation of the cross section.

And the section can be easily found on the web

Extinction cross-section = sum of absorption cross section and scattering cross section. 

or sum of the possibility of a light/ particle to be absorbed and scattered by a molecule/medium 

The absorption cross section is a measure of a particle's ability to absorb incoming light, the scattering cross sections measures how well a particle scatters light, and the extinction is the sum of these.  IE all the light that is either absorbed or scattered by a particle is it's 'extinction'

Extinction cross section = absorption cross section + scattering cross section. For a particle having no imaginary part of permittivity, there will be no absorption. Absorption cross section = 4*pi*k*Real{i*alpha}; alpha is the polarizability of the particle.

I would like to find out the Equation 3.23 from “Absorption and scattering of light by small particles” Book. Could you help me to derive this equation or can you send me the text or lectures to find this derives?