What is the relationship between the optical cross-section and the physical cross-section of a particle? - Semiconductor surface engineering

Regarding surface engineering, specifically the reflection and scattering of a semiconductor material, I have the following question in response to the problem below.

On a surface with reflectance R = 0.35, a power of 5 x 10⁻⁵ W/µm² is applied. Knowing that the total power scattered by the particle is 5 x 10⁻² W, determine the optical section. What is the relationship between the optical section and the physical section of the particle?

Scattering Section or Optical Section = σ sc
Physical or geometric section = σ geom
Scattering efficiency factor = Q sc

Substrate reflectivity (R): 0.35.
Incident intensity (I): 5*10E-5 w/(μm^2)
Total scattered power (S or Psc): 5*10E-2 W
Determination of the Optical Section σsc = ?


σ sc= Q sc* σ geom

S: Total power of scattered light (measured in Watts).
I: Intensity of incident light (measured in Watts/μm²).

σ sc= (S(spread))/(I (incident)) or σ sc= (P/ I )

σ sc=((5 ×10^(-2) ) W) / (5 ×10^(-5) W/(μm^2 )) = 10^3 μm^2


What I understood:

The irradiance that effectively interacts with the particle (Ief) is the result of modulating the incident power by the reflectance capacity of the substrate. Mathematically, the presence of the substrate defines the light available for scattering.
Surface reflectance (R) = 0.35
Incident Irradiance (I inc) = 5 E-5 W/(µm^2 )

I ef= R I inc
I ef= 0,35 (5 10^(-5) )
I ef= 1,75 10^(-5) W/(µm^2 )


σ opt=P esp/I ef

σ opt=((5 10^(-2) ))/((1.75 * 10^(-5) ) ) = 2857 µm^2




I'm honestly not sure if the concepts I used in the equations are correct. I would appreciate it if someone could correct me and, most importantly, provide me with bibliographic sources to help me delve deeper into the subject.