# How does the reflection coefficient change with scattering and absorption?

My professor of Biomedical Optics course asked us to think upon the evolution of the reflection coefficient with the absorption coefficient $$\mu_a$$, the reduced scattering coefficient $$\mu_s'$$ and the refractive coefficient of medium $$n_2$$.

Here I share what are my thoughts:

• For a highly absorbent medium, hence with high $$\mu_a$$ we will have less reflection since part of the incident light is absorbed in the medium itself

• For a highly scattering medium, hence with $$\mu_s'$$, it will be highly probable that the incident light will be back-scattered. Thus the reflection coefficient will be higher

• Changing the refractive index $$n_2$$ will change the angle of the refracted light but won't have any effect on the reflected light

I'm not very sure about my answers and I feel like thay are not correctly supported by a convincing explanation.

Can you help me provide better answers?

Thank you in advance!

## 1 Answer

Try thinking about this in terms of Fresnel equations. Have you seen those? They relate the reflection of an EM wave at a boundary to the wave impedances of the two media. Impedance is closely related to refractive index. See what happens to the reflection coefficient when you allow for a complex refractive index (so there’s absorption). One interesting example is that of metal, say silver, which has a small real part of refractive index, but large imaginary part. What is the reflection coefficient like for silver? What is the power absorption coefficient?

Also remember that reflection typically refers to the coherently redirected wave at the interface, which has angle of reflection equal to angle of incidence. Whereas since scattering is usually taken to be incoherent and at all angles, then it would be in a different category.