# Relationship between diffused light and intensity

I was wondering if the relationship of the intensity of diffused light is a linear correlation to the diffusing material. Basically will the intensity of the diffused light change in a linear fashion as the diffusing factor increases/decreases?

• What does "diffusing factor" mean? – DumpsterDoofus Mar 5 '14 at 22:33
• Maybe I have a confused understanding of how diffusion works but i thought different materials diffuse light more or less because of their properties. I am sorry but I don't know the name for the property that determines how much light is diffused. – Julian G. Mar 5 '14 at 22:46
• Couldn't one define a "diffusing factor" $D$ such that $I_\text{transmitted}=\frac{1}{D}I_\text{incident}$? By definition, this would be linear. The interesting physics would then be to determine how $D$ depends on wavelength, thickness, etc. – BMS Mar 6 '14 at 0:14

If the characteristic length of the material is $L=d^{-1}$, where $d$ is a "diffusivity factor" for the material, then it's easy to show that if the incoming beam is collimated, the amount of light that exits the material and remains collimated is $$P_c=Pe^{-Td}$$ where $P$ is the power of the incoming beam and $T$ is the thickness of the diffusing material.
Meanwhile, the scattered light will be isotropically radiated, with an intensity $$P_s=\frac{P}{4\pi}(1-e^{-Td})\approx \frac{PTd}{4\pi}$$ per steradian in the far field in the low diffusion limit $Td\ll1$. As a result, scattered intensity is roughly linear with diffusion factor (up to a point).