Electromagnetic Attenuation Conceptual Question

[Orlando]

Hello,

Why does electromagnetic wave intensity attenuate exponentially with depth from its incident intensity in an object? Why is the relationship exponential? I just need a nudge in the right direction or more if you are willing. Thank you for any help!

 

[mikeph]

Because the rate of stimulated absorption is proportional to the amount of radiation present, and the solution to this kind of differential equation is an exponential decay function.

 

[Drakkith]

Let's say that we have a group of 1,000 photons entering a material. Let us also say that every 1 cm has a 50% of absorbing each photon. So, 1,000 photons enter and 1 cm later we have approximately 500 left. Now, these 500 photons travel ANOTHER cm. What is the chance per photon to be absorbed? 50% still! So now we have about 250 photons left. These 250 travel another cm, leaving 125. And so on and so on.

So every cm reduces the amount of EM radiation by 50%. This is referred to as a halving thickness. Each layer you add multiplies the percents to absorb. Two layers is 50% x 50%, which is 0.5 x 0.5 = 0.25. So 25% of the radiation gets through while 75% is absorbed. Add 2 more layers is 0.5 x 0.5 x 0.5 x 0.5 = 0.0625. That is 6.25% of the radiation gets through and 93.75% is absorbed.

 

[Orlando]

Excellent, thank you both