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

 

[sardar]

Hi there,

The attenuation of electromagnetic waves is a result of the wave's interaction with the material it is passing through. As the wave travels through the material, it can be absorbed, scattered, or reflected by the atoms and molecules in the material. This results in a decrease in the wave's intensity over distance.

The relationship between the intensity and depth is exponential because as the wave travels deeper into the material, it encounters more and more atoms and molecules that can interact with it. This leads to a cumulative effect of attenuation, where each interaction reduces the intensity of the wave. This is why the decrease in intensity is not linear, but rather exponential.

I hope this helps to clarify the concept for you. If you need more information, please let me know. Good luck with your studies!