How Does Electromagnetic Wave Intensity Decrease with Depth?

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SUMMARY

The intensity of electromagnetic (EM) radiation decreases with depth according to the formula I(z) = Ie^(-2niωz/c), where I represents the initial intensity, ni is the complex part of the refractive index, ω is the angular frequency, and c is the speed of light. The discussion emphasizes the application of the Poynting vector to analyze this phenomenon. Participants suggest assuming normal incidence of the EM wave on the surface to simplify calculations and derive the electric field. This foundational understanding is essential for further exploration of wave propagation in different media.

PREREQUISITES
  • Understanding of electromagnetic wave theory
  • Familiarity with the Poynting vector
  • Knowledge of complex refractive indices
  • Basic calculus for solving exponential equations
NEXT STEPS
  • Study the derivation of the Poynting vector in detail
  • Explore the concept of complex refractive indices in optics
  • Learn about wave propagation in different media
  • Investigate the implications of normal incidence on EM wave behavior
USEFUL FOR

Students and professionals in physics, particularly those focusing on optics and electromagnetic theory, will benefit from this discussion. It is also relevant for researchers exploring wave interactions with various materials.

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Homework Statement



Show that intensity of radiation(EM wave) falls off with depth z
as
I(z)= Ie^(-2niwz/c)

where I = initial intensity
and ni=complex paert of refractive index

Homework Equations


I have tried the solving the solution using poynting vector.


I have been pondering over the question over the last two days without any success. I think i am making it more complicated than it needs. to be. I would appreciate it if you point me in the right direction .
 
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Determine the electric field. You are probably supposed to assume that an EM wave is normally incident on the surface.
 

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