E&M: Energy Transported over medium w/ total internal reflection

Click For Summary
SUMMARY

The discussion centers on demonstrating that the average rate of energy transport across the boundary during total internal reflection (TIR) is zero. The key insight is that the wave number in the material becomes purely imaginary under TIR conditions, leading to the conclusion that the real part of the product of the electric field (E) and magnetic field (B) is zero. The method suggested for finding the time average involves using the formula = (1/2)Re. This approach is essential for understanding energy transport in optical physics.

PREREQUISITES
  • Understanding of total internal reflection (TIR)
  • Familiarity with electromagnetic wave theory
  • Knowledge of complex numbers and their applications in physics
  • Ability to perform time averaging of wave functions
NEXT STEPS
  • Study the principles of total internal reflection in optics
  • Learn about the mathematical representation of electromagnetic waves
  • Explore the concept of complex wave numbers in different media
  • Investigate time averaging techniques in wave physics
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying optics and electromagnetic theory, as well as educators seeking to clarify concepts related to energy transport in wave phenomena.

astrosag
Messages
1
Reaction score
0

Homework Statement


In the case of total internal reflection, show that the average rate of energy transport across the boundary is zero.


Homework Equations


None Provided

The Attempt at a Solution



All that I have come to is that I should use some form of the following method to find the time average of a product:

<fg> = (1/2)Re<fg*> ...(fg on the RHS can have real and/or imaginary parts)

I am quite lost on this problem and have hit a brick wall for this homework problem. Any help is appreciated, thank you.
 
Physics news on Phys.org
astrosag said:

Homework Statement


In the case of total internal reflection, show that the average rate of energy transport across the boundary is zero.


Homework Equations


None Provided

The Attempt at a Solution



All that I have come to is that I should use some form of the following method to find the time average of a product:

<fg> = (1/2)Re<fg*> ...(fg on the RHS can have real and/or imaginary parts)

I am quite lost on this problem and have hit a brick wall for this homework problem. Any help is appreciated, thank you.
The wave number in the material is purely imaginary for TIR,
so Re(E*B)=0.
 

Similar threads

E<V Potential Step Confusion
  • · Replies 7 ·
Replies
7
Views
3K
Why Does Light Transition to a Second Medium During Total Internal Reflection?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate What's the amount of energy lost in Total Internal Reflection?
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad EM wave reflected or transmitted?
  • · Replies 8 ·
Replies
8
Views
3K
Blackbody Radiation - Entropy and Internal Energy
  • · Replies 4 ·
Replies
4
Views
4K
Graduate Frustrated total internal reflection: Where does energy come from?
  • · Replies 1 ·
Replies
1
Views
3K
High School Can light escape the medium when total internal reflection occurs?
  • · Replies 10 ·
Replies
10
Views
3K
Poynting Vector in Total Internal Reflection Wave (TIR)
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Multiple reflections and transmissions of light inside a cube
  • · Replies 2 ·
Replies
2
Views
3K
Thermal energy density of the milky way
  • · Replies 3 ·
Replies
3
Views
2K