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

[astrosag]

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.

 

[Meir Achuz]

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.