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

In summary, the problem involves finding the average rate of energy transport across a boundary in the case of total internal reflection. The suggested method is to use the equation <fg> = (1/2)Re<fg*>, where the wave number in the material is purely imaginary for TIR. This results in Re(E*B) being equal to zero.
  • #1
astrosag
1
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.
 
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  • #2
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.
 

1. How is energy transported over a medium?

Energy is transported over a medium through electromagnetic waves. These waves consist of both electric and magnetic fields that vibrate and propagate through the medium, carrying energy with them.

2. What is total internal reflection?

Total internal reflection occurs when a light ray traveling through a medium reaches the boundary of a new medium at an angle greater than the critical angle. This causes the light to reflect back into the original medium, rather than refracting into the new medium.

3. How does total internal reflection affect the transport of energy?

Total internal reflection can affect the transport of energy by causing it to be reflected back into the original medium instead of being transmitted into the new medium. This can lead to a loss of energy and a decrease in the overall amount of energy being transported.

4. What factors can influence total internal reflection?

The angle of incidence, the difference in refractive indices between the two mediums, and the wavelength of the light can all influence total internal reflection. Additionally, the surface roughness and the presence of any impurities can also affect the amount of energy that is reflected back into the original medium.

5. How is total internal reflection used in technology?

Total internal reflection is used in various technologies, such as fiber optics, where it allows for the transmission of light over long distances without significant loss of energy. It is also used in devices like prisms and mirrors, which utilize total internal reflection to manipulate and redirect light for various purposes.

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