Understanding Destructive Wave Interference

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Discussion Overview

The discussion revolves around the concept of destructive wave interference, particularly in the context of electromagnetic waves and their interactions with materials. Participants explore the implications of energy conservation during destructive interference and how it relates to phenomena such as anti-reflective coatings.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question where energy is contained during destructive interference, particularly when waves on a string reach a rest position.
  • One participant suggests that the energy is contained in the kinetic energy of the string, as it is still in motion despite being at rest at a moment.
  • Another participant discusses a scenario involving electromagnetic waves and anti-reflective coatings, proposing that energy is dissipated in the material of the planes due to the work done by the waves on the matter.
  • Some participants express uncertainty about whether the energy remains in the electromagnetic wave or is absorbed by the material, with references to perfect absorption in anti-reflective coatings.
  • There is a suggestion that anti-reflective coatings utilize destructive interference to reduce reflection while increasing transmission, with energy conservation being a key point of discussion.
  • One participant posits that not all energy is transmitted through the film, and some energy may be absorbed, while others argue that energy conservation is maintained without necessarily requiring absorption at the surface.

Areas of Agreement / Disagreement

Participants express varying views on the nature of energy conservation during destructive interference, particularly regarding whether energy is absorbed or remains in the electromagnetic wave. There is no consensus on the specifics of energy storage or the mechanisms at play in anti-reflective coatings.

Contextual Notes

Participants discuss the implications of energy conservation in different contexts, including free space versus the presence of matter, and the specific conditions under which destructive interference occurs. The discussion highlights the complexity of energy transfer and storage in wave interactions.

aaaa202
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Sometimes I find it hard to understand how energy is conserved in destructive interference. Consider two waves on a string which interfere destructively such that the string is at its rest position. Where is the energy contained?
Edit: the string example is not very good at illustrating what I don't understand. Consider instead the following example.
A plane electromagnetic wave approaches two planes. Now the wave is both reflected and travels through the plane to the next wave is reflected again. If we now choose the spacing of the planes such that the reflection on the 2nd plane differs by exactly a 180degree phase to the first reflected wave a situation is created where we have constant destructive interference in the resulting reflected wave. Where is the energy stored?
 
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aaaa202 said:
Sometimes I find it hard to understand how energy is conserved in destructive interference. Consider two waves on a string which interfere destructively such that the string is at its rest position. Where is the energy contained?
In the kinetic energy of the string. The string may be at its rest position for a moment, but it is not at rest, it is moving. That motion has KE.

aaaa202 said:
A plane electromagnetic wave approaches two planes. Now the wave is both reflected and travels through the plane to the next wave is reflected again. If we now choose the spacing of the planes such that the reflection on the 2nd plane differs by exactly a 180degree phase to the first reflected wave a situation is created where we have constant destructive interference in the resulting reflected wave. Where is the energy stored?
This is how anti-reflective coatings work. The energy is dissapated in the material of the planes, i.e. the waves do work on the matter.
 
aaaa202 said:
A plane electromagnetic wave approaches two planes. Now the wave is both reflected and travels through the plane to the next wave is reflected again. If we now choose the spacing of the planes such that the reflection on the 2nd plane differs by exactly a 180degree phase to the first reflected wave a situation is created where we have constant destructive interference in the resulting reflected wave. Where is the energy stored?

This is how anti-reflective coatings work. The energy is dissapated in the material of the planes, i.e. the waves do work on the matter.

Forgive me if I'm wrong, but isn't the energy still in the EM wave?
 
In free space the energy of the wave is conserved, but in the presence of matter the energy of the wave can change due to absorption or radiation. The case the OP mentioned is one with perfect absorption of the reflected wave. It is used in anti reflective coatings.
 
DaleSpam said:
In free space the energy of the wave is conserved, but in the presence of matter the energy of the wave can change due to absorption or radiation. The case the OP mentioned is one with perfect absorption of the reflected wave. It is used in anti reflective coatings.

Oh, okay, I see that now in the situation the OP gave. How is this the same for anti-reflective coatings? I mean, I know they use destructive interference to work, but in this case the energy is still in the non-reflected EM wave, right?
 
Drakkith said:
I know they use destructive interference to work, but in this case the energy is still in the non-reflected EM wave, right?
Not 100% of the energy is transmitted through the film, but 0% (at a specific wavelength) is reflected due to the complete destructive interference. The difference is absorbed.

I am not certain, but I think that antireflective coatings increase the amount of light transmitted, so there may be some constructive interference on the other side of the film for the transmitted wave. But I don't know the details.
 
The interference reduces the amount of energy being reflected while increasing the amount of energy being transmitted in such a way that (surprise) energy is conserved. No energy needs to be absorbed at the surface for that to work (Though there might be some absorption depending on what the coating is made of, of course)
 

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