Destructive Interference and the Conservation of Energy

[Rattus_norveg]

This is a question concerning the wave nature of light and the conservation of energy.

Consider a prism that combines two sources of monochromatic, coherent (laser) light into one beam. The sources are adjusted so that the laser beams combine in phase resulting in constructive interference. So, the resultant beam has the same wavelength as the parent beams but it's electric and magnetic vectors have twice the amplitude.

Now consider the same setup but with the one parent beam adjusted so that the beams combine 180 degrees out of phase, resulting in 100 percent destructive interference. The electric field vector of the first beam exactly cancels the electric field vector of the second beam and vice versa; the same is true for the magnetic field vector.

It seems that at this point, with the two light beams perfectly combined 180 degrees out of phase that the resultant beam of light is effectively obliterated. If so, where does the energy go? How is the law of conservation of energy maintained when considering this system?

 

[netheril96]

You asssume that the light has only one way out
In fact,the light beams can be reflected at the surface
Once the refracted light is canceled out,the reflected light will be strengthened.

 

[Dadface]

Sorry if this seems nit picky but the optical arrangement shown will not bend both beams through 90 degrees and bring them together.

 

[Dale]

I do not believe that this image is an accurate representation. The two beams of light are internally reflecting off of different surfaces, so they are not spatially colocated. Therefore, they cannot exhibit complete destructive interference. I think this is also what Dadface noticed.

 

[Rattus_norveg]

Don't take the drawing too literally, the whole question is meant as a thought experiment. Here I'm assuming that there is some optical arrangement that would blend the two beams. It is probably not possible to create optics to blend the beams perfectly in real life.

 

[JDługosz]

Hmm, why would two (different) beams give interference? I thought each quantum only interferes with itself. Is it a boson thing?

 

[Dale]

Here I'm assuming that there is some optical arrangement that would blend the two beams. It is probably not possible to create optics to blend the beams perfectly in real life.

That is correct, you can get destructive interference in some places and constructive interference in others, but energy is conserved overall. You can also, of course, have interactions with matter where energy is transferred between the fields and matter, but again energy is conserved overall.