B Does Destructive Interference Affect Starlight in a Double Slit Experiment?

[Devin-M]

Here are the resulting plots:

Figure 8: Both slits open plot.

Figure 9: Left slit covered plot.

Figure 10: Right slit covered plot.

The shapes of the diffraction/interference patterns also agree with theory.

Notice the central peak of the both slits open plot is interestingly 4 times as high as either single slit plot.

So adding the second slit results in double the total photon detections & roughly 4x the intensity in certain places and significantly reduced intensity in others. That’s consistent with conservation of energy, but how do you rule out destruction of energy in some places and creation of energy in others, proportional to the square of the change of intensity in field strength (ie 2 over lapping constructive waves but 2^2 detected photons in those regions?

To further illustrate the question posed, at 2:38 in the video below, when he uncovers one half of the interferometer, doubling light, the detection screen goes completely dark:

 

[hutchphd]

That’s consistent with conservation of energy, but how do you rule out destruction of energy in some places and creation of energy in others, proportional to the square of the change of intensity in field strength (ie 2 over lapping constructive waves but 2^2 detected photons in those regions?

Conservation of energy is all that I require. The rest is your problem.

 

[Devin-M]

At exactly 3:00 in the video he uncovers the mirror on the right side arm of the interferometer and the light on the detector screen that had been bouncing off the left side mirror of the interferometer goes completely black. You can tell there’s light headed toward that right arm mirror because you can see the red dot on the index card before he uncovers the right mirror. What happens to the light that reflects off the right the hand mirror? It appears as if the portion of that light that reflects off the right side mirror and then passes straight through the beam splitter is being completely destroyed by having a 1/2 wavelength path length difference with the beam reflecting off the left arm mirror.

 

[hutchphd]

Did you watch the entire video? (whose title is "where did the light go?")

?!

 

[Devin-M]

Yes at the very end he end he asks the viewer if the path difference of the 2 mirrors is 1/2 wavelength, why does the light going to one screen cancel out and the other add constructively. He doesn’t answer this question and leaves it for the viewer to answer. It seems like before he adds the second detection screen, half the light from the mirrors is going to the screen and the other half is going back to the laser source. When he adds the second detection screen now 1/2 is going to the 1st screen, 1/4th is going to the 2nd screen, and 1/4th is going back to the laser. As far as why on one screen there’s a half wavelength path difference and the other there isn’t, I believe it’s due to the thickness of the beam splitter. It seems there must be an extra half wavelength path length (or odd multiple of 1/2 wavelength) for the light from the left mirror that goes back through the beam splitter. I’m not yet fully convinced that when the light cancels out its really going back to the source because once its adding destructively the path length back to the source should be identical all the way back to the source so it should add destructively all the way back to the source.

For example with a different thickness beam splitter it may be possible to have the light on both detection screens add constructively at the same time or both destructively at the same time.

 

[collinsmark]

Yes at the very end he end he asks the viewer if the path difference of the 2 mirrors is 1/2 wavelength, why does the light going to one screen cancel out and the other add constructively. He doesn’t answer this question and leaves it for the viewer to answer. It seems like before he adds the second detection screen, half the light from the mirrors is going to the screen and the other half is going back to the laser source. When he adds the second detection screen now 1/2 is going to the 1st screen, 1/4th is going to the 2nd screen, and 1/4th is going back to the laser. As far as why on one screen there’s a half wavelength path difference and the other there isn’t, I believe it’s due to the thickness of the beam splitter. It seems there must be an extra half wavelength path length (or odd multiple of 1/2 wavelength) for the light from the left mirror that goes back through the beam splitter. I’m not yet fully convinced that when the light cancels out its really going back to the source because once its adding destructively the path length back to the source should be identical all the way back to the source so it should add destructively all the way back to the source.

For example with a different thickness beam splitter it may be possible to have the light on both detection screens add constructively at the same time or both destructively at the same time.

Don't forget about phase shifts. A reflected wave gets a phase shift of \pi*. Are there any differences in the total phase shifts between the two beams in question (one on the laser side of the interferometer, and the other on the wall side of the interferometer), even if their path lengths are the same?

*(For the purposes here, ignore the nuances about reflections caused by the glass itself -- the reflections going from one index of refraction to another. That makes things things overly complicated, and can be ignored for this discussion. A good beam splitter will have coatings to minimize these types of reflections anyway. Instead, treat all reflections as being caused solely by the very thin, half mirrored surface -- the light either gets reflected with a phase shift of \pi, or it gets transmitted with no phase shift at all.)

 

[Devin-M]

Don't forget about phase shifts.

On wikipedia it says “Also, this is referring to near-normal incidence—for p-polarized light reflecting off glass at glancing angle, beyond the Brewster angle, the phase change is 0°.”

https://en.m.wikipedia.org/wiki/Reflection_phase_change

 

[collinsmark]

On wikipedia it says “Also, this is referring to near-normal incidence—for p-polarized light reflecting off glass at glancing angle, beyond the Brewster angle, the phase change is 0°.”

https://en.m.wikipedia.org/wiki/Reflection_phase_change

Right. As I mentioned, let's ignore the air-glass or glass-air interfaces.

What's important here are the air-silver and glass-silver interfaces. (Well, on second though, that's just an example of one type of beam splitter. See below for clarification.)

Here's an image from the Beam Splitter entry in Wikipedia:

Phase shift through a beam splitter with a dielectric coating.

Source: https://en.wikipedia.org/wiki/Beam_splitter#Phase_shift

And as mentioned in the article, the details are dependent upon the type and geometry of the beam splitter. So the details of the experiment might change a little depending on your choice of beam-splitter type. So there isn't necessarily a one-size-fits-all simple answer to this topic.

But in any case, it will always work out, one way or the other, that energy is conserved. A decrease of energy via destructive interference somewhere will always lead to a corresponding increase of energy somewhere else. That much we can count on.

 

[Devin-M]

Phase shift through a beam splitter with a dielectric coating.

Source: https://en.wikipedia.org/wiki/Beam_splitter#Phase_shift

That diagram predicts what will be observed in the experiment but it tends to refute his claim that the destructively interfering beams on the 1st detection screen go back to the source.

 

[Devin-M]

What I mean is in this video at 4:24 he uses quarter wave plate on the right arm to rotate the polarization of that one arm, which then prevents destructive interference even if there is a half wavelength path length difference. So suppose he used a quarter wave plate on one arm of the original setup, would the combined output on both detection screens have higher intensity from lack of destructive interference on either screen?

see 4:24:

 

[vanhees71]

Don't forget about phase shifts. A reflected wave gets a phase shift of \pi*. Are there any differences in the total phase shifts between the two beams in question (one on the laser side of the interferometer, and the other on the wall side of the interferometer), even if their path lengths are the same?

*(For the purposes here, ignore the nuances about reflections caused by the glass itself -- the reflections going from one index of refraction to another. That makes things things overly complicated, and can be ignored for this discussion. A good beam splitter will have coatings to minimize these types of reflections anyway. Instead, treat all reflections as being caused solely by the very thin, half mirrored surface -- the light either gets reflected with a phase shift of \pi, or it gets transmitted with no phase shift at all.)

provided the reflection is on the side of the medium with the larger index of refraction.