A Energy problem of light interference

[liuxinhua]

During equal thickness interference, adjust the inclination of the two plates to expand the spacing of interference fringes to 10mm.

Then, if a light with a width of 5mm is used for equal thickness interference, whether an interference pattern will be observed, and the width of the interference pattern is less than the spacing of the interference fringes?

Move the light with a width of 5mm to present a bright fringe interference. The energy of the bright fringe will be greater than that of the light participating in the interference.

How can we reasonably explain this phenomenon?

 

[Ibix]

The energy of the bright fringe will be greater than that of the light participating in the interference.

How can we reasonably explain this phenomenon?

When you've come to an obviously absurd conclusion, it would be helpful to show us how you reached it. That way we can point out the problem in your reasoning, rather than simply reproducing a textbook explanation that you've presumably got access to anyway.

That said, the obvious guess is that you are using the output pattern from an input plane wave, which means an (approximately) infinitely wide beam, and assuming that it's the same for a narrow beam. If that's not the case, I suggest you post your analysis and we can see what's going on.

 

[vanhees71]

Intensity is not the energy but the energy density. There's no contradiction with energy conservation in electromagnetic theory, because as any reasonable Poincare invariant field theory also classical electromagnetism energy is conserved due to temporal translation invariance. Any conclusion that claims otherwise must thus be wrong.

So from where did you get the wrong statement about the relation between intensity and energy? I'd not use the corresponding source any further or read it as an exercise to find all the mistakes and misconceptions in it. That can help to really understand a subject very well, but of course you have to learn it first from good sources!

 

[liuxinhua]

The problem is derived from the derivation in the textbook. I didn't do the experiment. After discovering the contradiction, I don't know whether the explanation in the textbook is completely correct.
I don't think a 5mm wide slit should be a narrow slit.

My question is really, can light only with a width of one bright fringe, produce interference?

an (approximately) infinitely wide beam, and assuming that it's the same for a narrow beam.

 

[vanhees71]

You have to be more precise in your descriptions! You have to precisely describe the complete physical situation. Of course to get diffraction fringes in, say, a double-slit experiment, you need a sufficiently coherent light source which "illuminates" both slits.

 

[Ibix]

My question is really, can light only with a width of one bright fringe, produce interference?

One bright fringe from what input light? The interference pattern you get out will depend on what you put in, but you'll get some interference pattern from anything.

You still haven't shown us any helpful reasoning. "A derivation from a textbook" doesn't tell me what assumptions the textbook is making in its derivation. So I can only guess that it's deriving the interference pattern for a wide input beam, and you are considering a narrow input beam, assuming the output pattern is the same, and finding a contradiction. As I say, the output pattern depends on the input beam, specifically on its amplitude and phase structure.

 

[sophiecentaur]

Of course to get diffraction fringes in, say, a double-slit experiment, you need a sufficiently coherent light source which "illuminates" both slits.

You will always get a diffraction pattern, whatever the object is that blocks the light path. The simplest calculation assumes perfect coherence. How near your get to that result will depend on the coherence length. Unfortunately, the calculation involved is far more complicated than just doing a diffraction integration over the two finite slits (which, is, in turn more complicated than the simple max / min calculation for two thin slits). The basic interference pattern would only apply for a plane wave front hitting the screen with the slits normal to the plane of the screen.

If the OP has a problem interpreting the message he has got from his textbook then whatever message, the conservation of energy has to be the bottom line. We'd need to see details of the book work.

 

[Dale]

If the OP has a problem interpreting the message he has got from his textbook then whatever message, the conservation of energy has to be the bottom line. We'd need to see details of the book work.

Agreed, and since the OP has been asked to provide said details and has not been forthcoming then we will close this thread as there is nothing left to do.

@liuxinhua in the future please be more considerate in your posts. Try to provide complete information in the OP and when additional clarification is requested, please provide it.