Quarker
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The energy of an EM wave is described by a fairly simple equation. Why isn’t there an equation to describe how that energy is redistributed by destructive interference?
The energy of an electromagntic field is given by Poynting's Theorem. Destructive interference describes some points where the field is zero.Quarker said:The energy of an EM wave is described by a fairly simple equation. Why isn’t there an equation to describe how that energy is redistributed by destructive interference?
Just take the "fairly simple equation" three times. One with the first source alone, one with the second source alone, and one with both sources together. Then subtract the two individual sources from both sources together. That will give the redistribution.Quarker said:The energy of an EM wave is described by a fairly simple equation. Why isn’t there an equation to describe how that energy is redistributed by destructive interference?
I’m thinking more of the interference pattern, not the entire EM field. In a double-slit experiment, or even a telescope’s Airy disc, there’s no way to predict how much energy will be pushed into the areas of constructive interference, even under ideal situations, as far as I know.PeroK said:The energy of an electromagntic field is given by Poynting's Theorem. Destructive interference describes some points where the field is zero.
I suspect you have a misunderstanding about the electromagnetic field to ask this question.
Do you mean cases where you end up with a solution that cannot be expressed in terms of elementary functions and requires numerical methods?Quarker said:I’m thinking more of the interference pattern, not the entire EM field. In a double-slit experiment, or even a telescope’s Airy disc, there’s no way to predict how much energy will be pushed into the areas of constructive interference, even under ideal situations, as far as I know.
It sounds like there’s no way to verify that the energy going into an interference pattern equals the energy coming out, at least experimentally.PeroK said:Do you mean cases where you end up with a solution that cannot be expressed in terms of elementary functions and requires numerical methods?
In physics generally, the neat analytic solutions that look so nice are very much the exception.
The total energy absorbed by a detector screen could be measured. You could calculate the energy with one slit open; then with the other open; and then both together. And, you could move the screen nearer or further from the slits and check the total energy remains the same for the different interference patterns.Quarker said:It sounds like there’s no way to verify that the energy going into an interference pattern equals the energy coming out, at least experimentally.
Thanks!PeroK said:Here are some relevant threads:
Hello !
As we know by definition that:
"Constructive interference occurs when the phase difference between the waves is an even multiple of π (180°), whereas destructive interference occurs when the difference is an odd multiple of π."
But my question is in the case of destructive interference, what happens to the energy carried by the two electromagnetic waves that annihilate, the energy carried by the electromagnetic waves also disappears, or is transformed into some other type of energy.
Because according to the law of conservation of energy, energy can neither be created nor...
Hello! I am a bit confused by the formula for light intensity in the case of interference. In the books and online resources that I read, this is given as: $$I = I_0 \cos^2(\frac{\pi d \sin \theta}{\lambda})$$ where ##d## is the distance between the slits, ##\lambda## is the wavelength of the light and ##\theta## is the angle where we do the measurements. But in this form it looks like the intensity will be equal to the maximum value ##I_0## an infinite number of times. Shouldn't the intensity maximum go down with the distance from the center, as the energy stored in the wave gets diluted...
I can't find the thread about predicting the energy distribution in the double slit.
Would an artificial star and a sensor in a telescope serve the same purpose, or would the introduction of a lens in the light path create too many variables? It seems like it would be easier to measure the total energy of an Airy disc than a double-slit interference pattern.PeroK said:The total energy absorbed by a detector screen could be measured. You could calculate the energy with one slit open; then with the other open; and then both together. And, you could move the screen nearer or further from the slits and check the total energy remains the same for the different interference patterns.
In fact, I think there was a thread about this a while back.
I can't answer tat question. It seems somewhat random.Quarker said:Would an artificial star and a sensor in a telescope serve the same purpose, or would the introduction of a lens in the light path create too many variables?
Perhaps.Quarker said:It seems like it would be easier to measure the total energy of an Airy disc than a double-slit interference pattern.
Please don't draw that conclusion from the comment you replied to. So-called closed form solutions (that give exact results) are indeed not the norm, even though those are what you tend to learn in school.Quarker said:It sounds like there’s no way to verify that the energy going into an interference pattern equals the energy coming out, at least experimentally.
Quarker said:Why isn’t there an equation to describe how that energy is redistributed by destructive interference?
Those comments are actually not true. Energy is not 'redisributed' in a diffraction pattern because there's nowhere for it to be distributed from or to. There's no reason to suspect that the diffraction equations are not right. You need to get familiar with diffraction theory.Quarker said:there’s no way to predict how much energy will be pushed into the areas of constructive interference, even under ideal situations, as far as I know.