Why isn’t there an equation to describe how energy is redistributed by destructive interference of an electromagnetic wave?

[Quarker]

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?

 

[PeroK]

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.

I suspect you have a misunderstanding about the electromagnetic field to ask this question.

 

[Dale]

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]

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.

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]

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.

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.

 

[Quarker]

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.

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]

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.

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.

 

[PeroK]

Here are some relevant threads:

M

Undergrad Thread 'Energy of Electromagnetic Waves in Destructive Interference'

May 19, 2022

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...

• MartinG
• Destructive interference Electromagnetic Electromagnetic waves Energy Interference Waves
• Replies: 71
• Forum: Optics

• 

B

Graduate Thread 'Interference Intensity: Questions & Answers'

Dec 5, 2019

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...

• BillKet
• Intensity Interference
• Replies: 7
• Forum: Optics

I can't find the thread about predicting the energy distribution in the double slit.

 

[Quarker]

Here are some relevant threads:

M

Undergrad Thread 'Energy of Electromagnetic Waves in Destructive Interference'

May 19, 2022

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...

• MartinG
• Destructive interference Electromagnetic Electromagnetic waves Energy Interference Waves
• Replies: 71
• Forum: Optics

• 

B

Graduate Thread 'Interference Intensity: Questions & Answers'

Dec 5, 2019

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...

• BillKet
• Intensity Interference
• Replies: 7
• Forum: Optics

I can't find the thread about predicting the energy distribution in the double slit.

Thanks!

 

[Quarker]

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.

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]

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?

I can't answer tat question. It seems somewhat random.

It seems like it would be easier to measure the total energy of an Airy disc than a double-slit interference pattern.

Perhaps.

 

[hutchphd]

Being fond of Airy discs, the OP may wish to investigate th Optical Theorem of Lord Rayleigh. This was a somewhat shocking result in its day and has been extended and rediscovered many times in EM and Quantum theory showing conservation of energy (or probability).

 

[Herman Trivilino]

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.

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.

Approximate solutions are not what they may seem. In cases where closed form solutions are not possible (for example, a solution to the three-body problem) numerical methods can produce results to any desired amount of accuracy. Think about an infinite series that converges to a value. You can get an answer as close as you desire to that value by adding a sufficient number of terms in the series. The more terms you add the closer you get. There is no limit on how close you can get.

 

[sophiecentaur]

Why isn’t there an equation to describe how that energy is redistributed by destructive interference?

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.

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.

If you really wanted to verify, practically, that the total energy in the Airy Disc is (within certain limits, of course) defined by the area, all you need to do is to take two lenses of different radii. The two Airy Discs will have different apparent 'diameters' but an image of the Sun on a large thermal detector will produce the same heating effect when scaled according to lens areas. The diffraction patterns of each lens will have different disc and outer ring sizes. The nulls that you are so concerned about will be in different places but the total energy (limited by the same apertures of the lenses) will be 'conserved'.

Why would you have a problem with that? Not knowing the theory doesn't justify disagreeing with it.