Where Does Energy go During Interference?

Most recent answer: 03/16/2013

Q:
Where does the energy go when Destructive Interference happens? I tried searching on the web, all I cam to know was that the energy lost in the Destructive Interference simply adds up to the energy of Constructive Interference, but the question is how? I want to know how this happens in the Young's Double Slit Experiment!!
- Vishwajeet Mishra (age 18)
Silvassa, Dadra and Nagar Haveli, India
A:

Hi Vishwajeet,

You are absolutely correct that whenever you have destructive interference, there must be some constructive interference somewhere else. This much is obvious from the law of conservation of energy: anytime energy disappears from one place, we know it can be found in some form somewhere else.

However, exactly how this happens is often not at all obvious in a specific case, for which you can prove this fact only by careful calculations. In a few cases, the calculations involved aren't terribly difficult, and just require some algebra. One of these cases is the two-slit experiment, if you look far away from the slits. (Close to the slits, the math is a bit trickier, and you get a pretty but complicated pattern like .)

As you know, destructive and constructive interference (and everywhere in between) happens whenever two waves which are out of phase add together. Anytime you have two spatially separated sources of light, you will get interference of some sort. There is a surprising amount of useful literature on the two-slit experiment. shows nicely how two different observation points will see a different relative phase between the two beams, leading to a different total intensity:


As you can see, interference in light waves is just a re-distribution of energy, depending on exactly which parts of the light wave overlap at each point in space. The pattern of light you see is then determined by the geometry; in the double slit case, you get something like the :



To summarize: if you understand how destructive interference happens, then you know how constructive interference happens too. If you choose a specific case and add up all the energy, you find that none is lost. This calculation usually amounts to a lot of geometry.

You might think that you could devise an interferometer or other device which combines two beams in such a way as to cancel completely, without having observation points for which the wave crests align. In fact, I tried my best before writing this answer. I encourage you to try as well, but if you are careful to take everything into account, you will find it just isn't possible!

Hope that helps,
David Schmid


(published on 03/16/2013)

Follow-Up #1: energy conservation in interference patterns

Q:
My question also involves Young’s ‘double-slit’ experiment of 1803. As I understand the classic mathematical solution, the geometry of the test apparatus yields the wave length of the light. Where the interval coefficient is an integral, light bars appear, and at the integer plus 0.5 locations, dark bars occur. Thus, dark areas occur where the negative abscissas of the waves coincide. This solution still seems to me to violate conservation of energy. I would think the dark regions should occur where the waves crossing the neutral axis coincide because at that point neither wave has amplitude and thus where I assume no energy resides. As I understand the answer giving for the previous question, the energy is somehow shifted into the zones of constructive interference and the total energy striking the target remains the same. This implies that the energy striking the light areas must be some factor (such as 4) times the energy that is received from a single slit. Has this been verified experimentally? Also, is there an explanation of the mechanism by which this occurs?
- John (age 53)
Cary, North Carolina
A:

Your understanding of our old answers is correct. Those factors of 4 are observed countless times in all sorts of interference experiments. There's no mystery to it. For classical electromagnetism, the energy flow is given by the Poynting vector, proportional to ExB, where those are the electric and magnetic fields. Just following that energy flow around gives the right amount arriving in the right places.

Mike W.


(published on 01/02/2014)

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