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This question is related to the Michelson-Morley experiment. See below an illustration of the setup: enter image description here

When looking at this image, I am wondering where and how exactly the interference occurs. Is it only at the intersection point, or are the two beams cancelling each other out when travelling back together in the same parallel direction?

Let me put it another way: Assume you have two beams of light polarised in the same direction, and travelling at perpendicular paths. Is it then possible to cancel out the two beams, so that the beams will not go further than the intersection where they met?

I would actually expect the two interfering with each other at the crossing point, but then continue their paths with their amplitudes unchanged. However then, two beams that travel parallel like at the last stage of the Michelson-Morley experiment, even with a phase shift where they cancel each other out, because you can never have two rays be perfectly 100% parallel to each other, over a long enough distance you would suddenly start seeing two beams again. (When they are apart far enough to stop interfering with each other.) Which seems strange, because that would seem like out of nothing two beams would appear...

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Interference of light waves occurs at each point in space, not along a direction. Interference patterns are three dimensional and the pattern seen on the screen is only a two dimensional cross section of the full pattern.

Two light waves cannot cancel each other at all points in a volume of space (a box, if you like) because this would violate conservation of energy. They cancel each other (destructive interference) at some points but reinforce each other (constructive interference) at other points.

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  • $\begingroup$ Right. But if you have one observer/sensor in that volume, where he would see the ray of light if the other ray wasn’t interfering, then when they do interfere, he would not see anything, correct? Also, doesn’t an interference pattern require a series of rays? Like a beam or a source? $\endgroup$ Oct 11 '20 at 4:57
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Light interference has little to do with rays; it has a lot to do with local intensity of a light field. Here are some general principles (for linear optics) that might be helpful:

  1. Rays travel entirely independently of each other. When rays cross each other, they pass through the point of intersection and simply continue on their own way. There is no interaction between rays.

  2. Interference is the local effect at each point on a measuring device, resulting from superposition of two or more light rays at that point. The measuring device, whether it's your eye, a camera, photographic film, or anything else that detects light, responds in proportion to the intensity (the square of the sum of the amplitudes) of all the light rays passing through each point on the device.

So, in response to each part of your question:

  • Interference occurs wherever light rays cross each other
  • Two beams propagating perpendicular to each other simply pass through each other without interaction. One cannot stop the other.
  • If you digest the two principles I've written above, and also digest Huygens Principle, you will be able to answer the question implied in your last paragraph.

NOTE: The above statements are only strictly true for linear optics. In the case on nonlinear optics, where the medium interacts with light by changing its refractive index or other optical properties in response to light intensity, then some very strange and useful things can happen.

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