Video Transcript
Which of the following statements most correctly describes the result of waves passing through a single gap that is approximately the same width as the wavelength of the waves that pass through it? (A) No diffraction pattern is generated because waves only pass through a single gap and there are no other waves for them to interfere with. (B) The waves are diffracted from either side of the gap and the waves from each side interfere with each other, but no diffraction pattern is generated because these waves are all in phase with each other. (C) A diffraction pattern is generated because waves that pass through the gap interfere with other waves that pass through the gap after them. (D) A diffraction pattern is generated because the waves are diffracted from either side of the gap and the waves from each side interfere with each other.
In this situation, we have a series of waves. And here, we’re representing these waves using their wavefronts. We can think of each of these lines as representing a crest or a peak in the wave. And we’ll say that overall the wave is moving to the right. We can think of these wavefronts then as moving in that direction all at the same speed. These waves then encounter a barrier that has one opening in it. The size of that gap is about the same as the wavelength of the wave, measured as the distance between successive crests of these wavefronts.
When the wave reaches this gap, something called diffraction will occur. Diffraction is the bending of a wave around a corner. We see here that because of this gap, we have one corner at the top and one corner at the bottom. Our wave then will bend around each of these corners. And as a result, the wavefront spreads out like we see here. Just as a side note, when a wave diffracts, that doesn’t change the wavelength of the wave. The distance between successive crests of our wave is the same as it was before. Due to diffraction though, the wave is now traveling in directions it wasn’t traveling in before.
Our question asks us about something called a diffraction pattern as it relates to this scenario here. Let’s say that the particular type of waves we’re thinking of here are light waves. If that’s so, then if we were to hang up a screen some distance away from the gap, any diffraction pattern that formed on that screen would be a series of alternating bright and dark spots. This fact helps us see that a diffraction pattern actually relies on two different properties of waves. It relies on the property of diffraction that waves bend when they move around corners, but also on wave interference. Wave interference means that different waves can combine together either constructively to add to one another or destructively to subtract from one another.
Knowing this and seeing our last two answer options, let’s review what answer options (A) and (B) said. Clearing a bit of space to write summaries of (A) and (B), answer choice (A) effectively said that in this scenario, we’re considering no diffraction pattern forms on the screen because there’s no wave interference taking place. Answer option (B) essentially says that the waves do diffract and interfere, but no diffraction pattern is formed because the waves are all in phase with one another. In contrast to this, we see that answer choices (C) and (D) claim that a diffraction pattern is generated.
According to a theory of waves, any point on a wavefront, literally any point at all, can be considered a source of waves itself. As waves move out from these point sources, they indeed interfere with one another. As they do, they sometimes interfere constructively and sometimes destructively. That is, it’s not the case that all of these waves are in phase with one another. Because the waves aren’t all in phase, we can eliminate answer choice (B). And because there is actually wave interference going on, we can also eliminate answer choice (A). Therefore, answer choices (C) and (D) remain. And indeed, a diffraction pattern is formed on the screen across from our gap. That pattern will look something like this with alternating bright and dark spots.
The difference between our remaining options is that option (C) says that the diffraction pattern is formed because waves that pass through the gap interact with other waves that pass through the gap after them. This is a bit like saying that this wavefront here that has passed through the gap already is going to interfere eventually with this wavefront. From a timing perspective though, we don’t expect this to happen. It’s true that light in adjacent wavefronts, say these two wavefronts here, will have a chance to interfere with one another. But that doesn’t mean that waves separated by a large amount of time as they pass through the gap will interfere.
In contrast to this, answer choice (D) says that a diffraction pattern is generated because the waves are diffracted from either side of the gap and the waves from each side interfere with each other. It’s indeed true that the waves are diffracted from either side of the gap. And as we see from these point sources of waves, according to our wave model, the waves from each side of the gap do interfere. Note that these wave sources, because they lie along the same wavefront, have all passed through the gap at the same moment in time. At any given instant then, we expect that the diffraction pattern on our screen will show the result of diffraction and interference for a given wavefront after it passes through the gap. That is, the waves from each side of the wave do indeed interfere with one another, and this generates the diffraction pattern.
Since our question asks us to identify the most correct explanation for what happens when a wave passes through a gap like this, we can eliminate answer choice (C), which talks about waves at different points in time, and choose as our answer option (D). When waves pass through a single gap approximately the same width as the wavelength of the waves, a diffraction pattern is generated because the waves are diffracted from either side of the gap and the waves from each side interfere with each other.
