Which of the following statements most correctly describes the relationship between the number of nearby gaps that waves pass through and the diffraction pattern produced by the waves? (A) A diffraction pattern is only produced if there is one gap. (B) A diffraction pattern is only produced if there are two gaps. (C) A diffraction pattern is produced by any number of gaps. And (D) a diffraction pattern is only produced by a number of gaps equal to the wavelength of the waves.
As we consider this question, let’s clear some space on screen and remind ourselves just what a diffraction pattern is in the first place. A diffraction pattern is something that is produced by waves. Any type of wave, whether a water wave or a sound wave or a light wave, is capable both of diffracting, that is, bending around corners, and interfering with other waves, combining constructively and destructively. It turns out that both wave diffraction and interference are involved in creating a diffraction pattern.
In this example, we’ll depict waves using what are called wavefronts. Each one of these lines represents a wavefront. And we can consider these lines to represent the peaks of successive wavelengths of our wave. This wave, we’ll say, is in motion to the right. If we were to put a barrier in front of this wave like this and then open up a small gap in that barrier, part of our incoming wave would pass through this gap. And because this gap gives two corners for the wave to bend around or diffract, it will indeed diffract as it passes through the gap. So we now have a diffracted wave, but what about a diffraction pattern?
Let’s imagine that our wave is a light wave. And let’s say further that some distance away from this gap, we put up a screen that the light can land on. If wave diffraction was the only wave phenomenon occurring here, then as the light wave landed on our screen, there would be an equal level of light intensity at every point. Experimentally though, we know that that’s not what actually happens. That’s because when our light wave passes through this gap, along with diffracting, it also interferes with itself. It may seem strange to think of a single wave interfering with itself. There’s a model though of light waves that says that any point on the wavefront of such a wave can be thought of itself as a source of waves. The waves from all these effective wave sources do interfere with one another.
The reason we know that something like this is indeed going on is by looking at the diffraction pattern that forms on the screen. For a single gap, like we have here, that pattern looks like this. There’s a big bright spot right here at the center of the screen in line with the gap. And then above and below that, there are dark spots, where the light intensity is effectively zero. But then above and below those, there are again bright spots, though not as bright as the central bright spot. This pattern of alternating bright and dark spots continues. This then, what we see on the screen, is the diffraction pattern produced by the wave passing through this gap.
We’re seeing here that a diffraction pattern is indeed created when there’s just one gap. Notice though that answer option (A) says that a diffraction pattern is only produced if there is one gap. But actually, if we replace our single gap with two gaps near one another like this, then as our waves pass through these two gaps, they would again diffract or bend as well as interfere with themselves and with one another. This interference leads to yet another diffraction pattern on the screen different from the first one.
We’re seeing then that a diffraction pattern is formed for waves when there is one gap and when there are two. In fact, if we keep on adding more gaps, the waves from our source will again pass through these gaps, diffract, and interfere. Once again then, on our screen, we’ll have an alternating pattern of bright and dark spots: bright spots where the light constructively interferes at that point and dark spots where it destructively interferes. We’re seeing then that it’s not the case that a diffraction pattern is only produced if there is one gap or only produced if there are two. Along with this, we’re seeing that it’s not necessary for the number of gaps to be equal to the wavelength of the incoming waves. Even without knowing the wavelength of these waves, we know that gaps that the waves pass through will create diffraction patterns.
For our answer then, we choose option (C). For incoming waves incident on a barrier with some number of gaps in it, a diffraction pattern is produced by any number of gaps.