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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

This lesson explores double-slit diffraction, including the significance of Young's double slit experiment and how the diffraction pattern forms. You will also learn to use equations to calculate the positions of minima and maxima in the pattern.

Newton was a pretty smart guy. People tended to trust him. But he wasn't right about everything, and one thing he got wrong was the nature of light. He certainly didn't think light was a wave or could in any way behave as a wave. And when people like Christian Huygens proposed it, they were dismissed by a lot of people who preferred to agree with super-smarty Newton. But then came Young's double slit experiment.

In 1801, Young shined light through two slits and found that the light coming through each slit interfered with each other, producing an interference pattern on a distant screen. This pattern showed that light could be seen as a wave, because for interference to happen, you need peaks and troughs. When two troughs or two peaks meet on a screen, you get a bright area, which is called **constructive interference**. When a peak from one slit and trough from the other meet on the screen, they cancel out to produce a dark area, which is called **destructive interference**.

But why did it take so long to realize this? Was Young really the first person to shine light through slits?

Well, no, he wasn't. But he was the first to do it in a particular way that made the pattern easy to see. For one thing, he put the light through a single slit first, to make it coherent. **Coherent light** is light where all the peaks are lined up together and all the troughs are lined up together. Most light, such as light directly from the sun, is a mix of waves in all kinds of orientations and phases - just a jumbled mess. So this was necessary for the diffraction pattern to appear. Another thing he did was to use slits that were extremely close together. For the double-slit diffraction pattern to happen, the distance between the slits needs to be similar to the wavelength of light, which is very small. There's another thing that Young would have done if he could - he would have used a single wavelength (or color) of light. Unfortunately, Young had to use sunlight, which is a mixture of wavelengths and made the pattern harder to see. But in this video, everything you see will be done with **monochromatic light**, or light of a single color (or wavelength). This makes the result much more clear.

Before we look at the double-slit diffraction pattern, we should answer the all-important question: what is diffraction? **Diffraction** is when waves like light or sound spread out as they move around an object or through a slit. When light passes through each of the slits, it will spread out and overlap with the light from the other slit. It's through this overlapping that the diffraction pattern of dark and bright areas is created.

Think about it this way: the distance from one slit to a particular point on the screen will almost never be quite the same as the distance from the other slit to the same point on the screen. Because of this, when the two waves meet at the screen, you could get any combination of peaks or troughs from each of them. Maybe you get a trough from the right slit and a peak from the left. It's through these combinations that we get the constructive and destructive interference we've already talked about, and that's what creates the pattern. The double-slit diffraction pattern looks something like this:

If you've already watched the lesson on single-slit diffraction, you might notice that it's similar, but it's decidedly more stripy. It still has a large maxima in the middle and smaller ones on each side, but each of those maxima are also broken down into bright and dark bands.

Just like with single slits, we need an equation to describe the positions of each minima and maxima. For double slits we have one equation for minima and one equation for maxima. To figure out whether minima or maxima occur, we have to look at the **path length** - how far the wave from each slit has to travel. If the difference in the length of the paths is equal to a whole number of wavelengths, then two peaks or two troughs will arrive at the screen together, making a bright patch. But if the difference in the length of the paths is equal to a half number of wavelengths, then a peak and trough will arrive together, making a dark patch.

When you do a bit of simple geometry, you get these two equations:

One helps you figure out the positions of the minima and the other, the positions of the maxima. In these equations, *d* is the distance between the slits measured in meters, lambda is the wavelength of the light going through the slits (also measured in meters) and *m* is the so-called 'order' of the minima or maxima. Or, in other words, whether it's the first minima, second minima or third minima, but you start counting at zero. So for the first maxima, you plug in *m* = 0, and for the second, you plug in *m* = 1, and you continue like that. Last of all, the angle theta is the position of the minima or maxima on the screen measured from the center line. Straight forward is zero degrees, so if theta for the first maxima is 32 degrees, that means that the first maxima appears at 32 degrees above the center of the two slits. You then can use this information to figure out where it'll appear on the screen.

Maybe this would be easier if we go through an example problem. Let's say you're shining light of wavelength 7.1 * 10^-7 meters through slits that are 5 * 10^-6 meters apart, and you're asked to calculate the angle of the third maxima.

First of all, write down what you know. We were told that lambda is equal to 7.1 * 10^-7 meters, *d* is equal to 5 * 10^-6 meters, and since we're asked for the third maxima, *m* is equal to 2 because you start counting at zero. Do some algebraic rearrangement and you find that sine of the angle theta is equal to 2(7.1 * 10^-7) / (5 * 10^-6). But we don't want sine theta, we want the angle itself. To get rid of the sine part, you take the inverse sine of both sides of the equation. Then we can type all of that into a scientific calculator and it comes out as 16.5 degrees. And that's it; that's your answer.

**Diffraction** is when waves like light or sound spread out as they move around an object or through a slit. When Young shined light through two slits, he found that the light that came through those slits interfered with each other, producing a pattern of dark and bright areas on a distant screen. This showed that light acts like a wave, because it could only be explained with peaks and troughs. When two troughs or two peaks meet on the screen, you get a bright area, which is called **constructive interference**. When a peak from one slit and a trough from the other meet on the screen, they cancel out to produce a dark area, which is called **destructive interference**. Young's experiment was special because he put the light through a single slit first to make it coherent and used slits that were close together.

The double-slit diffraction pattern looks like this:

It's similar to the single-slit diffraction pattern, but with more dark and bright bands. To figure out whether minima and maxima occur, we have to look at the path difference between the rays from each slit. Doing this leads to an equation for the position of minima and one for the position of maxima.

In these equations, *d* is the distance between the slits measured in meters, lambda is the wavelength of the light going through the slits (also measured in meters) and *m* is the so-called 'order' of the minima or maxima. Or, in other words, whether it's the first minima, second minima or third minima, but you start counting at zero. So, the first maxima, you plug in *m* = 0, and for the second, you plug in *m* = 1, and you continue like that. Last of all, the angle theta is the position of the minima or maxima on the screen from the center line.

Young's double-slit experiment is a classic and extremely important experiment in physics, because it finally proved that light acts like a wave. Later we would discover that it also acts as a particle, leading to a concept known as wave-particle duality. But Young helped us in this vitally important first step.

Following this lesson, you should be able to:

- Define diffraction
- Explain how Young's experiment showed that light acts like a wave
- Differentiate between constructive and destructive interference
- Identify how a double-slit diffraction pattern looks and the equations for determining the positions of the minima and maxima

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UExcel Physics: Study Guide & Test Prep18 chapters | 201 lessons | 13 flashcard sets

- Go to Vectors

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- Single-slit Diffraction: Interference Pattern & Equations 6:04
- Double-slit Diffraction: Interference Pattern & Equations 7:47
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