# Double-slit Diffraction: Interference Pattern & Equations

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• 0:01 Young's Double Slits
• 2:07 Double-Slit…
• 3:20 Equation
• 4:54 Calculation Example
• 5:55 Lesson Summary

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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.

## Young's Double Slits

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.

## Double-Slit Diffraction Pattern

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.

## Equation

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:

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