Hey, guys. In this video, we're going to talk about single slit diffraction. So what happens to the light as it passes through a single slit as opposed to what we saw before with a double slit. Alright. Let's get to it. Now light shown through a double slit had unexpected results as we talked about if you don't consider diffraction. Okay? If you do not consider diffraction, then it's an unobvious result. And, obviously, back before they understood diffraction, they had certain expectations for the experiment, and the experiment turned out differently. Likewise, light shown through a single slit also displays the same sort of unexpected result, which we call a diffraction pattern, which is alternating spots of brightness and darkness. Right? The big difference between the double slit experiment and the single slit experiment is concerned with the central bright spot. Okay? In a double slit, the central bright spot is just as wide as all of the others. It's the same width as all the others. So every single bright spot across the entire screen is going to be of uniform width. But in a single slit, the central bright spot is actually twice as large as all of the other ones. It's also considerably brighter. So that central one is definitely going to be larger than any of the other bright ones. But all the other bright spots, all the other bright fringes are going to have the same width. Okay? That only applies to the central bright fringe. All of the dark fringes have the same width in the single slit just as they did in the double slit experiment. Okay?

Let me minimize myself so we can see this figure. Like in a double slit, the diffraction pattern is produced due to interference. Okay? The big difference between the double slit and the single slit is that in the double slit you actually have 2 sources of light that are interfering. In the single slit, you have one source of light. It's just that light leaving at the top part of the slit and light leaving at the bottom part of the slit does not leave at the same angle. Okay? Light leaving different parts of the slit leaves at different angles. Okay? So you have all of these different angles that the light can travel at leaving both slits. Okay? Sometimes 2 beams of light will arrange themselves so that when they arrive they're both at a peak. Right? When they arrive on the screen they're both at a peak. This produces constructive interference, and light that constructively interferes produces bright fringes. The amplitude of the light increases under constructive interference. Other times, you can have a wave arrive at a peak and another wave arrive at a trough. And when you have a peak and a trough meeting, you have destructive interference, and light that destructively interferes produces a dark spot or a dark fringe. Okay? Because with destructive interference comes a smaller amplitude for the interfered wave. Smaller amplitude means it's darker. Okay? Just like we did for the double slit experiment, we talked about the single slit conceptually, and now we want to actually talk about the mathematics of solving single slit problems. Where are these fringes actually located? Okay.

Now the key difference in the math between the single slit and the double slit experiment is that in the single slit experiment you only have an equation for dark fringes. Okay? Dark fringes are located at angles given by sinθ_{m}=mλd. Okay? Where m is our indexing number this time. Okay? But because m indexes the dark fringes and not crucial to remember there's no m equals 0 index for dark fringes due to a single slit. Okay? So what we have here is we have the first dark fringe or the m equals 1 dark fringe. We have a corresponding m equals 1 dark fringe on the other side and then we would have the m equals 2 dark fringe on the top side and the bottom side. Right? And then we could say some arbitrary m, the nth dark fringe, is given by θ_{m} where theta follows this equation. Okay?

Now solving problems with a single slit is going to be exactly the same as solving problems with a double slit. Okay? The first thing that we're going to do is we're going to draw the figure that I have above me in the green box for a single slit, and it's going to look identical to the figure for a double slit. Okay? Let me minimize myself so I can draw this off to the side. Alright. So here's our single slit. Right? This drawing is going to look absolutely identical to that of a double slit. The only difference is that I've physically drawn 1 slit instead of 2. Now I'm going to draw that central axis. Okay?

And, well, let me read the problem before continuing. A 450nm laser is shown through a single slit of width 0.1mm. If the screen is at a distance of 1.4m away from the slit, how wide is the central bright spot? Okay. So the screen is a distance of 1.4m away which is equivalent to 1.4m. Okay? And what we are looking for is the width of the central bright spot. So the central bright spot looks like this, right? And it'll continue and there'll be a second bright spot and a third bright spot, etc. The equation that we have for the single slit tells us the locations of the dark fringes. So we know this is the m equals 1 dark fringe, This is the equivalent m equals 1 dark fringe on the bottom side. And this is theta1, that first dark fringe angle, and this is theta 1 as well. And notice this distance is just that distance that we are looking of the central bright spot. Okay?

Now to make solving this problem...