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Single Aperture - Example 3

In physics and optics, diffraction is the phenomenon in which waves, such as light or sound waves, spread out as they pass through a narrow opening, or aperture. The spreading occurs only for waves whose wavelength is comparable to or larger than the dimensions of the aperture.

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Rutgers, The State University of New Jersey

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Video Transcript

welcome to our third example Video, looking at single aperture diffraction in this video will consider a circular aperture for which we have equations. Data is equal to 1.22 times Lambda divided by deep. Now, in this case, we're going to ask ourselves if we have a lambda equal to 5 40 nanometers coming in and we have an aperture diameter equal to 100 micro meters, Then we're going to try and find how large the central spot will be on a screen that is 80 centimeters away. Given all this, we can say I see my theta here. I know that it's supposed to be 1.22 times Lambda over D, but I need to translate this into a thickness. So in order to do that, what we're going to do is the same thing that we've done before. When we want to find our wise, we're going to find that the Y is equal to land L Times Tangent of data. Where this is our theta is calculated by Lambda and D, and then we can plug it in here to find what why one would be if we multiplied it by two. Then we would find the total with which would be equal to two times l tangent of data notice here that if data is very small, tangent of data will approximate to just data, in which case we would have This is approximately equal to 1.22 times lambda L over D or in this case, we'd have 2.44 times lambda l over d plugging it in. Then, if we want to find art our height here, then we would say why is equal to 1.22 times lambda, which is 540 times 10 to the negative nine meters multiplied by L, which is 80 times 10 to the negative 2 m divided by D, which is 100 times 10 to the negative six meters and we'll be able to find our Y position and which will give us the radius doubling It will give us the diameter of our bright spot