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Multiple Aperture Interference - Example 4

Interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Interference effects can be observed with all types of waves, including water waves, sound waves, and light. If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the amplitude is increased. If a crest of one wave meets a trough of another wave, then the amplitude is decreased. Interference can also refer to the interaction of acoustic waves in the cochlea of the inner ear.

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Video Transcript

welcome to our fourth example video. Looking at the double slit interference and diffraction grating in this video, we're going to continue to look at interference due to a diffraction grating with light coming in that has a lambda equal to 540 nanometers and a screen behind it at a distance of 1.2 m. And giving these when we look at the M equals one position, it is a distance of approximately 28 centimeters above the M equals zero position. Given all these numbers, we want to be able to calculate what is the spacing d between the slits. Um, now, if we knew the total height of the diffraction grating, we could also calculate the absolute number of slits. So that's a rare to give. Usually it's given as number of slits per millimeter. So we want to find the spacing between the slits. And then we could also find the slits per millimeter. So the way we're going to do this is we're going to say that I know I have a Y is equal to l Times Tangent of data here, and I know I have a D is equal to sine theta time is equal to M times Lambda. Now, looking at these two equations we have to pick up, I apologize. Not d equals but d multiplied by sine data. So looking at these two equations, we know that we're going to want to pick one that has the right information in it to solve for D. Well, d only shows up in this equation and we have enough already given to us to be able to solve work because we have d is equal to m equals one times 540 times 10 to the negative 9 m, all divided by sine theta one which when we look at this, we know that we have a triangle of theta one 1.2 m and 0.28 m or, in other words, 28 centimeters. Therefore, data one is the inverse tangent of 0.28 meters, divided by 1.2 m. So you can calculate your data one Put it into this and we'll have our solution for the number of slaves Now remember D to the negative one is going to be equal to the total number of slits per meter. So if we write D and meters, then we could also find the number density of the slits in the diffraction grating, which is generally how diffraction grating czar categorized. So when you get a diffraction grating, it will have a number on it telling you the number of slits, usually not per meter, but per millimeter.