Unknown Wavelength of Laser through Double Slit

by Patrick Ford
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Hey, guys, let's do an example about Young's double slit experiment. Ah, laser of unknown wavelength shines monochromatic light through a double slit of 0.2 millimeter separation. If a screen is 5.5 m behind the double slit, you find the angular separation of each bright fringe to be 0.15 degrees. What is the wavelength of the laser? Okay, first I wanna approach. I just want to discuss this big word right here. Monochromatic. Okay, this is fancy for single colored. Okay. Mono is latin for one chrome. Oh, is Latin for color. Monochromatic. Single colored. This just means light at a single wavelength. Okay? And lasers are most typically monochromatic. Okay, but there are multi chromatic lasers. Okay, so it's specifically monochromatic. The light is on. Lee admitted at a single wavelength, and that wavelength is unknown. That's what we want to find. So the first thing we're gonna do is we're gonna draw the situation because that's what we always do with these double slit problems. We're told that the screen is 5.5 millimeters behind the double slit. Sorry. 5.5 m behind the double slip. And what we're told is that the angular separation of each bright fringe is 15 degrees. What does this mean? Well, we have our central bright fringe, right, and then the second bright fringe and third bright fringe, etcetera. What this is saying is the angle separating each bright fringe is 0. degrees. If I were to draw a line through the next bright fringe, that angle would also be 0.15 degrees. If I were to draw a line through this next bright fringe right here, this would also be 0.15 degrees of separation between every single bright fringe. The angular separation is 0.15 degrees. So notice that first raid that I drew this blue one right here. This has to be our fada zero angle because that's the angle. Sorry, Fatal one. My bed for M equals one. We're talking about the angle between the M equals zero fringe and the M equals one fringe. So that is fatal One. And remember, for the angular location of bright fringes, our equation is sign of Fada M equals M lambda D. We know that the angle that we're looking for is of that second bright fringe, the one just after the central bright fringe which occurs when m equals one. So we have m equals one. And so sign of Fada one that angle that we want to find is one lambda over tea. Lambda is our unknown. We know what data one is right is 10.15 degrees. Just out of curiosity, what do you guys think fatal to would be the angle at the location of the M equals to do you think it be 0.15 degrees? No, it's the entire sweep of this angle. So it's 0.15 plus 0.15 which is 0.3. And you could also solve this problem by doing that by finding the fate of two angle that would also tell you the same wavelength. All right. And you guys can double check what I'm saying at the end of the problem, if you want for the fate of two or the fate of three or the fate of four. Okay, but for theta one, we know what D is the separations. 10.2 millimeters. We know what fate of one is. 15 degrees wavelength is our unknown. So I'm gonna multiply the D up to the other side. And this lambda is just d sign fate of one which is 0.2 millimeters. So times 10 to the negative 3 m and fada is 0.15 degrees. So our wavelength is 5 to times 10 to the negative 7 m. Now you can leave it like this and be done. That's the answer. But I'm gonna rearrange this slightly. When I'm gonna do is I'm gonna increase the order of magnitude by two. I'm moving the decimal place over two points, which is gonna increase my order of magnitude by two. So I need to decrease my ex phone and by two Alright. If I'm gaining two in the decimal place, I have to lose two in the power. Alright, This times 10 to the negative nine is nanometer. So this is 524 nanometers and you're gonna see most of your problems are gonna describe wavelength in nanometers because on the hundreds of nanometers about nanometers to 750 nanometers. If I remember correctly, that is visible light. That's likely. You can see 450 nanometers is purple light. The lowest wavelength light in 750 nanometers. Is red light the highest wavelength light. All right, guys. Sorry That wraps up this problem. Thanks for watching.