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A horizontal beam of light enters a $45^{\circ}-90^{\circ}-45^{\circ}$ prism at the center of its long side, as shown in FlGURE $26-68 .$ The emerging raymoves in a direction that is $34^{\circ}$ below the horizontal. What is theindex of refraction of this prism?

1.7

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

McMaster University

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this question. We are given this prison, and the horizontal beam enters this prison. Ah, horizontally. And then it emerges 34 degrees. You know, the horizontal, uh, on the right side. Okay. And we want to find out and go off the index of refraction off this prison. Okay, so to do this is just to apply snow slaw, but for, uh, with the proper angles. Okay. So till we recognize that this is 45 degrees, and then we are also going to labor to more angles. So here is data one. And here is data to and I One thing we need to recognize that this angle is 100 and 35 degrees Mhm. Okay. Or in other words, uh, data one plus data to ISS, 45 degrees. Okay. Okay. So, uh, solution. Okay, So be using, uh, using Snell's law. Okay, so we have, uh, and it goes to signed 45 degrees nearby by scientist, the one this is also equal to scientific four degrees. You. Bye bye. Scientists to Okay. And then we know that, uh, later one class data to is 45 degrees. Okay, So what happens is that we're going to make, uh, to to be equal toe 45 degrees, minus data one. Okay. And then, uh, signed there, too, is equal to sorry. 45 degrees minus state of one. Um, you're going to use that? Ah, the Chicano metric formula. Okay, so sign 45 degrees minus 81 is equal to sign 45 degrees because I did one minus, uh, assigned 45 degrees. Sign did one. Mhm. And so we know that. Signed 45 degrees and consign 45 degrees are have the same value, which is 1/2. Be on thing is what we get. Okay, in the end. Okay, So I'm going to put that back into the above the equation of both harm. Hey, so signed. 45 degrees. See you. Bye bye. Side data one is equal to scientific four degrees. You know, by 1/2, cause I didn't one minus, uh, inside data. One can. So we have half. I'm doing cross multiplication. Uh huh. Okay, so So we have, because I did. One is equal to on one plus to sign 34 degrees times Scientist one. Okay, so, tangent data one is equal toe 1/1 plus to sign 34 degrees, which is a good to 0.472 And so this gives later one equal to 25.3 degrees. Okay, so the refractive index off the prism you go to sign 45 degrees. You are by sign Data one. Okay, so sign 45 degrees by sign, 25.3 degrees and you get 1.66 Yeah. So this is the answer for this question, and that's all.

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