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A transparent cylinder of radius $R=2.00 \mathrm{m}$ has a mirrored surface on its right half, as shown in Figure P 22.55 . A light ray traveling in air is incident on the left side of the cylinder. The incident light ray and the exiting light ray are parallel, and $d=2.00 \mathrm{m} .$ Determine the index of refraction of the material.

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Numerade Educator

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Hope College

University of Winnipeg

When you're given problem, we have a following situation. This slender cylinder is given and on the right side of the cylinder, let's call this right side. We have a mirror s o the Lightman eat interest from the left side. It reflects into slender and then reflects back and comes out, Comes out from here. The distance between these two is ah Dee. So from here to here is D. Then up to here, this will be deal with two so three rd over too, um, up to a center. From this point, we pull this point. A use red for thes is we call this foreign sea and this is a would be We call this angle gamma, and this angle from here to here is a bat up. When this angle alpha and we produced this, we call this angle they don't want on the radius. Off the slender is our, which is given two meters. Our is given and, uh, outside his hair. So air is outside and we are us to find what is their factory index off the surrender. So we are asked to find the fact index up soon from this diagram. We can write a Snell's Law. Ah, for the point, eh? I had to point a snail's long would be a sign. Sign of refracted index refracting Next offs Ellender times a sign off all four. So this English offer reflecting this offer is equal to perfecting Knicks off air Time's up. Your time's a fret. Ah, sign off incident, which is theta one. But we don't know that. The one that the one and angle also so we can find those angles from the given information fast letting this triangle this small triangle this trying reuses. So we assumed this triangle here. Well, this triangle, this angle will be again. There's one using a train, a metric rations. We can find that one here. So we're signed that the one will be the work the listings. Well, so prepare, Niccolo Hyper Chinese pumpernickel aviaries. Do you were two year and high put news. We areas are Oh, Eddie's at two meters. So to remember to use us a one and divided by, um two. This is 1/2. So that means that I was dead. No one will be 30 degrees. So we got our third of one here, But we need also all four years in order to find all four witches here, um, in a triangle. So when you're trying all ABC so a B C um, this triangle will be I Sicily stronger because the opposite sides are equal. They are the FBI off the same circle, so they are equal. Therefore, gamma will be called to alpha. Then our better will be simply total the angle off the triangle, which is 1 80 minus off minus game. This is a call to well, since these are equal So this will be 1 18 minus two also. Well, the better we can, right? Better from here. Better weekend. So if I assume this thing here So we have here, this is a better. And this is our 3rd 1 So better weekend right here is a 1 80 brightness. There's someone. Then our this angle will be, uh, the leftover angle, don't you? Some off these all find better will be, Ah 60 co 30. So do I. Buy two gives us. Also to be also will be theta one divider to which is a 15 degrees. So we got our all for ages of 15 degrees. So we got all the information needed to find the refractive index of slender. So we'll just follow those values playing those values. The refractive index off a cylinder will be affected next off areas one times the sign off. Better one, which is 30 degrees. Bye bye. Sign off. All five is 15 degrees. Excuse us one point in 93.