Problem

The focal length of a lens is inversely proportio…

05:35

Problem 85 Easy Difficulty

A horizontal incident beam consisting of white light passes through an equilateral prism, like the one shown in Figure $26-$
69. What is the dispersion $\left(\theta_{v}-\theta_{r}\right)$ of the outgoing beam if
the prism's index of refraction is $n_{v}=1.505$ for violet light and
$n_{r}=1.421$ for red light?

Answer

see work

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Physics 103

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Christina K.

Rutgers, The State University of New Jersey

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Video Transcript

his question. A horizontal beam, uh, enters unequal lateral prism. Okay. And so and And that horizontal beam is, uh, is a white light. So it has the rainbow colors, but we want to find the extreme dispersion. So we want to calculate the and go that while it light, uh, the outgoing being of the al violet light, the discussion of the are going to be. So the data violets minus of data read. Okay. And we are given that the refractive index off the violet light in glass is 1.505 and then the while the refractive index for red light in glass is 1.421 Okay, so the radar grand for both composed on the salmon. So the diagram shown over here, Okay. Ah, it's the dispersion off the white light, cause, uh, we expect the angle to be different. For why? That's light and red light. So So, uh, I'm just going to label those General Angus this data one to their tree and they fall. He was not the key. And go with it. We encounter in this s light passes through this equilateral prism. And then we also have this angle. Just 120 degrees came this, which is a data to past data tree because the 60 degrees, right. Uh, so that's something that is useful going to be used to in the question when you solve the problem. Okay, so and yeah, so to find the answer will be using snow slow a lot in this case. Okay, So solution. Okay, so we have, uh now it's law. He basically saying that, uh, and one sign data one is equal to and to I did too, then and to data tree is you go to and and one Alright, therefore. Okay, So anyone is air and two is the refractive index in this is for read. All right, I like. Okay, there's something that we would, uh, liver subscript. Okay, then on at the same time, There one is 30 degrees. Okay. Yeah. So this is the This is fixed. Okay. And then later, we'll be finding the the discussion will be data for me, minus data for our okay. Yeah, the discussion at the final angle. Hey. Okay. So first we want to find data to we end there too, are Okay, so um, yeah. Sign Data one is equal to and to me sign data to me. And then you also have signed data one is equal to and to our, uh, sign data to our mhm. So we have I data to me is sign 30 degrees. Did I buy? Ah, 1.505 And so there were two. B is equal to, uh, 19.4 degrees. Then similarly, science data to our is signed. 30 degrees C. Bye bye. 1.4 to 1. And so did the two. R is equal to 20.6 degrees. Yeah. Then we can find data TV. It's 60 degrees minus. Need to be and calculate these you get for the 0.6 degrees, and then the tree are is able to 60 degrees minus data to our get 39.4 degrees. Okay, then, um, we have ah, and be sign Data Tree V is equal to Uh huh, which is one times science data for me. Okay, so sign data for me is you go to 1.505 sign 40.6 degrees. And so data for B is equal to um 78.3 degrees. And for the relight we have nr side data tree are, uh if you go to sign data for our so sign data for are putting the numbers secretly 1.4 to 1. Sorry. 39.4 degrees and use a calculator. Data for our is 64 point clock degrees. Okay, so the discussion Hm? Seiko to for me, minus data for our. So this is 78.3 degrees minus 64.4 degrees, and you get 13.9 degrees. Okay, so this is the answer for this question, and that's all.

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