Problem

A narrow beam of white light enters a prism made …

03:54

Problem 34 Hard Difficulty

A narrow beam of light containing red ( 660 $\mathrm{nm} )$ and blue $(470$ nm) wavelengths travels from air through a 1.00 $\mathrm{cm}$ thick flat piece of crown glass and back to air again. The beam
strikes at a $30.0^{\circ}$ incident angle. (a) At what angles do the two colors emerge? (b) By what distance are the red and blue bseparated when they emerge?

Answer

a) $30^{\circ}$
b) $3.1 \times 10^{-5} \mathrm{m}$

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Physics 103

College Physics for AP® Courses

Chapter 25

Geometric Optics

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Video Transcript

maybe more flight. That contends. Um, yeah. Red and blue light strikes the glass here, making an Anglo from 30 degrees with a normal here, 30 degrees. And then, uh, it disperses inside the glass so the red goes like this on, then it leaves the glass. Um, where's the blue disperses like this. And then it leaves the glass again. We had asked to find the emergent ingles, Um, for, uh, these two lights. So this is for this is for red. And this is for a blue. No way we can find an emergent angles using the relationship one that is a hey from air to glass, which we can write using Snell's law in a time, sign off the instant England incident in these people to reflect index off a glass times angle off refraction. Um, so let us do first for rig are red, then for red. We get the angle off. A fraction former did we get here is by substituting the values for her and the factory nix for red light, which is a a 1.512 for a loss. So we'll substitute this value here in energy and then substitute any. Which is one and incident angle is 30 degrees or by substituting those values we get here in the loft refraction. 19.31 16 days. Where is it? For a blue we get Anglo. Infraction is equal. Thio 1919.15 Hate the refractive index for the blue light. We're last use a 1.5 to 4 24 s o we will use the same relations will use their these refract tangles which will be the angle off incident when the light is going from a glassed over here. Sorry. Um so then we can find our emergent angle for red and blue by writing the relationship and off a glass times off signing glow for incident that we found, which is, uh, one for red. And that is equal to her front index off air times saying loaf emergent. So emergent tingle. So, like e inversiones, then substituting the value off a glass for red light, which is 1.12 We already wrote it. Then we can find a angle off emergent, and the angle off incident we have for red is 19.316 than a margin angle. We get hearings and 30 degrees. Similarly, we get emergent angle for a blue light again and 30 degrees. So this was about a Barbie were asked to find the distance between these two light rays when the march out off the glass so we can find the distance by writing the relationship for these triangles. So one form here to here and another one from here to here one for ah, they're so let me appreciate it is this is for from here to here for a blue and from here to here, the best is for grand light. Then we can write. We can call this for red light. We call this Opie Hopi to for a blue light. We call this Opie soapy one then, uh, Opie to convey mutinies. So I hope you two can. Burton is one times the tank off taking off from the 19.316 And this gives us the distance. Opie, which is a zero point three pies, five centimeter centimeter for will be one weekend. Right here. Here is ah which will give us for for a blue light which you will give us syrup on three 47474 And then we can find the difference which will give us the distance between these two light rays when they emerge out off the gas. The difference is, is it a 0.0? There are 31 said You went to three once in the end off the problem. Thank you.

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