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The index of refraction for red light in a certain liquid is 1.305 the index of refraction for violet light in the same liquid is 1.336 .Find the dispersion $\left(\theta_{v}-\theta_{r}\right)$ for red and violet light when both areincident from air onto the flat surface of the liquid at an angle of$45.00^{\circ}$ to the normal.

0.33 $\mathrm{deg}$

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

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all right. So if this problem red and violently or both incident on a liquid from air and we want to find the dispersion between the two, the way we're gonna find the dispersion between the two is first we have to find the index of refraction of each the red and violet light, using the fact that the incident angle it's 45 degrees. The index of refraction of ares, about one and each have their own index of refraction into this liquid. The violent next fraction is 1.336 and the red index of refraction of is 1.305 So we're gonna find the dispersion were, first confined, the angle over fraction of the red light. So I want to say the end of air times the sign of 45 would be equal to the index of refraction of the red light 1.305 times the sign of the income of the angle of a fraction of red light. Now, because the index of refraction of ares about one, we just cancel that out, and we can say that the angle over a fraction of red light, evil too. The inverse sign of signed 45 over 1.3 or five, and that should give you an answer. The 32 0.81 degrees that's the angle of refraction of the red late from the normal. Now let's find the angle over fraction of the blue light, wherein you Snell's law again were to say, the index of refraction of air as the sign of 45. It's gonna be equal to 1.336 now the index of refraction for the violet light and C sine of the angle of refraction of the light. So now the index of refraction of arable cancel because one I would find the angle refraction of the violet light. It's gonna be equal to the inverse sign of signed 45 divided by 1.336 and that should give us an angle of 31 0.96 degrees. Now the dispersion is the difference between these two angles, so we're gonna find the difference Team two angles or to say data V minus data are because that's how it's written in the problem. However, I think the absolute value of it because it's just an angle that's going to be equal to the absolute value of 31.96 minus 32 going 81 and that should give you a dispersion of 0.85 degrees, and that is our answer.

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