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The index of refraction for crown glass is 1.512 at a wavelength of 660 nm (red), whereas its index of refraction is 1.530 at a wavelength of 410 nm (violet). If both wavelengths are incident on a slab of crown glass at the same angle of incidence, $60.0^{\circ},$ what is the angle of refraction for each wavelength?

$\theta_{r}=34.9^{\circ} \text { and } \theta_{v}=34.5^{\circ}$

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Cornell University

Rutgers, The State University of New Jersey

Hope College

McMaster University

So we're told that some light enters a crown glass from air. So the index of refraction of the medium it's coming from my call in someone is one for the index of refraction of air, and the angle of incidence is fatal. One, which is 60 degrees, and the index of refraction were told of the red light, which I call in to our. So that's the index of refraction. Of the second medium are for red is 1.512 and in the index of refraction for violet, light into V is 1.53 So using that it wants us to find the angle of refraction for both cases. So we're gonna use Snell's Law, which says that, uh, in one times it's rewrite this over here. So smells, Law says in one climbs the sign of the incident angle fatal. One is equal to in two times this sign of the angle of refraction. David too, which is what we're trying to find in both cases. So for part, a solving for data to here we find that this is equal to the inverse sine which we right here is signed to the minus one of the ratio of in one times the sign of fate a one and then for the first case, this is the, uh, two that's supposed to be They the one here. Since this is the first case, this is the case with the red light. So we call this into our for red. So taking the sign inverted the inverse sine of this ratio we find this is equal to 34 0.9 degrees. This could be boxed in. Is their solution for part a part B Reason the exact same thing smells law. So we're gonna find the exact same relationship here. Except this time we're using a different index of refraction. This time we're using the index of refraction for the violet light. So it's gonna be the inverse sine of in one times the sign of fatal one divided by the index of refraction for violet light, which we called into V plugging those values. In this expression, we find that this is equal to 34 0.5 degrees, so just slightly less in the red light weakened box it in is their solution for being