Problem 31 Hard Difficulty

A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of $50.00^{\circ} .$ The index of refraction of quartz is 1.455 at 660 $\mathrm{nm}$ (red light), and its index of refraction is 1.468 at 410 $\mathrm{nm}$ (violet light). Find the dispersion of the slab, which is defined as the difference in the angles of refraction for the two wavelengths.

Answer

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Video Transcript

this problem you had asked to fight the dispersion off. This slave, which is a delta theta, is equal to dispersion off the while it light minus this portion off of oil it. Right. So to be here, minus dispersion off the red light. So if you find these angles, then we'll just substitute those values and subtract them. They will get their dispersion off the sled. So let's find four for the red. All right. Brian. Todd, Greg, that red. We confined from Snell's law. So And our sign that are is important in one scientific one eso reflect angle for red will be 1.45 He's the factory. Next times signed that our is a good one is one sign 50. So solving for that are we get here 31.76 Age 57 porkers, three degrees. So what's up, street? This value here Sorry for this is for the This is for the red, Mrs Forman. Right. So this is for red and sorry about that. This is for the wallet. This is for the toilet. So now we'll find they Tahar or a state of oil. It so that that a wall. It would be a direct index for wallet. Um, the science that our wallet musical two in one. Sign that up. One. Then we can find then the world. 1.4 or six eighties differently. Let's were wallet. Sign that toilet is a cool too. One time signed 50 that the one will be same for both red and for a while then solving for a data of oil. It well, it We get angle here off 31 31.7 pretty 31.454993 So substitute this value here. And once we substitute those values, they Delta Tate are dispersion off the sled we get here he's a 0.3137