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A certain kind of glass has an index of refraction of 1.650 for blue light of wavelength 430 nm and an index of 1.615 for red light of wavelength 680 nm. If a beam containing these two colors is incident at an angle of $30.00^{\circ}$ on a piece of this glass, what is the angle between the two beams inside the glass?

$0.3953^{\circ}$

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Our question says that we have glass with an index every fraction for blue light in sabi of 1.65 and for red light inside are of 1.615 And it says that they have an angle of incident for the incoming light of 30 degrees on that glass, and I wants to figure out the difference in the angle between the two. So first we need to find the angle for the blue light refraction, the angle for the red light refraction. Then we confined the difference. So we're going to use Snell's Law, which says that the index of refraction of the first timesthe sign of the incident of the first is equal to the index of refraction of the second times the sign of the incident, the sine of the angle of the second. So we can use that, um, and use our specific scenarios to find these angles every fraction. So the angle of refraction for the blue light will call it. Fate of B is going to be equal to the inverse sine of the ratio of the index of refraction of air cause that's what it's coming out of times sine of the angle of incident. Call that status of I. R 30 degrees divided by the index of refraction, of blue light and Sabi plugging those values. In this expression, we find that data is equal to 17 0.6 40 grease. Then we can do the exact same thing for the red bite. Except for this time we have signed to the minus one of the same ratio except for instead of the index of refraction a blue like we're going to use the index of refraction of the red light, which we call ends of our so playing those values. Into this expression, we find that this angle is equal to 18.4 degrees. So now that we know both of our angles, we confined the difference between those two. When we start a new page since we ran out of room, we'll call that difference Delta Fada that's going to be equal to We'll call it fate us of our minus. Hey, this would be the values we just found. We find that this is equal to zero 0.40 degrees. We can go ahead and box set in as their solution to our question.