A laser pointer emits a ray which enters a quartz crystal at an angle 50° with the normal to the surface of the crystal. The ray bends inside the crystal, making an angle of 30° with the normal. Find the index of refraction of quartz.

Hey, everyone. Let's check out this practice problem here. So we have a laser pointer that's emitting a ray that makes a 50 degree angle with a normal to some quartz crystal or something like that. And then the angle or sorry, that ray refracts, it bends inside the crystal and it makes an angle of 30 with the normal. And we wanna calculate what the index of refraction is for quartz. So let me just draw a quick little sketch of what's going on here, and it actually doesn't matter which sort of orientation you draw it. So I want to imagine that the surface is going to be this horizontal line, and this is gonna be my normal. It's perpendicular to the surface. So I have a ray that's coming in at an angle. This is gonna be my incident ray, and it makes a 50 degree angle with the normal, and then it refracts. It's gonna bend inside the crystal, and it's gonna make an angle of 30 degrees after that. Now this angle gets smaller, so that means it's gonna be closer towards the normal. It'll be more normal, so it's gonna have to look something like this. And by the way, this is just for scale or sketch purposes. It's not exactly accurate. But I know this angle here is gonna be 30 degrees. Now one of the things that I can expect is that because the angle is smaller and because the ray got more normal, the index of refraction has to be higher inside of the crystal. Alright? So it's gonna have to be greater here. Now one of the things you'll also notice about this problem is that it doesn't tell you which material it's coming from. Whenever that happens, whenever you don't have that information, you can always just assume that it's coming from air. And that's okay because the n one is gonna equal 1. Right? So that's good there. So this is gonna be my quartz, and, ultimately, we have to figure out what is the index of refraction inside of this material, quartz. So this is gonna be my target variable here, my n 2. Alright? Now I've got some angles and some indexes of refraction. So this is gonna be a pretty classic example of using Snell's law. So let's set up our equation here. So it's n 1 sin theta 1 is equal to n 2 sin theta 2. Now I have n 1, and I also have the angle of incidence. That's the 50 degrees over here. I also have the index or sorry. I have the angle of refraction because that's the 30 degrees after it crosses the medium. So because I have 3 out of 4 variables, I could just go in and start solving for this n 2 over here. Alright? So I'm gonna start plugging in some numbers. This n one is just 1. The angle incidence is my 50 degrees. This is gonna be n 2 times the sine of my angle of refraction, and this is gonna be 30 degrees. Alright? So this ends up being 0.77, this is n 2, and then this ends up being 0.5 when you plug this in. Alright. So pretty straightforward, you just divide by 0.5, both sides, 0.5, and you get that n2 is equal to 1 point 54. So notice that's a number that's higher than 1, which is fine because all n should be higher than 1. And also, it is a number that is higher than the the medium the material that it came from. So in other words, that makes sense because it's more n and more normal. Alright? This is our new index of refraction for a quartz. Anyway, folks, so that's it for this one. Hopefully, this made sense, and, thanks for watching.

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A laser pointer emits a ray which enters a quartz crystal at an angle 50° with the normal to the surface of the crystal. The ray bends inside the crystal, making an angle of 30° with the normal. Find the index of refraction of quartz.

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