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Light enters a container of benzene at an angle of $43^{\circ}$ to the normal; the refracted beam makes an angle of $27^{\circ}$ with the normal.Calculate the index of refraction of benzene.

1.5

Physics 103

Chapter 26

Geometrical Optics

Wave Optics

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we're going to start by drawing a diagram. This line right here is showing us the surface of the benzene, so everything below that line is benzene. I'll go ahead and label it be, and everything above that line is air. So I will label that A. I'll also draw a dashed vertical line, so this is showing us the normal to that surface of benzene. So in our problem, we have a beam of light that is traveling through the air. And once it hits the surface of that benzene, the light is refracted or it's bent. So if I draw that you'll see it's not traveling in the same angle relative to the normal as it waas when it was traveling through the air. So let's look at what is given to us what is known in this problem. One thing that's known is this angle right here will call that angle a the angle that the light is traveling as it's going through the air. We know that that angle is equal to 43 degrees. Another thing that's known is this angle down here will call it. They'd be the angle that the light is traveling once it's refracted and that's equal to 27 degrees. There's actually 1/3 variable that's known, although it's not explicitly stated. And that is the index of refraction of the air will call that a and the index of refraction of air is approximately equal to one. What we're trying to find out is the index of refraction of the Benzie, and so we'll call that and be, and that is what we're looking for. So in order to solve this problem, where you're gonna use what's known as Snell's Law and Smells, Law states that and a times the sign I've played a is equal to and be times the sign have they to be. So we'll start by rearranging this equation since we're solving for N B will divide both sides by sign if they to be so. NB is equal to n a times the Sinus eat a divided by sign what they to be. No, we already talked about how, uh, the index of refraction of air is just equal to one. So this term is one simplifies things for us really nicely. That means that N B is equal to sign. They'd a divided by the sine hey, Toby. So we can go ahead and plug in the values that are given to us. Uh, data is 43 degrees, and fate of B is 27 degrees. So if you put that into your calculator, make sure you have it set to degree mode instead of radian load, you'll find that, uh, the index of refraction of benzene is equal to one 0.5. So that is our answer.

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