Index of Refraction - Video Tutorials & Practice Problems

Index of Refraction

Everyone. Welcome back. So in this video, we're gonna start talking about another phenomenon of lights uh called refraction. Now, we're actually not going to talk about the specifics of refraction. In this video, we're gonna talk about an important variable that you'll need for that video called the index of refraction and we'll get to it soon. All right. So let's just get started. Now, remember when we talk about light, we use this variable C which stands for the speed of light in a vacuum. This is the three times 10 of the 8 m per second. The problem is in everyday life, light travels in all different kinds of materials like air and water and glass, things like that. So what you need to know here is that in all other materials, light always travels slower. It's kind of like how we talked about the speed of sound, the speed of sound differed depending on the material. So does light and light always travels slower than anything that's not a vacuum. All right. So that actually kind of brings us to this important variable called the index of refraction. It's given by the variables N over here. And basically what it is is it's a ratio, it's a ratio of C. So C is the numerator to the speed of light in that material. So in other words, it's a ratio of the speed of light in a vacuum to the speed of light in a particular material. And that's what N is. So you can actually kind of expand this a little bit and rewrite this as just basically just three times 10 of the 8 m per second divided by whatever that speed in that material is. So there's really only two variables in this equation N and V because C is a constant. All right. Now, actually, I'm gonna get back to this point in just a second because we can just jump right into our example. I'm gonna show you how this works. So we uh we're told here that when light enters water, it slows to a speed of approximately 2.25 times 10 of the 8 m per second. And we're gonna calculate the index of refraction for water. All right. So you'll see these tables uh very commonly in your textbooks. They'll have all different kinds of, of uh variables. You'll never have to memorize them, they'll always be given to you. So don't worry about that. All right. So we're told the speed of light in water, which variable is that, is that N, is that C, is that V? Well, hopefully, you guys realize that the C is always just gonna be a constant and N is the index of a fraction. So really, they're actually just telling you, V there's telling you the speed of light in that material. So how do we calculate NN is just equal to C over V? So in other words, it's just equal to three times 10 to the eighth, divided by two points 25 times 10 to the eighth. Now, here's just a really quick shortcut. When you plug this into your calculator, if these have the same base of 10, you can kind of just ignore them and you can only just do, uh you could just do three divided by 2.25. Anyway, what you should get here is you should get 1.33. And if you look in your textbook, that is exactly what the index of a fraction of light is. All right. It's 1.33. Now notice that we got a number that was greater than one and that actually kind of brings me back to my point over here because what we said here is that light always travels slower in any material. So in other words, if V is always less, then C and what we can see from this equation here is that if you always have a lo a number that's lower than C in the denominator, then that means you're always gonna end up with a number that is lower or greater than one, less than, or greater. It's actually gonna be greater. So it's gonna be greater than one and notice how all of these numbers over here are gonna be greater than one. That will always be the case. You'll never see something that's less than one. All right. So that's just what you need to know about the index of refraction. The very last point that I have to make here actually has to do with air because it's a very common material that you'll see in problems. So if you look at this table here, it says that the index of refraction is very close to one, it's 1.0003. So usually what happens is that in most problems, you can kind of just approximate it and use one for the index of refraction when you're talking about air. All right, that's it for this folks. Let me know if you have any questions and I'll see you in the next video.

Diamond has a refractive index of 2.42. How fast would a light ray travel through a diamond?

• A. $2.26\times 10^8$
• B. $2.42\times 10^8$
• C. $1.24\times 10^8$
• D. $2.05\times 10^8$

You turn on one laser in air and shine a second laser through a glass block. How much farther does the light travel in air compared to light traveling in the glass over a period of 2 nanoseconds?

• A. 0.19m
• B. 0.15m
• C. 0.6m
• D. 1.1m

Example 1

Hey everyone, welcome back. So let's check out this problem here. So we have a light ray that's traveling vertically down a frozen lake bed and it's gonna travel through two different materials. The first one is a layer of ice that is 1.5 m thick. Then after the ice, it crosses into water and travels through another 2 m of water before hitting the bottom. So in other words, if this light ray starts at the surface and goes all the way down to the lake bed, what we want to do is we want to calculate how long it takes for it to actually do that. How long does it take for the travel from the surface all the way down to the lake bed? So we can actually just write that as a delta T because that's a time. Now, you can think of this time here because the light travels through two different materials as sort of being made up of two different parts. The first one is delta T, I'll call this delta T I for ice. And the second one is delta T for the water. And we know those two times are not gonna be different, are not gonna be the same because the distances involved are different. And also the light is gonna be traveling through two different materials with two different indexes of a fraction. So it's definitely not gonna be the same delta T. But if I can figure out both of those numbers, if I can figure out delta T I plus delta T for water, then I could just add these two things together. And that will be my final answer. All right. So all I have to do is actually just go get what those numbers are. So this is the first number. This is the second one, add them together. And this will be my final answer. Let's look at the first material. All right. So let's look just just at the ice. So we, that ice is going to travel or the light is gonna travel through ice at a certain speed. I'll call this V I because it's traveling through a, a material. Uh that's not a vacuum or air. So it's gonna have some kind of index of refraction. All right. So this is delta T I. Uh and in order to figure out a time, I can just use my distance and velocity formula V equals delta X over delta T. But instead we're calling them delta X's, we're just gonna call them delta Y because they're traveling vertically. All right. So this is the delta Y ice and this will be delta Y water. So in order to find a time, I'm gonna have to set up my equation that V ice is equal to uh delta Y I divided by delta T I. So I'm looking for the delta T I, so I could just rearrange this equation and it just becomes that delta T I is equal to two. If I rearrange this what happens? These two things trade places. So this is delta Y I divided by V ice. All right. Now, the problem is, I actually don't know what the ice is and I can't just assume that it's three times 10 to the 8 m per second because that's c that's the speed of light. So what I have to do is I actually, I have to go figure this out. This is the ice by relating it to the index of a fraction. So I'm gonna bring this down here. So N ice is equal to um N ice is equal to C over V ice. So I can rearrange this and say that V ice is equal to three times 10 to the eighth divided by 1.31. That's gonna be the index of a fraction for ice. Would you end up with this? What you end up getting for? This is you end up getting a speed of two points 29. So 2.29 times 10 to the eighth meters per second. So this is the number that I'm actually gonna plug back into this formula over here to figure out my delta T. So my delta Y is gonna be 1.5 m. I don't have to convert anything divided by 2.29 times 10 to the eighth. And what I get here out of this, by the way, for delta T I is I just get a time of this is gonna be 6.55 times 10 to the ninth, uh seconds. All right. So this is my delta T that's how long it takes for the first one. So now I have to just repeat the same exact step for the water and go ahead and pause and see if you can actually work it out yourself. All right. So let's do the same exact thing for water, right? So just delta T for water, this is gonna be, that's uh V water equals delta Y for water divided by delta T for water. All right. So this just means that delta T for water is just gonna be, again, you just flip these two over, you flip those, um you multiply and, and, and drop the other one down and this is gonna be delta Y for water divided by velocity for water. I don't know what that velocity is. So I'm gonna have to go to the index of a fraction and go get it. So this is just gonna be um that V water is gonna end up being uh C divided by N for water. In other words, it's gonna be three times 10 to the eighth, divided by 1.33. That's the index of refraction we use for water. And it's actually like you're gonna have to, you know, you can't just go ahead and assume these things are the same again, they're slightly different, but you have to go plug in the right number. So that's gonna be 1.33. So this V water ends up being uh this is 2.25 times 10 to the 8 m per second. This is the number that we plug back into this formula here. So this is gonna be two divided by uh two points 25 times 10 to the eighth. And we'll actually just write this down here that delta T for water ends up being, this is gonna be 8.89 times 10 to the negative nine in seconds. All right. So this is my delta T over here and this is my 8.89 and this is my delta T I. So actually I figured out what both of these numbers are and I can just go plugging them into my final equation. So this final one here is gonna be 6.55 times 10 to the negative nine. And this one is gonna be 8.89 times 10 to the negative nine when you work this out when you add these two numbers together, what you should get is a grand total of 1.544 times 10 to the negative eight. And that's in seconds. So this is our final answer. All right. So again, so when you have light that's traveling through multiple materials, just break it down. Look at each individual material, solve for those variables and then work your way down and you should be able to figure out um the total time for everything. All right. So that's it for this one. Let me know if you have any questions.