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?

Everyone, welcome back. So let's try out this practice problem here. So in this problem, we're gonna turn on 2 lasers. The first one is just gonna shine through air, and the second one, we're gonna shine that through a glass block. We're asked to calculate how much farther the light that travels in air goes compared to the light that's traveling in the glass over a period of 2 nanoseconds. So this is the time. So what's going on in this problem? Well, the first thing I like to do is always just draw sort of a sketch of what's going on. So let's turn on 2 lasers. The first one is just gonna fire straight through air, so it's gonna shine like this, and it's gonna go some distance. The distance it travels in this time, I'm gonna call this x one. Now the second laser is gonna travel through a glass block. So imagine having a blue laser and you turn this on, but it shines through glass. Now remember that light travels slower in every single medium except for a vacuum, So therefore, in the same amount of time, it's gonna travel a shorter distance. I'm gonna call this one x 2. And basically, what we're asked to figure out in this problem is what is the difference in those distances? So if you can imagine just drawing like a little line like this, basically, what is the extra distance that the light in air travels, because it's going a little bit faster. So it's delta x. That's really what's going on in this problem. So I actually set up an equation for this delta x in terms of the other two distances. My delta x is really just my x one minus my x 2. Right? It's just the differences in those two distances. So if I can figure out what those distances are, then I could just subtract them, and then that will be my final answer. Alright? That's really all there is to this problem. The tricky part is actually just going and finding what those distances are. So let's just start off with the first one here. Let's start off with x one. How do we calculate a distance when we when we're involving lights? We're gonna have to use some equations, but remember just the the basics of kinematics is that, velocity equals distance divided by time. So in other words, we can rearrange this equation and say that x one is just the velocity times time. And the time is actually going to be the same for both of the equations here. Remember, because the t is just 2 nanoseconds. This is 2 times 10 to the 9th. Okay? So this velocity here, I'm going to call this v one because it has to do with the red laser. Now how do I calculate the velocity of light that's traveling through a medium? Well, that's actually where our index of refraction comes in. So in other words, I have to sort of go off over here and I actually have to figure out what this v one is in terms of n and c. So I'm gonna see that the n one is equal to c over v one. That gives us the speed of light in that medium. Now fortunately for us, what happens is that the index of refraction for vacuum or air is just so you know, for air, it's so close to 1, they can just use 1. So this is actually just gonna be 3 times 10 to the 8th divided by 1. So this is just going to be 3 times 10 to the 8th. Okay? So I'm just going to pop this number inside of this equation. So x1 is just 3 times 10 to the 8th, times 2 nanoseconds, which is 2 times 10 to the negative 9. Now when you work out this, this distance over here, this x one ends up being 0.6 meters. Alright? So that's actually our first distance. X one is 0.6, and that's actually the first unknown inside of our equation. So we got one down. All we have to do is do the exact same thing for the other one, for x 2. Alright? So let's go over here now and just do the exact same thing. We'll repeat the same exact steps. So x 2 is just written as v 2 times t, right, velocity times time. It's the same t, but now we actually have to go figure out what that velocity is by using the index of refraction. So n 2 is equal to c over v 2. We can rearrange this and see that v 2 is equal to c, which is 3 times 10 to the 8th divided by n 2. And by the way, this n 2 is actually the n for glass. Remember, because it's traveling through glass. This is gonna be n glass over here. So that means that we're gonna use the index of refraction 1.46 over here, so 1.46. Now when you work this out, what you should get for the speed, is you should get 2.05 times 10 to the 8 meters per second. So this out is the number that you pop into this equation to find out the distance. So that means that my x2 is equal to 2.05 times 10 to the 8 times 2 nanoseconds. So 2 times 10 to the negative nine nanoseconds. And what you should get for x two is you should get a distance of 0.41 meters. So that is the distance that light travels in glass in the exact same amount of time. So this is just gonna be 0.41, and that is our second variable. So putting it all together, when we just subtract these numbers, 0.6 minus 0.41, you should get get a distance or a difference of 0.19 meters. That's basically how much farther light goes in the exact same amount of time. So this is, 0.19 meters. And that is our final answer. So, hopefully, that makes sense. Let me know if you have any questions, and let's move on to the next video.

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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?

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