Snell's Law

by Patrick Ford
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Hey, guys, in this video, we're gonna talk about something called Snell's Law. Snell's law is the mathematical law that governs refraction across a boundary. Okay, let's get to it. Remember that when light transmits through a boundary into a different medium, the angle of its path must change. Okay, What I have here is an image that shows one medium indicated by an index of refraction in one and another medium indicated by an index of refraction in two. So the light travels at different speeds in these two media, so long as in one and in two don't equal. If they do equal, then they travel at the same speed and no refraction occurs. Remember that refraction depends on Lee upon a change in speed. So what we have is some incident angle fate, a one and some refracted angle faded to the question is how did those angles relate to one another? Well, Snell's law gives us this angle of refraction, and it says that the number of the index of refraction times sine of the angle, is conserved across the boundary. So in time, sign of data on the left side is also equal to n times Sign of Fada on the right side. Okay, so that quantity the index or faction times sine of the angle is conserved across the boundary. All right, now, this is where our definition of angles becomes very, very, very important. Your angle, which appears here and here, has to be measured from the normal. Fada has to be measured from the normal. Okay, Okay. It has to be measured from the normal notice. These two angles are both measured with respect to this normal line that I drew. This is the normal. Okay, if you measure that angle, let's say with respect to the surface of the boundary, like so that is not going to give you the right answer. Your answer will absolutely unequivocally be wrong every single time you measure the angle with respect to the boundary, do not do this. Always measure it with respect to the normal. Okay, let's do a quick example. Ah, Light ray is incident on an air water boundary at 33 degrees to the normal, with the reflected with the refractive index of water being If the light ray passes from air toe water. What is the refracted angle. What if the ray were to pass from water to air? So we have two different scenarios. We have air, toe, water and then we have water to air. So let's start with air to water. We know the incident angle 33 degrees to the normal, which is always how we have to measure the angles. And we know the index of refraction of water 1. We're going from air to water. So theta one, the angle the incident angle is 33 degrees in one is our index of refraction. Of our initial medium in two is the index of refraction off the medium were passing into which in this case, is water right there toe water 1.33 and then theta two is are unknown. The only thing here that we're missing is the index of refraction of our original medium, which is air. Always remember, the index of refraction of air is one. Okay, so now we have enough to use Snell's law to solve this problem. Snell's law says in one signed theta one equals in two signed theater too. So I need to solve for sign of data to so rewriting this I get sign of fated to is in one over into sign of fate of one which is in one. The incident medium is just one into the medium that we're passing into, which is water is 1.33 and the incident angle was 33 degrees. Okay. And this is equal to 0.41 which means using the arc sine function on our calculators. That this angle is simply 24 degrees, right? Right relative to the normal in the second bound Sorry in the second medium, which in this case is water. All right, that's the first part. What about water to air now the media are flipped, right? We're going from water to air, but the incident angle is still the same. We're still incident at 33 degrees from the normal. So theta one is still 33 degrees. But now, in one, the refractive index of our original medium is now that of water 1.33 and in to the index of refraction for are transmitted medium is that of air, which is one. And we're looking for that refracted angle. So it's the same set up. Let me minimize myself. I'm already sorry. I already have the equation I need to use, so I'm just gonna write that out. Sign of faded. Two equals in one over in to sign of fatal one, which is now 13 3/1. Right. The industries of refraction are flipped, but the incident angle is still 33 degrees and is holding equals about 0.72 So if we use the ark sign on our calculator, we find that the refracted angle is 46 degrees from the normal. Okay, always from the normal. All right, guys, that wraps up our discussion on Snell's law. Thanks for watching.