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Current time:0:00Total duration:10:44

as promised let's do a couple of simple Snell's law examples so let's say let's say that I have let's say that I have two two media I guess plural of mediums so let's say I have air right here air and then right here is the surface that is the surface let me do that in a more appropriate color that is the surface of the water so this right here is the surface of water and I know that I have a light ray I have a light ray coming in with an incident angle of so it has an incident angle so relative to the perpendicular it has an incident angle of of 35 degrees and what I want to know is I want to know what the angle of refraction will be so it will refract a little bit it will bend inwards a little bit since this outside is going to be in the air a little longer if you buy into my car traveling to into the mud analogy so it will then bend a little bit and I want to figure out what this new angle will be I want to figure out the angle of refraction I'll call that theta - what is this and so we can just this is just straight up applying Snell's law and I'm going to use the version with the width using the refraction indices since we have a table here from the ck-12 org flex book on the refraction indices and you can go get it for free if you like and that just tells us that just tells us that the refraction index for the first medium so that is air the refraction index for air times the sign of the incident angle in this case it's 35 degrees is going to be equal to the refraction index for water is going to be equal to the refraction index for water times the sine of this angle right over here times the sine of theta - and we know what the refraction index for air and for water is then we just have to solve for theta - so let's just do that the refraction index for air is this number right over here one point zero zero zero to nine so it's going to be one point zero zero there's only there's three zero is one point zero zero zero to nine times the sine of thirty five degrees is going to be equal to the refraction index for water which is one point three three so it's one point three 3 times sine times sine of theta two now we can divide both sides of this equation by one point three three we divide one both sides by one point three three on this side we're just left with sine of theta two on the left hand side let's get our calculator out for this so let me get the handy calculator and so we want to calculate and I made sure my calculator is in degree mode one point zero zero zero two nine times the sine of thirty five degrees so that's the numerator of this expression right here the green part that's point five seven three seven divided by one point three three I'm just dividing by the numerator here this when you just do a divided this answer it means your last answer so that's the numerator up here divided by that denominator and so I get point four three one four I'll just round a little bit so I'll get so I get I'll switch colors zero point four three one four is equal to sine of theta two and now to solve for theta you just have to take the inverse sine of both sides of this so you get the inverse so you could get the inverse sine this doesn't mean sine to the negative one you can also do this the arc sine the sine inverse of zero point four three one four is going to be equal to the inverse sine of sine is just the angle itself or I guess when we're dealing with when we're dealing with angles in a normal range it's going to be the angle itself and that's going to be the case with this right over here and if any of that is confusing you might want to review the videos on the inverse sine and the inverse cosine and they're in the trigonometry playlist but we can very easily figure out the inverse sine for this right over here you literally you have sine here the when you press second you get the inverse sine so it's the inverse sine or the arc sine of that number right over there and instead of retyping it I can just put second and then answer something the inverse sine of that number so that's exactly that's exactly what I'm doing right over here and that will give me an angle that will give me an angle and I get twenty five point five five we're all rounded twenty five point six degrees so this theta 2 theta 2 theta two is equal to twenty five point six maybe I'll say approximately equal to some twenty five point six degrees so Snell's law goes with our little car driving into the mud analogy it's going to be a narrower degree it's going to come in words a little bit closer to vertical and theta two is equal to twenty five point six degrees and you could do the other way let's say let's do another example let's say let's say that we have just to make just to make things simpler let's say that I have some surface right over here so this is some unknown material and we're traveling in space we're on the Space Shuttle and so this is a vacuum this is a vacuum right over here or pretty darn close to a vacuum and I have light coming in at some angle I have light coming in at some angle just like that let me draw a drop of vertical so it's coming in at some angle actually let me make it interesting let me make the light go from the slower medium to the faster medium just because the last time we went from the faster to the slower so it's in a vacuum so let's say I have some light let's have some light traveling traveling like this and once again though if you view the just to get the the get of whether it's going to bend inward or bend outward the left side is going to get out first it's going to travel first it's going to it's going to travel faster first so it will bend inwards when it goes into the faster material so this is some unknown this is some unknown material where light travels slower and let's say we were able to measure let's say we were able to measure the angles let's let me drop a vertical right here let me drop a vertical right over here and so let's say that this right here that right there is let's say that this right here is 30 degrees and let's say we're able to measure the angle of refraction and the angle of refraction over here is let's say that this is 40 degrees so given that we're able to measure the incident angle and the angle of refraction can we figure out the refraction index for this material or even better can we figure out the speed of light in that material so let's figure out the refraction index first so the refraction index so we know the refraction index for this questionable material times the sine of 30 degrees is going to be equal to the refraction index for vacuum well that's just the ratio of the speed of light in the vacuum to the speed of light in the vacuum so this is going to be 1 so it's going to be 1 that's the this is the same thing as n for a vacuum and I'll just write a 1 there times the sine of 40 degrees times the sine of 40 degrees or if we wanted to solve for this unknown refraction index we just divide both sides of the equation by sine of 30 so our unknown refraction index is going to be this is just a sine of 40 degrees sine of 40 degrees over this over the sine of 30 degrees over the sine of 30 degrees so we can get our handy calculator out and so we have we have the sine of 40 sine of 40 divided by the sine sine of 30 degrees make sure you're in degree mode if you try this and you get one point let's just round it one point two nine so this is approximately equal to so our unknown refraction index for our material is equal to one point two nine so we're able to figure out the unknown refract the unknown refraction index and we can actually use this to figure out the velocity of light in this material because remember this unknown this unknown refraction index is equal to the velocity of light in a vacuum which is 300 million meters per second divided by the velocity in this material the unknown material so we know that one point two nine is equal to the velocity of light in a vacuum so we could write 300 million 300 million meters per second divided by the unknown velocity in this material I'll put a question mark and so we can multiply both sides times our own known velocity I'm running out of space over you have other stuff written over here so I could multiply both sides by this V and I'll get one point two nine times this V with a question mark is going to be equal to 300 300 million meters per second and then I can divide both sides by one point two nine the question mark is going to be this whole thing three hundred million three hundred million divided by one point two nine or another way to think of it is light travels one point two nine times faster in a vacuum than it does in this material right over here but let's figure out its velocity so in this material light will travel a slow so that's three hundred three hundred thousand three hundred million divided by one point two nine light will travel a super slow 232 million meters per second so this is approximately this is approximately just to round off so it's approximately two hundred and thirty two million million meters per second if we get to guess what this material is let's see I just made up these numbers but let's see if there's something that has a refraction index close to one point two nine so that's pretty close to one point two nine here so maybe this is some type of interface with water and a vacuum or the water somehow isn't actually evaporating because of the lack of pressure or maybe it's some other material let's keep it that way something that wouldn't maybe it's some type of solid material but anyway those were hopefully two fairly straightforward Snell's law problems in the next video we'll do a slightly more involved