welcome to chapter 14. this is about refraction and our first section here is on what refraction is so what we're going to do today is we are going to recognize situations where refraction will occur we'll identify which direction light bends when it passes from one medium to another and we're going to solve problems using snell's law so first i want you to think how are rainbows formed because it turns out that rainbows are formed through a process called refraction so what happens okay is refraction is just the bending of light as it travels from one medium to another but it turns out it depends on wavelength okay so light white light remember is a combination of all the different colors and so each wave bends a different amount as it goes through a rain droplet and what you see then is all the different colors reflecting back at you because they refracted through the rain droplets okay refraction is also what causes things like a pencil in a cup or a straw in a clear glass of water okay to look like it doesn't line up so what happens is you've got the angle of incidence here and we measure this from the normal line and then you have the angle of refraction the angle that it changes based on the medium so refraction happens as light travels between air and other transparent mediums or really between any two transparent mediums okay and as we mentioned before in the previous chapter the speed of light will change slightly as it changes medium and this causes the effects like we see in rainbows like we just discussed and when a strata glass doesn't look straight so how can we figure out how much the light will bend as it goes into a different mean well what we use is something called the index of refraction okay in this index of refraction we use the letter n here okay and it just means that it's the ratio of the speed of light okay compared to the speed of light in the vacuum okay so the speed of the light in the medium and the speed of the light in the vacuum because it's always going to be faster in a vacuum our index of refraction will always be greater than one so as we look at our index of refraction if an object moves from a lower index of refraction to a higher index of refraction so you can imagine this is our medium okay and it's going from a lower one so maybe this is n equals 1 to n equals 1.3 okay and we have our normal line here at 90 degrees okay then the angle measured from the normal will decrease from the incident ray to the reflected ray so what that means is if this light comes in this way it's going to come out like this so that this angle here we're going to call that the second angle and this is the first angle okay so the first angle for angle one will be greater than angle two okay so we've got n1 and n2 now if we switch that around k the opposite is true as well so if instead now we have n equals 1.3 is our n1 and our n2 is 1.0 okay then the opposite will happen so we've got our normal line okay and this will come in here and then it's going to bend greater okay so this angle and this angle theta 2 and theta 1 theta 1 will now be less than theta two okay so we can always tell how whether it will bend more or less depending on how the indices of refraction compare so one thing that this also ends up telling us is that when we're looking into water and we see an object that object isn't where it looks like because the light is bending as it goes through so here we've got a cat who's eyeing a fish and the cat sees the fish as though it's in a straight line okay but really that light has bent so because the index of refraction of water is greater or excuse me of air is greater than of water okay then what you get is this angle here ends up being smaller than this angle there and so the fish is closer to the cat than it appears the fish sees the opposite though because their indices of refraction are reversed now the fish is seeing the light traveling from the air to the water so the angle here ends up being smaller because this index of refraction is bigger than this index of refraction so objects always appear to be in different positions if you're looking through a medium because of refraction so one thing that we can use to calculate exactly what that angle is is called snell's law so snell's law just tells us that the indices of refraction of the first medium times the sine of the angle of incidence will equal the integral of excuse me the index of refraction of the second medium times the angle of refraction in that second medium so here the eyes this is the light coming in right so this here the angle of incidence is i and this here our angle of refraction is r so this is ni and this is nr so let's do an example problem with this now so we are going to find the angle of refraction for a ray of light entering a bucket this should say bucket not a buck a bucket of water where the n of 1.33 from air at an angle of 25 degrees to the normal so it turns out the n of air is almost always one okay because it's really close to a vacuum it doesn't really slow down the speed of light very much but water slows it down a bit more so our n of the water is 1.33 so it's going from air to water so this one is going to be our our incidence and this is going to be our refraction okay so snell loss tells us that we've got the index of refraction times the sine of the angle of incidence will equal the index of refraction of our refracted rate times the sine of our refracted angle okay so the light enters the bucket of water from the air at an angle of 25 because it says enters from that means that that is our incident angle so theta i will equal 25. so now we can go ahead and plug in our information okay n air is our i and n water is our refraction so we're going to have 1 times the sine of 25 equals 1.33 times the sine of theta r if we rearrange this to solve now 1 times sine 25 stays sine 25 and we're going to need to divide by 1.33 so we'll have sine 25 divided by 1.33 equals the sine of theta r whoops sorry not theta squared theta r okay and here if you guys aren't familiar with this the opposite of the sine function here is called sine inverse so i'm going to take the sine inverse of both sides so i'm going to have the sine inverse and the button looks just like this on your calculator it has that little negative 1 and then in that i'm going to put my sine of 25 over 1.33 and this will be my angle of refraction so if i plug this in now my angle theta r um make sure just before we solve this make sure this is this is 25 degrees so make sure your calculator is set in degree mode okay it's really important all you get the wrong answer so after we plug that in then we will find that our angle of refraction is 18 whoops 18 point