okay, gang, let's begin. we're gonna talk about reflection and refraction. but first of all, let's play a little game and the little game be called

fermat's principle of least time. it's kind of covered in the book so i wanna go over it kind of quickly. and if we play a little game where you want light to go from "a" to b in the shortest time, what would the path be? straight line. you want it to be a straight line? but let's suppose we made an added provision that it's gotta touch a line down below on the way. now, it's gonna go from "a," touch the line, and back to b. what would the path be for the shortest time? it turns out to be shortest distance. would it be like this? no. would it be like this? are there shorter paths? answer begins with a y. yes. yep, okay. how about right exactly in the middle, huh? no, no, no, no. how about it? right exactly in the middle and bend like this. would that be the path of shortest time? it turns out the answer begins with a n. - no. - no. and it turns out, there's a nice technique for finding it. let me go through it quickly. if you consider this, whip, boom, folded down, okay,

folded right down. so it's over here and call it b prime. i could ask you, guys, what's the shortest path between here and here, and you would all say what? a straight line. a straight line. in fact, you just go like this and say, "that's the shortest path between those two." what's the shortest path between here and here, touch this line? how many see it already? well, this line here, fold it up like that, the distance here and here is the same as the distance here and here, yeah? yeah. so it turns out, what the light will do, the light will hit here and then go up to here, see? like if you put your eye here and you will look down the mirror to see this, you will look right there to see it. not like here, okay? now, i've got an exercise for you. what i've done is i've shown where the image of b would be down here, huh? what would be the path of least time to go from b to "a"?

can you, at your seats, fold "a" down and do it? go. do you know what i'm saying? you would say, "i don't know what i'm gonna do." come on, you know what i'm saying? i'm saying, do it all over again. and this time, we wanna go from here to here, but we wanna know to go to touch the mirror. the only reason i'm having you do this is because if you do it, then you'd be learning. if i do it twice, you'll see me do it twice, and you'll be convinced that i know how to do it. and i want you to know how to do it. go. let's see who's the last one to finish. what did you do with this? you take "a" and fold that down, whip, boom, and call that "a" prime. now, if i ask you what's the shortest path between here and here, no contest, huh? you guys will just say this.

but, again, no-- but how about the shortest path between here and here and you gotta touch here? bam, there it is. because this distance, this distance, same, same. right. and let me tell you what this all turns out to give, gang. this angle and this angle, guess what? they'd be the same. will always be the same, okay? so light going from here to here, bo-boom, or coming back from here to here, bo-boom. you're at the restaurant and you're eating there all by yourself as usual, and you look in the mirrored wall and you look over and, oh, there she is. miss right, you could see the mirror image of miss right. so then, you start to kind of fix yourself up a little bit because you're wondering if you can see her, can she see you? and what's the answer? yes. check your neighbor. yes. [laughter] if i hold this mirror in such a way that i can see you, can i be assured that you can see me in the mirror? what's the answer? begin with a y, ends with a p. yes. yep, that's true, yeah. principle of reciprocity, okay?

from here to here, from here to here, same, same. the path would be no different if you change direction, okay? so the law of reflection, gang, is simply that the angle of incidence, light coming in hitting a mirror surface, will be equal to the angle of reflection. it's common to measure those from a vertical line perpendicular to the surface called the normal. so we usually say this angle, this angle, same, same. everyone that plays pool knows that. when you're playing pool where you bank your shots, you know that the angle that you come in, the angle you come out is the same. any question on that? now, this holds for not only plane mirrors but all kinds of mirrors, even curved mirrors. because any face, the light coming in, boom, will bounce off at the same angle. this angle, this angle, will always be the same. and that's even true of what's called diffused reflection. if you look at a surface that's very, very rough, okay? light coming in will hit right here. you see this angle here? it will bounce off like that.

maybe light coming right over here will hit there, and may be bounced like that. maybe a light hitting--maybe a light right in between here will hit a face like that and bounce off like that. it will go in a kind of all directions. some will even bounce right back to the origin if the surface is rough. and it turns out the paper that your books are made of is rough or smooth. that's a relative question. but it's rough compared to the wavelength of light. so for a light wave, this is a very, very rough surface and ain't that nice? because light coming down will bounce off in all directions and you can hold your head anywhere and see the book. see, if the book were a mirrored surface, you could only see it in certain places, isn't that neat? this happens at nighttime when you're driving. everybody driving at nighttime when it's raining out and it's very difficult to see the road ahead. you know why that's true? if the road is dry, the surface is rough

and your headlights will come down and some of that light will come back to you. and you, the driver, have enough light coming back through your windshield to see the road ahead. it's illuminated by your headlights. but what happens in a rainy night? is the surface rough? nope. the surface, honey, is mirrored. now, it's like a mirror surface. your headlights come down, bo-boom, bounce off ahead, nothing coming back to you, hardly. you see? and so you say, "hey, if i get the lights on, you can't be sure you even have the lights," because you're going from a diffused reflector, the surface, rough, to a mirrored reflector, the surface with that layer of water. you all noticed that. and that makes it even extra dangerous because that light that's coming down ordinarily some of which come back to you, now, bo-boom, all goes ahead to whom? to the other driver coming at you. and so the other driver has what? glare. so that's why rainy nights poor visibility for those reasons, huh? kind of interesting, yeah?

consider a candle. all optics books consider candles for objects, okay? now, we're gonna look at the image that this candle is in a mirror. let's suppose right here we have a mirrored surface. now, what happens as light-- let's just take from this point. light goes in all directions: some comes straight ahead, some comes up like this, some comes like this. the light hits the mirror in all directions. and when it hits the mirror, it bo-boom, reflects, yeah? right. and it reflects, how? there's a normal, a normal, a normal, a normal. it reflects such that this angle, for example here, will be equal to this angle here and reflects like that. and up here, this will reflect right back to where it came, yeah? because it gets flushed, huh, right angle, huh? up here, like that. and up here, like that. and down here, like that where this and this are the same. i don't have that drawn very well, yeah, like, maybe like that. you get the idea?

now, you have your eye out here and you're looking. these rays here are all diverging. they're spreading out, see. they're spreading out this way just as if they were this way, see? it's like this continuing, huh? but that's spread out, it looks to you like that ray came from back here. that ray, they came from back here, that ray came from back here, that ray came from back here. it looks to you out here like there's a flame here, and also a flame back here. and i could draw the same rays for the bottom of the candle. that's not in your book a little bit, yeah? okay. and the bottom of that candle, it would look to you like it's over there. and so, you will see the candle here and you would see the image of the candle. and let me ask you a question. what's the distance here and here, and the distance here and here? begin with ss. check your neighbor.

same, same, gang, same, same. so if you're taking a photograph of you and your friends standing in front of a mirror, all right? and you don't have a focus device you can look through, but you have a setting. and let's suppose you're, like, you are three mirror-- three meters in front of the mirror, and you're taking you and the gang, yeah? now, you want to set your setting for three meters or what for your image? check your neighbor. okay, gang. what would be the answer? you stand three meters in front of the mirror, what are you gonna set your setting for the image? where? how many meters? how many say answer begins with a-- [makes noise] how many say answer begins with a-- yehey, that's six, six meter. your image is gonna be six meters away. so your image would be as far behind the mirror as you are in front. makes sense? yeah. now, if you have a curved mirror, different rules, okay? and it turns your image distance will be more complex. we won't cover such thing now, you know why? because it's a little bit more complex and we want to get the easy stuff down cold.

reflection is one thing. refraction is another. in this case, the light hits the mirror and bounces off and stays in the air, or it could be under water. there is no change of medium. what happens when the light changes from one medium to another? what happened to the speed, gang? when light goes into a piece of glass, what's that do? - slow down. - slows down. when light goes into water, what's it do? - slow down. - slow down. when light goes from a vacuum of space to the atmosphere, what's it do? begin with sd. - slow down. - slow down, you get the idea. and we know why it slows, right? because the light is interacting with the particles, right? and that interaction, it involves a little time, we're into that, right? and different colors are interactive, and the different colors travel different speeds, we get all that sort of thing, right? and let's investigate that a little bit. in fact, let's talk about the example that richard feynman talks about when he talks about refractions a dandy. it's in your text. let's suppose you're a lifeguard right here, and this is a top view of the beach. and here's a sandy beach. there's sand and water down here.

this is a helicopter view. and down here is a person drowning. drowning in the water, so the sharks are coming and something like that. now, you're the lifeguard-type up here. and you want to get from here to here in the least time, okay? so, you might say, well, i'll take a straight line path. good idea, or not good idea? begin with n, g. not. not good idea. hc. has the person-- oh, you don't-- well--let me ask you a question, how fast can you go across the sand compared to how fast can you swim? fast enough. how can you move faster, across the sand or swimming? how many of you say, "honey, i'm not so good in the land, but man, you should see me in the water." [laughs] come on, come on, most of us could go faster across the land, yeah? so it might be that you would say, "hey, what i'll do, is i wanna go the shortest distance to the water." so i'll run over here, and then run straight down. do you think that's the shortest time? if you run very, very, very fast and swim very, very, very slow,

case to be made, you approach that. but let's suppose you run fairly fast and you can swim fairly fast, but not so fast, would it be that, this, or something in between? something in between. begin with ib. -- all right, begin with-- altogether, what is it? it's gonna be-- it turns out your path is gonna be something like this, see, okay? it's gonna kinda bend like that, okay? and guess what behaves the same way? begin with a l. light. light. light does the same thing. we call that refraction. go from one point to another in the least time, and do that by taking a bend. i can kinda show you that with this little demonstration. inclined plane and i get some wheels. and i'm just gonna roll the wheels down the incline plane, all right? what i'm gonna do is, i'm gonna roll the wheels

from a nice smooth sidewalk onto a rough piece of material. that's almost like wheels rolling along a sidewalk into the grass, or light coming down and interacting with the material and slowing down. true. did you see it bend? yeah. it came down like this, and then bent. let me put up that on the board. my wheels are coming down on this direction, and their coming from the smooth surface to the rough surface. when the wheels get to the rough surface, what happens to the speed of the wheels? slows down. slow down. do you know why they slow down? because there's an interaction with the wheel and the material. let's suppose it's like the little pieces of cloth on the towel, or maybe it's like grass, blades of grass on a lawn, okay? there'd be some interaction, so this part would slow down. but what happens to this other part over here,

it continues going quickly. so what happens it sort of-- and so what happens is it goes like this. when both wheels get in there, they're going the same speed and they continue at a straight line. so there's no mystery as to why the wheels will kind of bend over, is there? i mean, if you're gonna move along like that-- won't your arm go like this. part of it's slowed-- well, guess what behaves the same way, light waves. when waves of light come from above, as they hit water, maybe the rays of light are coming from the sun, something like that, and we got a ray coming down like that. incidentally, it turns out the light ray and the wave fronts that represents, these are like the crests of waves. think of water waves, yeah? right angle in here, gang, always a right angle. see, even the axis of a wheel and the direction in which it's traveling, right angle, okay? so what happens over here? these waves of light come down. and when they hit the water, what happened to the speed of the rays? slow down.

or you don't know that? well, check your neighbor. -- --somehow go faster. what's the answer, gang? slow down. it slowed down, okay? the wave slowed down. so, what happens, they hit, they bend, and they sort of bend like this. and they get closer together. so the wavelength gets a little less in here, but the frequency of the waves stays the same. does the frequency of a light wave change when it reflects from a surface, as we talked about before? what evidence do you have that the frequency of light does not change upon reflection? do you have any evidence of that? what evidence do you have that the frequency won't change? check your neighbor. how many people say, "well there's really no evidence of that, it's just in the textbooks and we believe it?" try it, gang. hint, shall i pass this mirror around?

if i pass this little mirror around, what would you do with the mirror to find out? look at it. you look at the color of your shirt. and you look at the color, "son of a gun. "hey, the shirt got the same color in the mirror. "wow. the ceiling got the same color. every one thing, everything in-- the same." what's that mean? it means there's no change in frequency, yehey. so if you got a blue shirt and you're standing in front of a mirror, gang, what's the image color? blue. begin with a bl. what if you got a red shirt, what would the image color be? red. yehey. so we see that, okay? it turns out going through a material to. the frequency stays the same, so the color stays the same. even though the wavelength gets squashed up a little bit, yeah? so that's refraction. show you an example of that, root beer. root beer is syrup in thick, thick mugs, why? why thick mugs? because they can give you less root beer for the same money, right? [laughs]

let me test this to make sure it's really root beer. [laughs] it tastes like pepsi to me. [laughs] by golly, it is pepsi, all right? now, you guys be seeing something. the root beer goes right out to the edge, make it look like you got a lot of root beer in there. you got a lot or a little, the answer begin with a l. a little. it turned out a little, because you got a lot of glass. but to the viewer, you see the right out to the edge. i wonder if there's a reason for that. oh, no. how many people say, "well, no, there's probably no reason for that, it's kind of just the way it is." hc, gang. let's look at a top view of that on the board. here's our root beer. let's look at a point right here. light is going in all directions from there, huh? now it bends when it gets outside,

so let me just put in here. light is traveling in all directions. and some of that light is coming like this, and some of that light is coming like that. and the light that's coming like this, when it comes through, what's that do, does it keep going straight? no. how many say that when the light comes out from the glass to the air, it will speed up? how many can't say anything, they're kind of just waiting to take notes? do you see it's gonna speed up gang, okay? it's like the opposite of this. when these wheels roll, roll from here out, this wheel gets out first, it starts going faster so it just unbends, okay? so what happens, this light over here, the waves of light, okay, will now kinda come like this, bend like that, see what i mean? and over here, a place over here, rays of light come in all direction, maybe light coming like that, bends like this,

a person's eye is right here. a person's eye looks out and sees root beer all along the edge. it's an illusion. the root beer is really in here. if the light didn't change speed going from here to here, then you would see the thickness of the glass. i saw a very, very neat thing one time. i saw a bottle of coca-cola. and the bottle of coca-cola was embedded in a piece of plastic. so it turns out that the light wouldn't change speed very much going from the glass to the plastic, and when you look at that, you can see the coke like this. and you could get a better representation of the true volume of the coke, do you know what i'm saying? do you know what i'm saying, okay? but when you take this out on the air, boom, there's a big change of speed, a big bend, and that bend makes it look like it's filling up more room than it really is, an example of refraction. any questions? could you get the same effect if you put it in water? let's try that. let's try that. let's try that. that's a good idea.

excellent idea. i never even thought of that. see ted right after class, will you? let's try that again. you kinda can. take a--can you kinda-- it's hard for you guys to see. it turns out i've got the water a little bit chalked up because i wanna show you something else. but yes, you do that effect. excellent, excellent, excellent question. how come i never thought of that before? [laughter] that's one thing about teaching, you continually get new ideas by people like you. and sometimes the simplest questions give the-- isn't that nice, see? do you guys know why you can, kind of, see the glass now and you couldn't before? how about that for a homework question? would that be a good one? we'll think about that. let me show you something else with that. here i've got a laser, gang. laser is emitting a nice clear single frequency red light.

see the red light gang? okay? a laser light, okay? it makes a nice, nice thin, thin beam. you guys can't see the beam right now because it's not scattering off anything. if i darken the room and put a little chalk dust here, you would see the beam shine and scatter. you know when you see a search light beam going up from a department store's opening or something like that? you see the beam only if there's a lot of gunk or something in the air. if the air were really, really clear, honey, you'd see no beam at all. so need something for the beam to scatter off. and what we have in here is some dairy creamer, a little dairy creamer and some water. so there's a scattering thing here. can you see the light beam? what i'm gonna do gang is put a mirror on the bottom here. and i'm gonna see if you can see the light refracting. lights, please. wow. can you be seeing such thing? neat. okay. oh what i just should have is-- does anyone have any-- does anyone smoke here? no. yeah.

someone with a smoke, come on blow some smoke in here. it's for a b. [laughter] light up, james, light up. yeah, just blow right in here. and then maybe we can see the beam that's off to either side. how come you smoke, james? you know about that? [laughter] blow a lot of it in there, james. get over here and-- careful of your eyes though. can you guys be seeing? watch your eyes. oh yeah, don't get in your eye, honey. that's lawsuits and all that, you know, you mind your eye and think about the lawsuits. so you can get some over here too, james. okay, what i want you guys to see, is it coming down to see the bending at the surface too. can you kind of see that? ain't that neat? is that dramatic enough that you're glad you came today? yes. okay, thank you, james. lights again, please.

okay, what we attempted to show there, gang-- james, after class, i want to talk to you about smoking, okay? [laughter] hey, that's true. i heard that the nicotine is tougher to kick than heroine, wow. here's what we wanted to show, gang. i got--most smokers begin while they're teenagers. very, very few people get to the age of 20 and then take up smoking. it's all done at an earlier age. the teenagers make the best smokers, make the best soldiers, i mean, make the-- you know what i mean? they make judgment a little differently. light coming in, laser light coming in like this, just look at the ray. now laser light forms an excellent example of a ray, it bent. and that's what i wanted you to see with the smoke. hits the mirror, and how's this angle compared to this angle?

same. same, same right? and when it comes out, does it continue like this? no. no. why? it refracts. it refracts. let me ask you a question, why does it refract and go in that direction? why? why does it refract to begin with? you got to know that. check your neighbor. okay, why the refraction gang? why does it refract anyway? what does light do when it goes from one medium to another? change speed. it changes speed. and when it changes speed and if it's coming in at an angle, what's it going to do like those wheels if one part changes speed and the other part doesn't, yeah? it's gonna bend? so we see why light refracts. get that. and so, there's a change of speed from here to here like that, okay? so here we're refracting, reflecting, refracting. all in one little illustration. question? wasn't there also a reflection off the water? did you see that? yeah. excellent, excellent. you saw the reflection off the water coming back down like that. excellent. also when the first beam that we--

and up here, up here. excellent, excellent. here i'm concentrating on the part i want to teach about, huh, and you saw the whole show, honey. that's great, okay? there is, there's a reflection here. it turns out water will also reflect light. you can't get any water that won't reflect a little bit. it's going to reflect some and refract some, okay? and coming down here at the mirror, reflect. some goes off here, huh? and some continued here. so you get all those, very good. lee? what's the angle of the reflected light that reflects before it goes down compared to the light reflected from the mirror. so the light reflected from the water and the light reflected from the mirror. yeah, this angle here and this angle here would be the same if this and this are parallel, okay? and this angle here would be the same as this angle here too, right? no. how many people are, "yeah, okay, whatever you say, hewitt." come on, no, that's wrong. this angle here is smaller than this angle. 'cause we're refracting now, okay?

and how about this angle here and this angle here? the law of reflection still holds. i want you to do something saturday night when you take your bath. saturday night when you take your weekly bath, get the tub all to yourself, all right? and take a flashlight, one of those waterproof jobs, take it in the bathtub and sit there and take that flashlight and shine it straight up. when you do, you'll see a spot in the ceiling. now take it and start turning it, turning it, turning it. and you turn it, turn it, turn it and it turns out, you get to a place, you know, light will be coming like this, huh? and then go out like that, yeah. and you keep turning, you'll get to a particular angle where the light will all reflect and none will come out. that particular angle is called the critical angle. and for water that critical angle, i believe, is 48 degrees, 48 degrees. less than 48 degrees some goes out and some reflects. but beyond 48 degrees, gang, all that light will be totally,

internally reflected. and you know what makes use of that idea is light pipes, fiber optics. you're into those things. fiber optics with the bend, the little decorative lamps and whatnot, okay? hey, fiber optics, it turns out that the hair on a polar bear, gang, the hair on the polar bear turns out to be a whole lot of fiber optics. and it has a preferential-- it has a preference for ultraviolet. and ultraviolet is high energy or low energy? high. and a polar bear want to get a lot of energy or don't care about the energy? honey, if you're up in the arctic, what do you want? a lot of--and you know what? it turns out the hairs on the polar bear fur are light pipes. and will guide the highest energy light right down to its skin. and the skin wants to absorb that light. guess what the color of the skin is, gang. black. so what's white and black and warm all under?

a polar bear, yey, physics, huh? okay. you ever be wondering about a rainbow? why do you get all the colors in a rainbow? to understand a rainbow, first of all, you got to understand a prism. you know if a white light comes in a prism, you get different refractions? different colors refracted different amounts. it turns out you get red here maybe, green here, and blue here and sort of like that. and you guys know with a prism you can get a nice, nice spectrum. we call it a rainbow in a loose sense, yeah? but you get that in the sky too, why? well, it turns out in the sky, rather than have prisms, you have little spherical drops and those little spherical drops sort of like this. and what happens there, sunlight coming in, the white light from the sun comes in, refracts, boom,