comes out here, this would be maybe violet. and it turns out you've got an angle between here and here of, i think it's 40 degrees for the violet. and here and here 42 degrees for the red, early printings of the book have a mistake there, okay? but it's this sort of thing. so when you're looking at a rainbow in the sky, if you're standing down here and you look at raindrops up in here, and these raindrops are being illuminated by sunlight in the back of you, note the sun is always on the back of you when you see a rainbow if you're facing the rainbow, yeah? and that sunlight come down and back, a refraction occurs in the drop, reflection and refraction, yes? and you're down here and, boom, you see the colors. now here you are right here if your eye is right here, for that particular drop you see red, okay? if you want to see the color violet, would you look up or down?

up. down. check your neighbor. let's take a look, gang. if you got your eye down here, you're seeing red. to see violet, this one here, up or down? up. how many say you would look down? one. let's try that again. how many people say you would look down to see violet? two. [laughter] they're right. how many say you'd look down to see violet? how many gonna join the club? come on. study political science, they'll get you all into that sort of thing. it turns out, gang, you would look down. okay, can i have a volunteer come up here? julie. yeah, lee, two volunteers. julie, you stand here. lee, you get over here, okay?

we want to answer the question does everyone see the same rainbow or does everyone see their own rainbow. and why is the rainbow bow shaped? circle, okay? it turns out i took a flight in kawaii one time, on kawaii air helicopter flight. on the helicopter flight, the pilot says, "if you look out to the side, you'll see the rainbows are completely round." and from up there, sure enough, they were complete circles. and then the pilot added, "all rainbows are round. "it's just that when you're down there, the ground cuts them off." so rainbows, gang, are completely round without the ground in the way. let's see why they're round. okay, julie is the observer. face the board, julie. face the board? okay. now we're gonna have sunlight coming right behind, can you squat down just a little bit? sunlight is coming right behind julie, okay? and that's right here and this is a raindrop. and, julie, i want you to put your eye where the blue is, okay?

and hold that please. now, is there anywhere else that raindrops could come down and hit julie's eye like there? well, how about over here? no, there's no way. over here, it's gonna miss, okay? so let's try this again. julie, you hold that and let's see where else-- keeping this parallel. oh, you can get it there too. you can get that one, too, can't you? you can't get this one here, but she can get that one, can't she? and she can get this one and she can get that one, she can get that one. the criterion is that this angle remain constant for all those drops. and look at that, julie can see all these ones but lee can't. when lee looks over at this drop here, he gets no color. thank you, julie. lee, you're standing over here, stand right here, okay? so you have to squat down a little bit because this thing is a little high, okay? okay, you look at the red, lee. you look at the red, okay? now you hold that, lee. you hold that, okay? lee, can you see a drop here? mm-hmm. can lee see a drop way over there? no. lee can see a drop here, here, here.

lee can see those drops. lee, do you see the same rainbow that julie did? no. lee sees a different rainbow. so next time someone says, "oh, look at that rainbow." you say, "what rainbow?" i'm just kidding with you, you know? you say, "well, i'm not seeing the same rainbow you are." is that true or false? true. true. okay, julie, stand like this. lee, stand like this. closer, closer, now look at the rainbow, right this way. are you guys looking at the same rainbow? no, different rainbows. a little closer. [laughter] same rainbow? no. really close, get down there, lee. same rainbow? it looks better doesn't it, huh? [laughter] okay, thanks a lot, gang. let's hear it for lee and julie, huh? hey, all right. [applause] you've all done this. you've all gone scuba diving, if not snorkeling at least or just swimming in the water. how many people have not done this? swim in the water at some time in your life, go way down as far as you can and then look up and see what it looks like. how many people have not done that?

i want to see what you look like. we've all done that right? and what have we seen? it depends on how rough the water is, uh huh. what does a fish see when it looks up, okay? the water. the fish's point of view looking up is the same as the light coming down, see? light coming from straight above comes straight down to the fish. light coming like this bends like that to the fish. light like this bends like that to the fish. and over here, maybe light like that just bends to the fish. and if the fish looks up this way here, the fish sees the bottom. so what the fish sees is a-- fish are you? you see a patch. you see a great big circle. if that water were perfectly clear, you'd see a nice, nice circle. and the critical angle for water is 48 degrees, 48 in here, so what's 48 and 48? 96, 96, i did it myself, okay? 96 degrees.

so it turns out if you're down there, you can see from horizon to horizon in a 96 degree view. see, when you're up on the top of the air, you got to go like this, 180 degrees, 180 degrees from horizon to horizon. but underneath there, only 96 degrees. that's why a fish wants to see horizon to horizon. they don't have to go-- a fish doesn't have any neck, doesn't need a neck, they just go like this. [laughter] you see how that work, okay? so, in fact, what's a fish eye lens? a fish eye lens is just something that will compress a wide view into a-- that's what so that's here. so the whole view is up there. so if you look up here, you can see the sunrise. and look up here and see the sunset. everything is in that conical view, nice big circle at the top. the next time you go swimming, watch for that again, watch for that. you'll see little splotch where you can see out, that's where the water is a little bit tipped. but perfectly smooth,

you see a nice circle and you see a cone. you come over here across the circle, it move with you wouldn't it? hey, wow look at the-- how does the circle know? because you're special, that's how. okay, you get the idea. here's another thing too. people who are near sighted underneath the water can see very nicely. i wonder if there's a reason for that. oh, there's probably no reason for that. think about that the way the light bends going from water to eye is different than from air to eye. less change in speed, less bending, maybe that would have an effect, what do you suppose? i got a homework assignment for you guys. i got a homework assignment. that's the granddaddy homework assignment, okay? let me tell you what it is. you see that door? let's suppose that whole door is a mirror. pretend it's a mirror. if i stay one body length away, could i see my whole image in that mirror?

how many say, "no, the mirror would have to be bigger than that, hewitt"? stand up. nobody, right? we know you could see yourself on that whole, huh, okay? how about if i made the mirror smaller? could i see myself? could i see myself if i made the mirror like this big? exactly the size of my body right here, huh? and i get over here. would the mirror be big enough to see all of myself? how many say, "no, no. it has to be bigger than you"? who said that? it got to be big enough, yeah? could i make the mirror smaller still? could i stand one body length away and see myself full image in a mirror smaller than my height? to make the numbers easy, let's suppose i'm six feet, not quite, huh? six feet. could i make my mirror, like, three feet, four feet, two feet, one foot, tiny, tiny? how big would the mirror have to be? and guess who's gonna do that for homework, you.

and you know what? you can stand in front of a mirror at home. you don't have a full length mirror, stand in front of a face mirror. stand in front of a mirror like this. and here's what i want you to do. stand in front of a mirror, mark where you see the top of your head, all right. now mark where you see the bottom of your chin, don't move now. now mark where you see the bottom of your chin. measure the distance between those two marks compare it to the distance between your face. if it's the same, then you give me an answer it's the same, same but it won't be the same or will it? do it and find out. so how big the mirror got to be compared to your height to see you? that's question number one. question number two is this. okay, you find out what size the mirror got to be. you can have a friend help you by standing in front of a full mirror and putting a little piece of tape or lipstick or something like that and put some marks, you know? you see the top of your head, the bottom of your feet, yeah? now, what effect does distance have on your answer?

if you step back further and further and further, what happens? can you still see yourself on that mirror or can you see yourself on a smaller mirror or do the mirror have to be bigger? the answer to that question is very surprising to a lot of people. what effect does distance have on your previous answer? check that out, try it. you're gonna see something that perhaps has escaped your notice all your life. now, when is the last time you guys looked in the mirror? last week, something like that, yeah? and you probably won't look in the mirror for another few days, yeah? okay, with this assignment, you look in the mirror today. and when you look in the mirror, look for the physics in the mirror, huh? come on, you guys look in the mirror all the time, ain't that true? look at the physics in there too, next time, yeah. [music] captioning performed by aegis rapidtext

welcome to another session of beliefs and believers. we're having a wild discussion of religious doctrine in the context of christianity, and virginia just brought a cartoon out here that is really, you know, quite apropos. some new visitors to heaven are talking to what i assume is god, i imagine, and it says ... god's saying, "why, no, we have no catholic or protestant districts here." and you know, there we are.