1 00:00:00,673 --> 00:00:03,924 In the last couple of videos we talked about reflection. 2 00:00:03,924 --> 00:00:08,600 And that's just the idea of the light rays bouncing off of a surface. 3 00:00:08,600 --> 00:00:17,067 And if the surface is smooth, the incident angle is going to be the same thing as the reflected angle. 4 00:00:17,067 --> 00:00:21,266 We saw that before, and those angles are measured relative to a perpendicular. 5 00:00:21,266 --> 00:00:24,953 So that angle right there is going to be the same as that angle right there. 6 00:00:24,953 --> 00:00:27,041 That's essentially what we learned the last couple of videos. 7 00:00:27,226 --> 00:00:29,002 What we want to cover in this video is 8 00:00:29,002 --> 00:00:31,645 when the light actually doesn't just bounce off of a surface 9 00:00:31,645 --> 00:00:34,629 but starts going through a different medium. 10 00:00:34,644 --> 00:00:39,390 So in this situation, we will be dealing with refraction. 11 00:00:39,875 --> 00:00:46,321 Refraction. Refraction, you still have the light coming in to the interface between the two surfaces. 12 00:00:46,598 --> 00:00:50,059 So let's say--so that's the perpendicular right there, 13 00:00:50,105 --> 00:00:53,392 actually let me continue the perpendicular all the way down like that. 14 00:00:53,392 --> 00:00:59,613 And let's say we have the incident light ray coming in at some, at some angle theta 1, 15 00:00:59,613 --> 00:01:04,182 just like that...what will happen--and so let's say that this up here, this is a vacuum. 16 00:01:04,182 --> 00:01:06,777 Light travels the fastest in a vacuum. 17 00:01:06,777 --> 00:01:12,054 In a vacuum. There's nothing there, no air, no water, no nothing, that's where the light travels the fastest. 18 00:01:12,054 --> 00:01:17,438 And let's say that this medium down here, I don't know, let's say it's water. 19 00:01:17,438 --> 00:01:19,452 Let's say that this is water. 20 00:01:19,623 --> 00:01:22,618 All of this. This was all water over here. 21 00:01:22,618 --> 00:01:25,905 This was all vacuum right up here. 22 00:01:25,905 --> 00:01:30,921 So what will happen, and actually, that's kind of an unrealistic-- 23 00:01:30,921 --> 00:01:34,408 well, just for the sake of argument, let's say we have water going right up against a vacuum. 24 00:01:34,408 --> 00:01:38,725 This isn't something you would normally just see in nature 25 00:01:38,725 --> 00:01:40,931 but let's just think about it a little bit. 26 00:01:40,931 --> 00:01:44,515 Normally, the water, since there's no pressure, it would evaporate and all the rest. 27 00:01:44,515 --> 00:01:48,813 But for the sake of argument, let's just say that this is a medium where light will travel slower. 28 00:01:48,813 --> 00:01:51,464 What you're going to have is 29 00:01:51,464 --> 00:01:55,587 is this ray is actually going to switch direction, it's actually going to bend. 30 00:01:55,587 --> 00:01:59,315 Instead of continuing to go in that same direction, it's going to bend a little bit. 31 00:01:59,315 --> 00:02:02,875 It's going to go down, in that direction 32 00:02:02,875 --> 00:02:06,623 just like that. And this angle right here, theta 2, 33 00:02:06,623 --> 00:02:15,838 is the refraction. That's the refraction angle. Refraction angle. 34 00:02:15,838 --> 00:02:20,171 Or angle of refraction. This is the incident angle, or angle of incidence, 35 00:02:20,171 --> 00:02:24,854 and this is the refraction angle. Once again, against that perpendicular. 36 00:02:24,854 --> 00:02:28,100 And before I give you the actual equation of how these two things relate 37 00:02:28,100 --> 00:02:31,490 and how they're related to the speed of light in these two media-- 38 00:02:31,490 --> 00:02:34,038 and just remember, once again, you're never going to have vacuum against water, 39 00:02:34,038 --> 00:02:37,546 the water would evaporate because there's no pressure on it and all of that type of thing. 40 00:02:37,546 --> 00:02:41,008 But just to--before I go into the math of actually how to figure out these angles 41 00:02:41,008 --> 00:02:44,992 relative to the velocities of light in the different media 42 00:02:44,992 --> 00:02:47,202 I want to give you an intuitive understanding of 43 00:02:47,202 --> 00:02:50,264 not why it bends, 'cause I'm not telling you actually how light works 44 00:02:50,264 --> 00:02:51,967 this is really more of an observed property 45 00:02:51,967 --> 00:02:54,500 and light, as we'll learn, as we do more and more videos about it, 46 00:02:54,500 --> 00:02:55,723 can get pretty confusing. 47 00:02:55,723 --> 00:02:59,002 Sometimes you want to treat it as a ray, sometimes you want to treat it as a wave, 48 00:02:59,002 --> 00:03:01,238 sometimes you want to treat it as a photon. 49 00:03:01,238 --> 00:03:02,802 But when you think about refraction 50 00:03:02,802 --> 00:03:05,854 I actually like to think of it as kind of a, as a bit of a vehicle, 51 00:03:05,854 --> 00:03:10,879 and to imagine that, let's imagine that I had a car. 52 00:03:10,879 --> 00:03:14,223 So let me draw a car. So we're looking at the top of a car. 53 00:03:14,223 --> 00:03:17,864 So this is the passenger compartment, and it has four wheels on the car. 54 00:03:17,864 --> 00:03:19,659 We're looking at it from above. 55 00:03:19,659 --> 00:03:23,171 And let's say it's traveling on a road. 56 00:03:23,171 --> 00:03:25,479 It's traveling on a road. On a road, the tires can get good traction. 57 00:03:25,479 --> 00:03:30,090 The car can move pretty efficiently, and it's about to reach an interface 58 00:03:30,090 --> 00:03:35,454 it's about to reach an interface where the road ends and it will have to travel 59 00:03:35,454 --> 00:03:41,469 on mud. It will have to travel on mud. Now on mud, obviously, the tires' traction 60 00:03:41,469 --> 00:03:46,171 will not be as good. The car will not be able to travel as fast. So what's going to happen? 61 00:03:46,171 --> 00:03:49,469 Assuming that the car, the steering wheel isn't telling it to turn or anything, 62 00:03:49,469 --> 00:03:52,515 the car would just go straight in this direction. 63 00:03:52,515 --> 00:03:56,413 But what happens right when--which wheels are going to reach 64 00:03:56,413 --> 00:04:01,541 the mud first? Well, this wheel. This wheel is going to reach the mud first. 65 00:04:01,541 --> 00:04:04,490 So what's going to happen? There's going to be some point in time 66 00:04:04,490 --> 00:04:07,664 where the car is right over here. Where it's right over here. 67 00:04:07,664 --> 00:04:10,771 Where these wheels are still on the road, this wheel is in the mud, 68 00:04:10,771 --> 00:04:13,152 and that wheel is about to reach the mud. 69 00:04:13,152 --> 00:04:15,767 Now in this situation, what would the car do? 70 00:04:15,767 --> 00:04:20,632 What would the car do? And assuming the engine is revving and the wheels are turning, 71 00:04:20,632 --> 00:04:29,377 at the exact same speed the entire time of the simulation. 72 00:04:29,377 --> 00:04:34,725 Well all of a sudden, as soon as this wheel hits the medium, it's going to slow down. 73 00:04:34,725 --> 00:04:37,767 This is going to slow down. But these guys are still on the road. 74 00:04:37,767 --> 00:04:39,952 So they're still going to be faster. 75 00:04:39,952 --> 00:04:43,782 So the right side of the car is going to move faster than the left side of the car. 76 00:04:43,782 --> 00:04:46,013 So what's going to happen? 77 00:04:46,013 --> 00:04:49,956 You see this all the time. If the right side of you is moving faster than the left side of you, 78 00:04:49,956 --> 00:04:52,229 you're going to turn, and that's exactly what's going to happen to the car. 79 00:04:52,229 --> 00:04:56,787 The car is going to turn. It's going to turn in that direction. 80 00:04:56,787 --> 00:05:02,433 And so once it gets to the medium, it will now travel, it will now turn-- 81 00:05:02,433 --> 00:05:05,362 from the point of the view from the car it's turning to the right. 82 00:05:05,362 --> 00:05:09,664 But it will now travel in this direction. It will be turned when it gets to that interface. 83 00:05:09,664 --> 00:05:13,125 Now obviously light doesn't have wheels, and it doesn't deal with mud. 84 00:05:13,125 --> 00:05:17,295 But it's the same general idea. When I'm traveling from a faster medium 85 00:05:17,295 --> 00:05:21,721 to a slower medium, you can kind of imagine the wheels on that light 86 00:05:21,721 --> 00:05:26,356 on this side of it, closer to the vertical, hit the medium first, slow down, 87 00:05:26,356 --> 00:05:27,752 so light turns to the right. 88 00:05:27,752 --> 00:05:35,362 If you were going the other way, if I had light coming out of the slow medium, 89 00:05:35,362 --> 00:05:39,202 so let's imagine it this way. Let's have light coming out of the slow medium. 90 00:05:39,202 --> 00:05:47,510 And if we use the car analogy, in this situation, the left side of the car is going to-- 91 00:05:47,510 --> 00:05:51,782 so if the car is right over here, the left side of the car is going to come out first 92 00:05:51,782 --> 00:05:58,854 so it's going to move faster now. So the car is going to turn to the right, just like that. 93 00:05:58,854 --> 00:06:04,136 So hopefully, hopefully this gives you a gut sense of just how to figure out which direction 94 00:06:04,136 --> 00:06:06,762 the light's going to bend if you just wanted an intuitive sense. 95 00:06:06,762 --> 00:06:11,229 And to get to the next level, there's actually something called Snell's Law. 96 00:06:11,229 --> 00:06:13,454 Snell's Law. 97 00:06:13,454 --> 00:06:21,423 Snell's Law. And all this is saying is that this angle-- 98 00:06:21,423 --> 00:06:26,264 so let me write it down here--so let's say that this velocity right here is velocity 2 99 00:06:26,264 --> 00:06:29,264 this velocity up here was velocity 1, going back to the original. 100 00:06:29,264 --> 00:06:33,162 Actually, let me draw another diagram, just to clean it up. 101 00:06:33,162 --> 00:06:36,925 And also that vacuum-water interface example, I'm not enjoying it, 102 00:06:36,925 --> 00:06:40,679 just because it's a very unnatural interface to actually have in nature. 103 00:06:40,679 --> 00:06:44,767 So maybe it's vacuum and glass. That's something that actually would exist. 104 00:06:44,767 --> 00:06:51,156 So let's say we're doing that. So this isn't water, this is glass. Let me redraw it. 105 00:06:51,156 --> 00:06:53,364 And I'll draw the angles bigger. 106 00:06:53,364 --> 00:06:57,125 So let me draw a perpendicular. 107 00:06:57,125 --> 00:07:00,377 And so I have our incident ray, 108 00:07:00,377 --> 00:07:04,531 so in the vacuum 109 00:07:04,531 --> 00:07:06,869 it's traveling at v1--and in the case of a vacuum, 110 00:07:06,869 --> 00:07:09,854 it's actually going at the speed of light, or the speed of light in a vacuum, 111 00:07:09,854 --> 00:07:13,757 which is c, or 300,000 kilometers per second, 112 00:07:13,757 --> 00:07:18,536 or 300 million meters per second--let me write that-- 113 00:07:18,536 --> 00:07:21,725 so c is the speed of light in a vacuum, 114 00:07:21,725 --> 00:07:24,762 and that is equal to 300-- 115 00:07:24,762 --> 00:07:27,008 it's not exactly 300, I'm not going into significant digits-- 116 00:07:27,008 --> 00:07:31,685 this is true to three significant digits--300 million meters per second. 117 00:07:31,685 --> 00:07:34,731 This is light in a vacuum. 118 00:07:34,731 --> 00:07:39,500 Light in vacuum. And I don't mean the thing that you use to clean your carpet with, 119 00:07:39,500 --> 00:07:42,464 I mean an area of space that has nothing in it. 120 00:07:42,464 --> 00:07:45,952 No air, no gas, no molecules, nothing in it. That is a pure vacuum 121 00:07:45,952 --> 00:07:47,962 and that's how fast light will travel. 122 00:07:47,962 --> 00:07:52,715 Now it's travelling really fast there, and let's say that--and this applies to any two mediums-- 123 00:07:52,715 --> 00:07:57,577 but let's say it gets to glass here, and in glass it travels slower, 124 00:07:57,577 --> 00:08:00,875 and we know for our example, this side of the car 125 00:08:00,875 --> 00:08:02,300 is going to get to the slower medium first 126 00:08:02,300 --> 00:08:03,705 so it's going to turn in this direction. 127 00:08:03,705 --> 00:08:07,177 So it's going to go like this. 128 00:08:07,177 --> 00:08:09,264 We call this v2. 129 00:08:09,264 --> 00:08:11,029 Maybe I'll draw it--if you wanted to view these as 130 00:08:11,029 --> 00:08:13,762 vectors, maybe I should draw it as a smaller vector 131 00:08:13,762 --> 00:08:15,679 v2, just like that. 132 00:08:15,679 --> 00:08:19,685 And the angle of incidence is theta 1. 133 00:08:19,685 --> 00:08:23,952 And the angle of refraction is theta 2. 134 00:08:23,952 --> 00:08:27,479 And Snell's Law just tells us 135 00:08:27,479 --> 00:08:31,900 the ratio between v2 and the sin-- 136 00:08:31,900 --> 00:08:34,381 remember Soh Cah Toa, basic trig function-- 137 00:08:34,381 --> 00:08:37,858 and the sin of the angle of refraction 138 00:08:37,859 --> 00:08:45,331 is going to be equal to the ratio of v1 and 139 00:08:45,331 --> 00:08:49,054 the angle--the sin of the angle of incidence. 140 00:08:49,054 --> 00:08:50,936 Sin of theta 1. 141 00:08:50,936 --> 00:08:52,377 Now if this looks confusing at all, we're going to 142 00:08:52,377 --> 00:08:54,971 apply it a bunch in the next couple of videos. 143 00:08:54,971 --> 00:08:55,895 But I want to show you also that 144 00:08:55,895 --> 00:08:58,613 there's many many ways to view Snell's Law. 145 00:08:58,613 --> 00:09:01,562 You may or may not be familiar with the idea of 146 00:09:01,562 --> 00:09:03,746 an index of refraction. 147 00:09:03,746 --> 00:09:05,398 So let me write that down. 148 00:09:05,398 --> 00:09:08,115 Index of refraction. 149 00:09:08,115 --> 00:09:11,398 Index, or refraction index. 150 00:09:11,398 --> 00:09:14,771 And it's defined for any medium, for any material. 151 00:09:14,771 --> 00:09:17,438 There's an index of refraction for vacuum, for air, 152 00:09:17,438 --> 00:09:19,095 for water. 153 00:09:19,095 --> 00:09:21,233 For any material that people have measured it for. 154 00:09:21,233 --> 00:09:24,685 And they usually specify it as n. 155 00:09:24,685 --> 00:09:28,721 And it is defined as the speed of light in a vacuum 156 00:09:28,721 --> 00:09:36,377 That's c. Divided by the velocity of light in that medium. 157 00:09:36,377 --> 00:09:40,315 So in our example right here, we could rewrite this. 158 00:09:40,331 --> 00:09:43,131 We could rewrite this in terms of index of refraction. 159 00:09:43,131 --> 00:09:45,167 Let me do that actually. Just cause that's sometimes 160 00:09:45,167 --> 00:09:47,254 the more typical way of viewing Snell's Law. 161 00:09:47,254 --> 00:09:51,956 So I could solve for v here if I--one thing I could do 162 00:09:51,956 --> 00:09:54,910 is just--if n is equal to c divided by v 163 00:09:54,910 --> 00:09:58,392 then v is going to be equal to c divided by n. 164 00:09:58,392 --> 00:10:01,208 And I can multiply both sides by v 165 00:10:01,208 --> 00:10:02,492 if you don't see how I got there. 166 00:10:02,492 --> 00:10:05,423 The intermediary step is, multiply both sides times v, 167 00:10:05,423 --> 00:10:08,562 you get v times n is equal to c, and then 168 00:10:08,562 --> 00:10:10,046 you divide both sides by n, you get 169 00:10:10,046 --> 00:10:12,038 v is equal to c over n. 170 00:10:12,038 --> 00:10:16,521 So I can rewrite Snell's Law over here as 171 00:10:16,521 --> 00:10:21,552 instead of having v2 there, I could write 172 00:10:21,552 --> 00:10:23,244 instead of writing v2 there I could write 173 00:10:23,244 --> 00:10:28,382 the speed of light divided by the refraction index 174 00:10:28,382 --> 00:10:30,100 for this material right here. 175 00:10:30,100 --> 00:10:31,946 So I'll call that n2. 176 00:10:31,946 --> 00:10:36,336 Right, this is material 2, material 2 right over there. 177 00:10:36,336 --> 00:10:37,359 Right, that's the same thing as 178 00:10:37,359 --> 00:10:44,792 v2 over the sin of theta 2 179 00:10:44,792 --> 00:10:52,582 is equal to v1 is the same thing as c divided by n1 180 00:10:52,582 --> 00:10:58,085 over sin of theta 1. And then we could do a little bit 181 00:10:58,085 --> 00:11:01,238 of simplification here, we can multiple both sides of 182 00:11:01,238 --> 00:11:04,156 this equation--well, let's do a couple of things. Let's-- 183 00:11:04,156 --> 00:11:06,418 Actually, the simplest thing to do is actually 184 00:11:06,418 --> 00:11:08,543 take the reciprocal of both sides. 185 00:11:08,543 --> 00:11:09,797 So let me just do that. 186 00:11:09,797 --> 00:11:11,013 So let me take the reciprocal of both sides, 187 00:11:11,013 --> 00:11:21,500 and you get sin of theta 2 over cn2 is equal to 188 00:11:21,500 --> 00:11:30,054 sin of theta 1 over c over n1. 189 00:11:30,054 --> 00:11:31,492 And now let's multiply the numerator and 190 00:11:31,492 --> 00:11:34,623 denominator of this left side by n2. 191 00:11:34,623 --> 00:11:37,362 So if we multiply n2 over n2. 192 00:11:37,362 --> 00:11:38,077 We're not changing it, 193 00:11:38,077 --> 00:11:40,002 this is really just going to be 1, 194 00:11:40,002 --> 00:11:41,838 but this guy and this guy are going to cancel out. 195 00:11:41,838 --> 00:11:43,031 And let's do the same thing over here, 196 00:11:43,031 --> 00:11:44,438 multiply the numerator and the denominator 197 00:11:44,438 --> 00:11:48,156 by n1, so n1 over n1. 198 00:11:48,156 --> 00:11:50,136 That guy, that guy, and that guy 199 00:11:50,136 --> 00:11:51,531 are going to cancel out. 200 00:11:51,531 --> 00:12:01,664 And so we get n2 sin of theta 2 over c is equal to 201 00:12:01,664 --> 00:12:06,700 n1 sin of theta 1 over c. 202 00:12:06,700 --> 00:12:07,967 And now we can just multiply both sides 203 00:12:07,967 --> 00:12:10,982 of this equation by c and we get the form of 204 00:12:10,982 --> 00:12:13,971 Snell's Law that some books will show you, 205 00:12:13,971 --> 00:12:16,736 which is the refraction index for the slower medium, 206 00:12:16,736 --> 00:12:18,869 or for the second medium, the one that we're entering, 207 00:12:18,869 --> 00:12:23,269 times the index of the sin of the index of refraction 208 00:12:23,269 --> 00:12:24,941 is equal to 209 00:12:24,941 --> 00:12:27,279 the refraction index for the first medium 210 00:12:27,279 --> 00:12:31,956 times the sin of the angle of incidence. 211 00:12:31,956 --> 00:12:34,079 The incident angle. 212 00:12:34,079 --> 00:12:36,295 So this is another version right here 213 00:12:36,295 --> 00:12:38,440 This is another version right there of Snell's Law. 214 00:12:38,440 --> 00:12:39,956 Let me copy and paste that. 215 00:12:39,956 --> 00:12:41,613 And if this is confusing to you, 216 00:12:41,613 --> 00:12:43,267 and I'm guessing that it might be, 217 00:12:43,267 --> 00:12:45,254 especially if this is the first time you're seeing it, 218 00:12:45,254 --> 00:12:47,046 we're going to apply this in a bunch of videos, 219 00:12:47,046 --> 00:12:49,931 in the next few videos, but I really just want to make sure, 220 00:12:49,931 --> 00:12:51,479 I really just want to make sure you're comfortable with it. 221 00:12:51,479 --> 00:12:55,085 So these are both equivalent forms of Snell's Law. 222 00:12:55,085 --> 00:12:58,121 One deals with the velocities, directly deals with 223 00:12:58,121 --> 00:12:59,469 the velocities, right over here, 224 00:12:59,469 --> 00:13:02,705 the ratio of the velocity to the sin of the incident 225 00:13:02,705 --> 00:13:03,836 or refraction angle 226 00:13:03,836 --> 00:13:07,095 and here it uses the index of refraction. 227 00:13:07,095 --> 00:13:09,941 And the index of refraction really just tells you 228 00:13:09,941 --> 00:13:13,515 it's just the ratio of the speed of light to the actual velocity. 229 00:13:13,515 --> 00:13:16,833 So something where light travels really slowly 230 00:13:16,833 --> 00:13:18,556 where light travels really slowly, 231 00:13:18,556 --> 00:13:21,618 this will be a smaller number. 232 00:13:21,618 --> 00:13:22,610 And if this is a smaller number, 233 00:13:22,610 --> 00:13:23,971 this is a larger number. 234 00:13:23,971 --> 00:13:25,038 And we actually see it here. 235 00:13:25,038 --> 00:13:27,500 And you're going to see a little tidbit of the next video 236 00:13:27,500 --> 00:13:29,323 right over here. 237 00:13:29,323 --> 00:13:33,402 But here's a bunch of refraction indices 238 00:13:33,402 --> 00:13:34,548 for different materials. 239 00:13:34,548 --> 00:13:38,202 It's obviously 1 for a vacuum, because for a vacuum 240 00:13:38,202 --> 00:13:40,238 you have the refraction index is going to be c 241 00:13:40,238 --> 00:13:43,033 divided by the speed of light in that material. 242 00:13:43,033 --> 00:13:45,756 Well, in a vacuum it's traveling at c. 243 00:13:45,756 --> 00:13:47,387 So it's going to be 1. 244 00:13:47,387 --> 00:13:50,121 So that's where that came from. And you can see in air, 245 00:13:50,121 --> 00:13:52,971 the speed is only slightly smaller, 246 00:13:52,971 --> 00:13:54,998 this number's only going to be slightly smaller 247 00:13:54,998 --> 00:13:56,556 than the speed of light in a vacuum. 248 00:13:56,556 --> 00:13:59,315 So in air, it's still pretty close to a vacuum. 249 00:13:59,315 --> 00:14:03,382 But then for a diamond, it's traveling a lot slower. 250 00:14:03,382 --> 00:14:05,146 Light is travelling a lot slower in a diamond 251 00:14:05,146 --> 00:14:08,023 than it is in a vacuum. 252 00:14:08,023 --> 00:14:08,646 Anyway, I'll leave you there, 253 00:14:08,646 --> 00:14:10,408 we're going to do a couple more videos, 254 00:14:10,408 --> 00:14:12,582 we're going to do more examples using Snell's Law. 255 00:14:12,582 --> 00:14:14,990 Hopefully you got the basic idea of refraction. 256 00:14:14,990 --> 00:14:19,459 And in the next video, I'll actually use this graphic right here to help us visualize 257 00:14:19,459 --> 00:00:00,000 why it looks like the straw got bent.