1 00:00:00,090 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,030 Your support will help MIT OpenCourseWare 4 00:00:06,030 --> 00:00:10,120 continue to offer high quality educational resources for free. 5 00:00:10,120 --> 00:00:12,690 To make a donation or to view additional materials 6 00:00:12,690 --> 00:00:16,650 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,650 --> 00:00:17,550 at ocw.mit.edu. 8 00:00:21,348 --> 00:00:22,390 SE BAEK OH: Good morning. 9 00:00:22,390 --> 00:00:24,830 My name's Se Baek, and I'm a postdoc working 10 00:00:24,830 --> 00:00:26,350 with Professor Barbastathis. 11 00:00:26,350 --> 00:00:30,910 And he has a personal emergency today, so he couldn't make it. 12 00:00:30,910 --> 00:00:34,510 So actually Pepe and I will give a lecture today. 13 00:00:34,510 --> 00:00:39,550 And just for a reminder, you can turn in your first homework 14 00:00:39,550 --> 00:00:43,500 today before class or after class. 15 00:00:48,050 --> 00:00:52,950 OK, so yesterday, we talk about a bunch of different things. 16 00:00:52,950 --> 00:00:57,100 The first one we derived-- 17 00:00:57,100 --> 00:01:01,530 by the way, excuse me, we are going 18 00:01:01,530 --> 00:01:03,360 to do the same thing, same format. 19 00:01:03,360 --> 00:01:05,580 So if you have any questions, just feel free 20 00:01:05,580 --> 00:01:10,690 to interrupt and ask questions, OK? 21 00:01:10,690 --> 00:01:17,480 So the last time, we actually derived 22 00:01:17,480 --> 00:01:21,400 the ray transfer matrix for a thin lens, which 23 00:01:21,400 --> 00:01:24,760 is the spherical lens has two curvatures, the first one 24 00:01:24,760 --> 00:01:30,850 and second one, which is here, the 1 and negative 1 over f. f 25 00:01:30,850 --> 00:01:32,710 is focal length and 1, 0. 26 00:01:32,710 --> 00:01:35,210 And the focal length 1 over f, this 27 00:01:35,210 --> 00:01:37,100 actually we derived this equation, 28 00:01:37,100 --> 00:01:38,470 the [INAUDIBLE] equation. 29 00:01:38,470 --> 00:01:43,720 So if you know the reflective index and the radius curvature, 30 00:01:43,720 --> 00:01:45,490 the left side and right side, then you 31 00:01:45,490 --> 00:01:50,560 can just easily compute the focal length of your thin lens. 32 00:01:50,560 --> 00:01:55,660 Then, also, we talked about the object at infinity 33 00:01:55,660 --> 00:01:57,770 and the image at infinity. 34 00:01:57,770 --> 00:02:01,760 So for example, in this case, we have the object at infinity. 35 00:02:01,760 --> 00:02:06,010 So we have this ray is coming from the infinity. 36 00:02:06,010 --> 00:02:10,900 And we are going to have the focus point at the focal plane. 37 00:02:10,900 --> 00:02:14,380 That's the definition of the focal length and focal plane. 38 00:02:14,380 --> 00:02:18,820 And the other way, if we had the point object at focal plane, 39 00:02:18,820 --> 00:02:21,350 then we are going to have an image at infinity. 40 00:02:21,350 --> 00:02:26,630 So that's the same thing. 41 00:02:26,630 --> 00:02:29,350 And if you have the negative length, I mean, 42 00:02:29,350 --> 00:02:32,750 the focal length is negative, then we have the same thing. 43 00:02:32,750 --> 00:02:35,470 We have parallel coming in. 44 00:02:35,470 --> 00:02:37,180 In this case, it bent outside. 45 00:02:37,180 --> 00:02:40,330 But if you extract and extend, then we 46 00:02:40,330 --> 00:02:45,020 have the focal point here. 47 00:02:45,020 --> 00:02:48,730 So as you know the object and image they are conjugate. 48 00:02:48,730 --> 00:02:53,210 And in this case, [INAUDIBLE] object or image is at infinity. 49 00:02:53,210 --> 00:02:56,380 So we call it, I mean this configuration, 50 00:02:56,380 --> 00:02:58,362 as infinite conjugate. 51 00:03:04,640 --> 00:03:07,235 [INAUDIBLE], please. 52 00:03:07,235 --> 00:03:07,735 Yeah. 53 00:03:10,585 --> 00:03:15,920 Because, you know, one of them is at infinity. 54 00:03:15,920 --> 00:03:19,100 So yeah, that's what we talked about yesterday. 55 00:03:19,100 --> 00:03:22,730 And today, we're going to be talking 56 00:03:22,730 --> 00:03:24,750 about interesting topic. 57 00:03:24,750 --> 00:03:30,640 So what if we have our object or an image is at finite distance? 58 00:03:30,640 --> 00:03:32,240 It's more realistic case. 59 00:03:32,240 --> 00:03:35,180 Just like when you take a picture of your person, 60 00:03:35,180 --> 00:03:38,630 I mean, of a friend, then your friend is not 61 00:03:38,630 --> 00:03:40,890 going to be at infinity, right? 62 00:03:40,890 --> 00:03:43,200 So it's more realistic case. 63 00:03:43,200 --> 00:03:46,620 And then we'll talk about thick lens. 64 00:03:46,620 --> 00:03:51,320 Because so far, we just assume our lens is infinitely thin. 65 00:03:51,320 --> 00:03:54,800 So thick lens is more like the realistic case. 66 00:03:54,800 --> 00:03:59,720 And then the paper we'll talk about is human visual system. 67 00:04:05,930 --> 00:04:08,810 So I guess this slide is probably 68 00:04:08,810 --> 00:04:12,430 one of the most important slides of this whole course. 69 00:04:12,430 --> 00:04:16,550 Because, you know, we are dealing with the object 70 00:04:16,550 --> 00:04:18,380 and image at finite distance. 71 00:04:18,380 --> 00:04:19,769 So the situation is like this. 72 00:04:19,769 --> 00:04:24,320 We have a lens with focal length F. And in object space, 73 00:04:24,320 --> 00:04:29,300 we are given our object as some distance. 74 00:04:29,300 --> 00:04:30,890 You know, the situation's like this. 75 00:04:30,890 --> 00:04:31,940 You have a camera. 76 00:04:31,940 --> 00:04:33,850 And you take a picture of a person. 77 00:04:33,850 --> 00:04:40,070 Then where should I put my screen or detector? 78 00:04:40,070 --> 00:04:44,120 Or in the other way around, there 79 00:04:44,120 --> 00:04:47,640 must be some condition that makes the perfect image, right? 80 00:04:47,640 --> 00:04:50,600 So if you take a picture at some distance, 81 00:04:50,600 --> 00:04:55,700 then the other object which is not at that distance 82 00:04:55,700 --> 00:04:58,220 will look blurry in your final image, right? 83 00:04:58,220 --> 00:05:03,980 So we are going to find what condition should be satisfied 84 00:05:03,980 --> 00:05:08,390 here in terms of the distance in object space and focal length 85 00:05:08,390 --> 00:05:10,670 and distancing image space. 86 00:05:10,670 --> 00:05:15,950 And we're going to see what kind of image we will get 87 00:05:15,950 --> 00:05:19,170 or how big it is, OK? 88 00:05:19,170 --> 00:05:24,540 So the first one is, what is image. 89 00:05:24,540 --> 00:05:26,430 So what it image? 90 00:05:26,430 --> 00:05:30,390 So image is just replicate of an object, right? 91 00:05:30,390 --> 00:05:33,960 So in terms of this ray picture, we 92 00:05:33,960 --> 00:05:38,070 have infinite number of rays-- 93 00:05:40,709 --> 00:05:57,990 oh, sorry-- emanating from the object point. 94 00:05:57,990 --> 00:06:02,330 And if this configuration is an image configuration, which 95 00:06:02,330 --> 00:06:06,210 means you make a perfect image, then all these rays, at least 96 00:06:06,210 --> 00:06:08,400 most of them, they should be converge 97 00:06:08,400 --> 00:06:11,507 at a point in object space somewhere, right? 98 00:06:11,507 --> 00:06:12,840 So that's the image in question. 99 00:06:12,840 --> 00:06:15,540 You have bunch of ray coming from this point, 100 00:06:15,540 --> 00:06:19,810 and they should meet at one point. 101 00:06:19,810 --> 00:06:25,060 So you can draw many, many ways, but of your choice 102 00:06:25,060 --> 00:06:37,520 is just two rays here, this first ray and the second way. 103 00:06:37,520 --> 00:06:41,900 And since every ray should meet at one point in image space, 104 00:06:41,900 --> 00:06:45,890 these two ways also should meet at the same point. 105 00:06:45,890 --> 00:06:50,060 And the reason why we chose only two rays is kind of obvious, 106 00:06:50,060 --> 00:06:53,390 because we know the infinite conjugate configuration, right? 107 00:06:53,390 --> 00:07:01,840 So the first ray, the upper ray here, this ray, 108 00:07:01,840 --> 00:07:04,890 it looks like coming from the object at infinity, right? 109 00:07:04,890 --> 00:07:06,770 It's parallel to the optical axis. 110 00:07:06,770 --> 00:07:14,410 So after the lens, it should pass the focal point like this. 111 00:07:14,410 --> 00:07:17,960 And we call this point as back focal plane, 112 00:07:17,960 --> 00:07:21,610 since it is behind the lens. 113 00:07:21,610 --> 00:07:23,730 And what about the second ray here? 114 00:07:27,040 --> 00:07:32,890 So if you choose, that ray is passing through the focal point 115 00:07:32,890 --> 00:07:35,850 which is in front of the lens, we call the front focal plane, 116 00:07:35,850 --> 00:07:42,550 then at the lens it looks like coming from the focal point, 117 00:07:42,550 --> 00:07:43,050 right? 118 00:07:43,050 --> 00:07:47,110 So it should be going to the infinity. 119 00:07:47,110 --> 00:07:50,920 So it's collimated and parallel to the optical axis. 120 00:07:50,920 --> 00:07:54,860 And these two rays meet at this point. 121 00:07:54,860 --> 00:07:59,150 So that point is where you get the image. 122 00:07:59,150 --> 00:08:02,990 And the other rays, the infinite number rays, 123 00:08:02,990 --> 00:08:05,930 should meet at that point. 124 00:08:05,930 --> 00:08:11,120 So this is how we draw the configuration image. 125 00:08:11,120 --> 00:08:16,220 So we have bunch of ray and bunch of ray in image space. 126 00:08:16,220 --> 00:08:19,165 Any questions so far? 127 00:08:19,165 --> 00:08:19,665 OK. 128 00:08:27,630 --> 00:08:32,809 So to find the relation between the object distance and image 129 00:08:32,809 --> 00:08:36,390 distance, let's define two distance here. 130 00:08:36,390 --> 00:08:40,039 So first one is x0, the distance from the object 131 00:08:40,039 --> 00:08:41,970 to the front focal plane. 132 00:08:41,970 --> 00:08:46,160 And this second one is xi, so from that focal point 133 00:08:46,160 --> 00:08:47,040 to the image. 134 00:08:47,040 --> 00:08:52,040 So we are going to see how they relate to the focal length 135 00:08:52,040 --> 00:08:52,920 here. 136 00:08:52,920 --> 00:08:58,670 So first thing is we can compare it to a big triangle here. 137 00:08:58,670 --> 00:09:02,886 So the first one is-- 138 00:09:02,886 --> 00:09:13,400 oops-- this triangle OPFf and this one, BCFf. 139 00:09:19,950 --> 00:09:26,210 Since they are similar, so if you see this height of PO 140 00:09:26,210 --> 00:09:30,900 and this BC is same as h-- 141 00:09:30,900 --> 00:09:37,830 actually, they are h object over xo, so ho and xo. 142 00:09:37,830 --> 00:09:42,370 And it should be same as negative h i. 143 00:09:42,370 --> 00:09:44,670 The negative sign is because h i is negative. 144 00:09:44,670 --> 00:09:46,080 So to make the positive, you have 145 00:09:46,080 --> 00:09:48,680 to put the negative sign here. 146 00:09:48,680 --> 00:09:50,340 And this [INAUDIBLE], right? 147 00:09:50,340 --> 00:09:53,250 So you get this first relation. 148 00:09:53,250 --> 00:09:58,260 And you can compare the other triangles 149 00:09:58,260 --> 00:10:09,540 at image space, so this ACFb and IQF, this one. 150 00:10:09,540 --> 00:10:13,970 So if you do the same thing, then we have this relation. 151 00:10:13,970 --> 00:10:22,730 So QI, which is the image height, and FPQ, this is xi. 152 00:10:22,730 --> 00:10:28,430 And we have the h, the object height, over focal length. 153 00:10:28,430 --> 00:10:33,270 So we have this relation and the second relation. 154 00:10:33,270 --> 00:10:36,950 So if you combine them, we have two interesting equation here. 155 00:10:36,950 --> 00:10:40,100 The first one is h, the image of height, 156 00:10:40,100 --> 00:10:47,530 over x, or the object height, is xi over h or equal to negative 157 00:10:47,530 --> 00:10:49,640 f over xo. 158 00:10:49,640 --> 00:10:53,060 And it's also same as negative xi over f. 159 00:10:53,060 --> 00:10:55,040 Can anyone guess what this quantity 160 00:10:55,040 --> 00:11:05,480 means, So h i over ho, so image height or object height? 161 00:11:05,480 --> 00:11:05,980 Yes. 162 00:11:05,980 --> 00:11:06,920 AUDIENCE: [INAUDIBLE] 163 00:11:06,920 --> 00:11:08,045 SE BAEK OH: Right, exactly. 164 00:11:08,045 --> 00:11:10,400 AUDIENCE: [INAUDIBLE] 165 00:11:14,846 --> 00:11:17,330 SE BAEK OH: Yeah, for he said magnification. 166 00:11:17,330 --> 00:11:17,830 Yeah. 167 00:11:17,830 --> 00:11:19,460 Course, you know, this is a ratio 168 00:11:19,460 --> 00:11:22,730 of the size of the image and object. 169 00:11:22,730 --> 00:11:26,750 So actually, this term indicate the magnification 170 00:11:26,750 --> 00:11:29,120 of your imaging system, right? 171 00:11:29,120 --> 00:11:38,550 So magnification actually is defined by this, just h i 172 00:11:38,550 --> 00:11:40,170 over ho. 173 00:11:40,170 --> 00:11:45,120 If the absolute value of magnification is larger than 1, 174 00:11:45,120 --> 00:11:48,060 then you're going to get the magnified image. 175 00:11:48,060 --> 00:11:51,030 Course, the image height is bigger than object height, 176 00:11:51,030 --> 00:11:51,540 right? 177 00:11:51,540 --> 00:11:53,310 And if it is smaller than 1, we are 178 00:11:53,310 --> 00:11:57,830 going to get the smaller image, right? 179 00:11:57,830 --> 00:12:01,160 And if you combine the rest, these two equations, 180 00:12:01,160 --> 00:12:06,080 so f over x and xo and xi over f, 181 00:12:06,080 --> 00:12:09,590 then you can get this equation. 182 00:12:09,590 --> 00:12:14,180 xo times xi should be f squared. 183 00:12:14,180 --> 00:12:17,380 So xo is this distance, so object to the focal plane, 184 00:12:17,380 --> 00:12:18,740 the front focal plane. 185 00:12:18,740 --> 00:12:22,350 And xi is from that focal point to the image plane. 186 00:12:22,350 --> 00:12:27,827 So this tells you where should you put the detector 187 00:12:27,827 --> 00:12:29,660 or object to make an image condition, right? 188 00:12:29,660 --> 00:12:32,320 So they are related like this. 189 00:12:32,320 --> 00:12:37,850 So this is one of the form of the imaging condition. 190 00:12:37,850 --> 00:12:39,962 And we it Newton's form, OK? 191 00:12:44,590 --> 00:12:47,620 And sometimes it is more convenient to define 192 00:12:47,620 --> 00:12:51,080 the distance from object to the lens, not the focal plane. 193 00:12:51,080 --> 00:12:54,490 So we define two other distance, so s o, object 194 00:12:54,490 --> 00:12:59,500 distant from object to the lens, and image distance, si, 195 00:12:59,500 --> 00:13:01,780 from lens to image. 196 00:13:01,780 --> 00:13:05,120 And actually in this picture in this figure, 197 00:13:05,120 --> 00:13:11,890 we can draw another way, which is from object to the image. 198 00:13:11,890 --> 00:13:14,590 But it passed through the center of the lens, 199 00:13:14,590 --> 00:13:19,170 and it looks like just a path straight through the lens. 200 00:13:19,170 --> 00:13:20,880 And can anyone guess why? 201 00:13:28,460 --> 00:13:31,430 Because at the center of the lens, at the very center, 202 00:13:31,430 --> 00:13:34,520 the radius curvature is kind of infinite, right? 203 00:13:34,520 --> 00:13:39,450 So it just looks like just piece of flat glass. 204 00:13:39,450 --> 00:13:41,630 So if you have this piece of glass, 205 00:13:41,630 --> 00:13:44,130 then you know from the [INAUDIBLE] law 206 00:13:44,130 --> 00:13:46,540 the incident ray and the outgoing ray, 207 00:13:46,540 --> 00:13:50,150 they are parallel, right, if you have the same median here 208 00:13:50,150 --> 00:13:51,650 and here. 209 00:13:51,650 --> 00:13:54,990 And also, we are talking about the very thin lens here. 210 00:13:54,990 --> 00:13:59,360 So we don't really consider the thickness of the lens. 211 00:13:59,360 --> 00:14:05,750 So that's why it looks like just passing straight 212 00:14:05,750 --> 00:14:06,610 through the lens. 213 00:14:06,610 --> 00:14:09,980 So you can draw actually three rays here, so 214 00:14:09,980 --> 00:14:18,810 the first one, this one, and this one, and this one. 215 00:14:21,940 --> 00:14:25,640 And then you can compare two, actually, 216 00:14:25,640 --> 00:14:40,860 another big triangles, so OCA this one, and IQC, this one. 217 00:14:40,860 --> 00:14:43,940 So if you compare that triangle, then we're going to get-- 218 00:14:47,230 --> 00:14:52,370 so CA over CB, so CA [INAUDIBLE] CB, which 219 00:14:52,370 --> 00:14:57,410 is the, actually, magnification here, ho over negative h i 220 00:14:57,410 --> 00:15:03,920 should be same as this object distance and image distance. 221 00:15:03,920 --> 00:15:08,010 So this tells you, if you have the object distance and image 222 00:15:08,010 --> 00:15:10,010 distance, they are related to the magnification. 223 00:15:10,010 --> 00:15:14,420 So if your object is very far away from the lens, 224 00:15:14,420 --> 00:15:17,150 then you're going to get very small image, right? 225 00:15:17,150 --> 00:15:19,730 Because you have [INAUDIBLE]. 226 00:15:19,730 --> 00:15:22,082 So you have the very big one here, 227 00:15:22,082 --> 00:15:23,540 so you're going to get a small one. 228 00:15:23,540 --> 00:15:26,180 But if you move your object to the lens, 229 00:15:26,180 --> 00:15:28,400 then there are big change. 230 00:15:28,400 --> 00:15:31,310 You're going to get the magnified one, magnified image. 231 00:15:34,930 --> 00:15:39,460 And if you combine this equation and this relation 232 00:15:39,460 --> 00:15:43,930 and these two, then we are going to have the si over s o. 233 00:15:43,930 --> 00:15:48,160 And it's the same as f over xo. 234 00:15:48,160 --> 00:15:55,670 So xo is actually s o minus f, right, so s o minus f. 235 00:15:55,670 --> 00:15:58,230 Yeah, let me do the [INAUDIBLE],, please. 236 00:15:58,230 --> 00:16:01,690 So let me rewrite that equation. 237 00:16:01,690 --> 00:16:05,480 I just flip the numerator and denominator. 238 00:16:05,480 --> 00:16:13,780 So s o over si is same as s o minus f and f. 239 00:16:13,780 --> 00:16:17,380 And it should be same as s o over f. 240 00:16:17,380 --> 00:16:19,430 And it's minus 1, right? 241 00:16:19,430 --> 00:16:22,830 And I divide by s o here. 242 00:16:22,830 --> 00:16:26,972 So I get 1 over si should be 1 over f-- 243 00:16:26,972 --> 00:16:28,847 AUDIENCE: [INAUDIBLE] s i or [INAUDIBLE] s o, 244 00:16:28,847 --> 00:16:32,840 or so over [INAUDIBLE]? 245 00:16:32,840 --> 00:16:36,130 SE BAEK OH: No, I just flipped the numerator, denominator. 246 00:16:36,130 --> 00:16:44,450 So it was si over s o, but I wrote s o over si. 247 00:16:44,450 --> 00:16:48,370 So this one also flips, right, s o minus f over f. 248 00:16:54,840 --> 00:17:04,339 And I end up with 1 over si equal to 1 over f minus 1 249 00:17:04,339 --> 00:17:14,020 over s o, which is the final equation. 250 00:17:14,020 --> 00:17:15,460 So we call this the lens law. 251 00:17:15,460 --> 00:17:18,849 So 1 over object distance versus 1 over image distance 252 00:17:18,849 --> 00:17:20,410 should be 1 over f. 253 00:17:20,410 --> 00:17:22,859 So, yeah. 254 00:17:22,859 --> 00:17:26,670 So actually, that's the equation in most of time 255 00:17:26,670 --> 00:17:27,810 we are going to use. 256 00:17:32,301 --> 00:17:36,320 OK, so we just finished probably one 257 00:17:36,320 --> 00:17:38,240 of the most important slides. 258 00:17:38,240 --> 00:17:39,250 Any questions? 259 00:17:44,250 --> 00:17:46,590 So by using this equation, we can 260 00:17:46,590 --> 00:17:49,512 analyze different situation. 261 00:17:49,512 --> 00:17:51,720 So let's first see the four different situation here. 262 00:17:51,720 --> 00:17:54,810 We have positive lens and negative lens. 263 00:17:54,810 --> 00:17:59,550 And the upper left situation is what we just described. 264 00:17:59,550 --> 00:18:03,130 So the object distance is longer than front focal length. 265 00:18:03,130 --> 00:18:05,950 So you draw the two rays, the upper one and right one. 266 00:18:05,950 --> 00:18:08,490 And you just trace them, and they meet at one point. 267 00:18:08,490 --> 00:18:10,590 And you're going to get the image. 268 00:18:10,590 --> 00:18:12,300 And we call this one as real image, 269 00:18:12,300 --> 00:18:18,210 because all this ray MRI is departing at that point. 270 00:18:18,210 --> 00:18:20,680 They actually meet at this point. 271 00:18:20,680 --> 00:18:23,010 So if you put a screen there, then you 272 00:18:23,010 --> 00:18:25,630 can actually see those image of the object. 273 00:18:25,630 --> 00:18:27,570 So that's why we call the real image. 274 00:18:27,570 --> 00:18:29,130 And it's inverted, right? 275 00:18:29,130 --> 00:18:31,160 Because it was going up right. 276 00:18:31,160 --> 00:18:34,130 It's down right. 277 00:18:34,130 --> 00:18:37,750 And magnification is definitely small. 278 00:18:37,750 --> 00:18:40,460 It's negative, because inverted. 279 00:18:40,460 --> 00:18:45,500 And also, if you see the distance, object distance, 280 00:18:45,500 --> 00:18:48,470 this one and this one, then you can easily 281 00:18:48,470 --> 00:18:49,790 see you're going to have-- 282 00:18:53,730 --> 00:18:57,300 actually, it depends on the object distance, but yeah. 283 00:18:57,300 --> 00:19:00,720 And in terms of equation, so this s o 284 00:19:00,720 --> 00:19:03,240 is bigger than focal length, right? 285 00:19:03,240 --> 00:19:09,040 So this 1 over s o is actually smaller than 1 over f. 286 00:19:09,040 --> 00:19:12,835 So si should be positive. 287 00:19:12,835 --> 00:19:14,210 You need to add something, right? 288 00:19:14,210 --> 00:19:16,770 Because this one is smaller than this one. 289 00:19:16,770 --> 00:19:18,800 So that's why we have the si, which 290 00:19:18,800 --> 00:19:21,690 is positive distance here. 291 00:19:21,690 --> 00:19:24,080 But if you think about this situation, 292 00:19:24,080 --> 00:19:28,180 so object distance now is smaller than focal length. 293 00:19:28,180 --> 00:19:31,610 It's closer than the front focal plane. 294 00:19:31,610 --> 00:19:36,580 Then you can still draw these two rays. 295 00:19:40,080 --> 00:19:42,300 One is parallel to the optical axis. 296 00:19:42,300 --> 00:19:45,890 And the other one is passing through the front focal plane. 297 00:19:45,890 --> 00:19:47,600 But after the lens, actually they 298 00:19:47,600 --> 00:19:50,660 don't meet, because they are diverging. 299 00:19:50,660 --> 00:19:54,140 So if you back trace, then they actually 300 00:19:54,140 --> 00:19:56,570 meet in front of the lens. 301 00:19:56,570 --> 00:20:00,050 So we call this as a virtual image, 302 00:20:00,050 --> 00:20:03,390 because it looks like coming from that point. 303 00:20:03,390 --> 00:20:05,380 But if you put a screen there, the-- 304 00:20:08,026 --> 00:20:08,970 just a second. 305 00:20:08,970 --> 00:20:12,010 So [INAUDIBLE],, I'm not using the [INAUDIBLE] right now. 306 00:20:12,010 --> 00:20:15,600 So OK, thanks. 307 00:20:15,600 --> 00:20:20,300 So if you put the screen there, then you don't really 308 00:20:20,300 --> 00:20:21,520 see the actual image. 309 00:20:21,520 --> 00:20:26,250 It just looks like these two rays behind the lens, 310 00:20:26,250 --> 00:20:28,510 they look coming from this point. 311 00:20:28,510 --> 00:20:31,340 So that's the definition of the virtual image. 312 00:20:31,340 --> 00:20:35,200 And as you can see here, we have the erect image. 313 00:20:35,200 --> 00:20:37,280 And it's bigger than the original object, 314 00:20:37,280 --> 00:20:38,330 which is green. 315 00:20:38,330 --> 00:20:41,570 So magnification is bigger than 1. 316 00:20:41,570 --> 00:20:46,280 In terms of the equation, so now s o is smaller than f. 317 00:20:46,280 --> 00:20:50,500 So 1 over s o is actually bigger than 1 over f, right? 318 00:20:50,500 --> 00:20:53,160 So actually this guy should be negative, 319 00:20:53,160 --> 00:20:57,200 which means si also should be negative, 320 00:20:57,200 --> 00:21:00,590 which indicate your image distance is negative. 321 00:21:00,590 --> 00:21:03,330 So you are going to have the image in front of your lens, 322 00:21:03,330 --> 00:21:03,830 right? 323 00:21:07,050 --> 00:21:12,010 And the negative lens, we have the negative focal length here. 324 00:21:12,010 --> 00:21:14,160 So that's why the front focal plane is actually 325 00:21:14,160 --> 00:21:16,830 behind the lens, not in front of the lens. 326 00:21:16,830 --> 00:21:21,150 So you can still draw these two rays, but they don't meet. 327 00:21:21,150 --> 00:21:24,000 They make a virtual image in front of the lens. 328 00:21:24,000 --> 00:21:28,890 And we have the virtual and erect image and magnification. 329 00:21:28,890 --> 00:21:31,080 We get actually the smaller image. 330 00:21:31,080 --> 00:21:33,240 And if you do the same thing here, 331 00:21:33,240 --> 00:21:34,890 we are going to get the virtual, erect. 332 00:21:34,890 --> 00:21:37,550 And it's also smaller image. 333 00:21:43,560 --> 00:21:47,370 OK, so, so far, we just talk about the thin lens 334 00:21:47,370 --> 00:21:51,010 and how they make the image-- 335 00:21:51,010 --> 00:21:56,490 sorry, Pepe will pass around the convex lens, 336 00:21:56,490 --> 00:22:01,190 which was the upper case. 337 00:22:01,190 --> 00:22:04,060 So if you move your screen or eyes, 338 00:22:04,060 --> 00:22:07,520 then you can see actually it was inverted, but it's erect. 339 00:22:07,520 --> 00:22:10,660 So you have to see the flipped image, right? 340 00:22:10,660 --> 00:22:12,380 So he's going to pass around. 341 00:22:12,380 --> 00:22:16,050 GUEST SPEAKER: So one way to do it is just look at the lens, 342 00:22:16,050 --> 00:22:19,410 look at your notebook. 343 00:22:19,410 --> 00:22:22,630 And you can have it just at the right distance, 344 00:22:22,630 --> 00:22:25,870 the image would look inverted and floating 345 00:22:25,870 --> 00:22:29,290 on top of the lens, which is the real image. 346 00:22:29,290 --> 00:22:31,510 And if you put it closer, which means that now we 347 00:22:31,510 --> 00:22:33,400 have the second case there, the image 348 00:22:33,400 --> 00:22:36,540 will be erect, so not inverted anymore, 349 00:22:36,540 --> 00:22:38,860 and would look behind the lens, right? 350 00:22:38,860 --> 00:22:41,205 So it's actually pretty dramatic, the change. 351 00:22:41,205 --> 00:22:41,920 SE BAEK OH: Yeah. 352 00:22:41,920 --> 00:22:45,730 Actually, the upper right configuration is the exact same 353 00:22:45,730 --> 00:22:46,850 from as magnifier. 354 00:22:46,850 --> 00:22:51,820 So you know, magnifier that detective are using? 355 00:22:58,650 --> 00:23:02,280 Yeah, So the next question is, what if we have multiple lenses 356 00:23:02,280 --> 00:23:03,930 like this, this case? 357 00:23:03,930 --> 00:23:06,750 So here we have two lenses. 358 00:23:06,750 --> 00:23:08,830 Each one has a focal length of 10. 359 00:23:08,830 --> 00:23:10,590 So let's say unit is a millimeter. 360 00:23:10,590 --> 00:23:14,190 So the focal length, is just 10 millimeter, 10 millimeter. 361 00:23:14,190 --> 00:23:16,740 And the gap between the lens is 5 millimeter. 362 00:23:16,740 --> 00:23:19,650 And we are given an object, which 363 00:23:19,650 --> 00:23:23,490 is the distance from the object to the first lens is just 5 364 00:23:23,490 --> 00:23:24,380 millimeter. 365 00:23:24,380 --> 00:23:28,470 And we want to find what kind of image we get 366 00:23:28,470 --> 00:23:33,220 and where it is at somewhere around here. 367 00:23:33,220 --> 00:23:36,590 So can anyone guess how to do it? 368 00:23:36,590 --> 00:23:39,690 Because we just talk about a single lens, 369 00:23:39,690 --> 00:23:41,590 but what if we have the multiple lens? 370 00:23:52,080 --> 00:23:52,815 No one? 371 00:23:52,815 --> 00:23:55,930 So actually the answer is pretty straightforward. 372 00:23:55,930 --> 00:23:59,160 So you just cascade, which means your first [INAUDIBLE] 373 00:23:59,160 --> 00:24:00,030 the first lens. 374 00:24:00,030 --> 00:24:02,910 So you just find the image of the object 375 00:24:02,910 --> 00:24:04,080 through the first lens. 376 00:24:04,080 --> 00:24:08,880 And that image becomes the object to the second lens. 377 00:24:08,880 --> 00:24:11,680 And do the same thing to find the image. 378 00:24:11,680 --> 00:24:13,380 And if you have more lens, you just 379 00:24:13,380 --> 00:24:15,330 repeat the same process, OK? 380 00:24:15,330 --> 00:24:17,790 So let's first try it. 381 00:24:17,790 --> 00:24:22,080 So here I just neglect the second lens. 382 00:24:22,080 --> 00:24:25,603 I only have the first lens, which has the object distance 5 383 00:24:25,603 --> 00:24:26,860 millimeter. 384 00:24:26,860 --> 00:24:28,390 And the focal length is 10. 385 00:24:28,390 --> 00:24:32,220 So I can draw the two or three rays to find the image. 386 00:24:32,220 --> 00:24:36,220 But to be precise, I just plug into equation. 387 00:24:36,220 --> 00:24:39,120 So 1 over 5, which is this distance, 388 00:24:39,120 --> 00:24:41,715 the 5 is this distance. 389 00:24:41,715 --> 00:24:44,650 We want to find the image distance. 390 00:24:44,650 --> 00:24:47,490 If it is positive, then we are going to get real image. 391 00:24:47,490 --> 00:24:49,210 But if it is negative, then we are going 392 00:24:49,210 --> 00:24:51,090 to get the virtual image here. 393 00:24:51,090 --> 00:24:52,980 And it should be 1 over 10, which 394 00:24:52,980 --> 00:24:54,530 is the focal length, right? 395 00:24:54,530 --> 00:24:58,140 And it turns out that this s prime, this image distance, is 396 00:24:58,140 --> 00:25:04,210 actually negative 10, which means 397 00:25:04,210 --> 00:25:08,050 we have the negative image, which is in front of the lens. 398 00:25:08,050 --> 00:25:10,060 This distance is 10 millimeter. 399 00:25:10,060 --> 00:25:13,400 And if you compare the magnification, which 400 00:25:13,400 --> 00:25:16,600 is defined by the object distance and image distance, 401 00:25:16,600 --> 00:25:19,070 so it's negative, there is a negative side. 402 00:25:19,070 --> 00:25:23,680 So negative, negative, negative 10 over 5 is actually 2. 403 00:25:23,680 --> 00:25:28,990 So we have a erect virtual image which 404 00:25:28,990 --> 00:25:31,410 is twice larger than original image. 405 00:25:31,410 --> 00:25:34,240 This is the first lens. 406 00:25:34,240 --> 00:25:39,580 And this image is now an object to the second lens. 407 00:25:39,580 --> 00:25:42,840 So we had the virtual image here, 408 00:25:42,840 --> 00:25:46,250 which was the 10 millimeter in front of the lens. 409 00:25:46,250 --> 00:25:48,040 But if you only think about second lens, 410 00:25:48,040 --> 00:25:52,600 then this object distance should be 15 millimeter, right? 411 00:25:52,600 --> 00:25:53,950 So if you do the same thing. 412 00:25:57,100 --> 00:26:00,860 so now we have the 1 over 15 from here to here. 413 00:26:00,860 --> 00:26:04,300 And we want to find the image distance. 414 00:26:04,300 --> 00:26:09,540 1 over s prime should be 1 over 10, 415 00:26:09,540 --> 00:26:18,070 which is just positive 30 millimeter. 416 00:26:18,070 --> 00:26:22,110 So after 30 millimeter, we are going to have the real image. 417 00:26:22,110 --> 00:26:24,000 And if you compare the magnification 418 00:26:24,000 --> 00:26:27,880 of the second lens, then it's negative 30 over 15. 419 00:26:27,880 --> 00:26:29,400 So we have the negative 2. 420 00:26:29,400 --> 00:26:35,340 So we have the real image here, which is inverted one. 421 00:26:35,340 --> 00:26:37,840 And that is twice larger than this virtual-- 422 00:26:37,840 --> 00:26:39,570 I mean, the object of the second image. 423 00:26:43,440 --> 00:26:47,670 Because, actually, we initially had two lens like this. 424 00:26:47,670 --> 00:26:50,790 So the overall magnification is just multiplication 425 00:26:50,790 --> 00:26:52,380 of individual magnification. 426 00:26:52,380 --> 00:26:55,530 So first one was positive 2. 427 00:26:55,530 --> 00:26:56,820 And this is negative 2. 428 00:26:56,820 --> 00:27:00,000 So the final magnification is minus 4. 429 00:27:00,000 --> 00:27:04,490 So the answer to the question is we 430 00:27:04,490 --> 00:27:08,550 are going to have the inverted real image 431 00:27:08,550 --> 00:27:11,800 behind the second lens, which is 30 432 00:27:11,800 --> 00:27:13,760 millimeter behind the second lens, 433 00:27:13,760 --> 00:27:17,970 and which is 4 times larger than the original object. 434 00:27:21,510 --> 00:27:24,150 So if you have fewer lens, like 2 or 3, 435 00:27:24,150 --> 00:27:26,440 then this approach is pretty straightforward, right? 436 00:27:26,440 --> 00:27:28,140 We just consider one by one. 437 00:27:28,140 --> 00:27:30,450 And just apply the lens law, and you're 438 00:27:30,450 --> 00:27:32,010 going to get the right answer. 439 00:27:38,497 --> 00:27:40,500 OK. 440 00:27:40,500 --> 00:27:44,120 So the previous slide we just derived 441 00:27:44,120 --> 00:27:48,080 the imaging condition, which was the xo times xi 442 00:27:48,080 --> 00:27:53,450 should be x squared or 1 over s o plus 1 over si is 1 over f. 443 00:27:53,450 --> 00:27:57,260 We just derived those equations from the geometry, right? 444 00:27:57,260 --> 00:27:59,540 We just compared the few triangles 445 00:27:59,540 --> 00:28:03,590 and get the final equations. 446 00:28:03,590 --> 00:28:07,640 Well, I can do the same thing with the ray matrix transform. 447 00:28:07,640 --> 00:28:11,600 So let me do [INAUDIBLE],, please. 448 00:28:19,720 --> 00:28:24,690 So the way you do it, in the ray transfer matrix, 449 00:28:24,690 --> 00:28:30,300 you first define the angle and height in object space 450 00:28:30,300 --> 00:28:31,050 and image, right? 451 00:28:31,050 --> 00:28:37,740 So here I have alpha i and xi, which 452 00:28:37,740 --> 00:28:44,560 is this angle and the height of the image, h i actually. 453 00:28:49,300 --> 00:28:55,300 And the input was xo and ho. 454 00:28:55,300 --> 00:28:59,765 It's just this angle and this height. 455 00:28:59,765 --> 00:29:03,780 This ray is propagating from left to right, 456 00:29:03,780 --> 00:29:08,000 but I write the metrics from right to left, right? 457 00:29:08,000 --> 00:29:11,990 So first thing is the propagation from here to here, 458 00:29:11,990 --> 00:29:15,000 which is the distance by s o. 459 00:29:15,000 --> 00:29:25,700 So the first matrix should be 1 0, s 1, am I right? 460 00:29:28,470 --> 00:29:34,790 Oh, as oh Yes so we just first consider from here to here. 461 00:29:34,790 --> 00:29:37,580 And then you have the lens, which we just 462 00:29:37,580 --> 00:29:46,360 derived last time, which was 1 negative 1 over f, 0 and 1. 463 00:29:46,360 --> 00:29:51,980 And the next one is from here to here, the same propagation. 464 00:29:51,980 --> 00:29:58,290 So we have 1 0, si 1. 465 00:29:58,290 --> 00:30:01,080 So this is the matrix formulation in this case. 466 00:30:06,580 --> 00:30:10,620 So if I compute these matrices, then 467 00:30:10,620 --> 00:30:13,440 actually I get this equation. 468 00:30:19,050 --> 00:30:35,766 So let me write s o f si plus s o minus si s o f 1 over f, 469 00:30:35,766 --> 00:30:39,526 1 minus i over f ho. 470 00:30:43,240 --> 00:30:51,840 So can you explain the imaging condition from this matrix? 471 00:30:51,840 --> 00:30:56,040 So we just derived the relation between angle and height 472 00:30:56,040 --> 00:30:59,730 in object, for the angle and height in image. 473 00:30:59,730 --> 00:31:02,050 And we have the transfer matrix here. 474 00:31:02,050 --> 00:31:05,070 So what's the imaging condition in this case? 475 00:31:14,437 --> 00:31:16,800 So let's go back to the first [INAUDIBLE].. 476 00:31:16,800 --> 00:31:18,400 So what is the image? 477 00:31:18,400 --> 00:31:23,700 So we have a bunch of rays starting from the object point. 478 00:31:23,700 --> 00:31:27,540 And then all they arrive at the same point in the image, right? 479 00:31:27,540 --> 00:31:34,200 So if you just think about the h i and ho here, so at that point 480 00:31:34,200 --> 00:31:37,560 all these rays have the same height, ho. 481 00:31:37,560 --> 00:31:41,940 But they have different alpha o, these guys, right? 482 00:31:41,940 --> 00:31:46,770 But the image aside, the same thing, all these rays 483 00:31:46,770 --> 00:31:48,690 they have the same height, h i. 484 00:31:48,690 --> 00:31:52,250 But they have a different angle, alpha i. 485 00:31:52,250 --> 00:31:56,220 So if you just compare the h i and ho, 486 00:31:56,220 --> 00:31:58,650 you know, those rays, even though they 487 00:31:58,650 --> 00:32:01,200 have different angles, but they have the same height, 488 00:32:01,200 --> 00:32:11,740 which means actually this h i should 489 00:32:11,740 --> 00:32:15,090 be independent from alpha 0. 490 00:32:15,090 --> 00:32:22,590 Because no matter how they depart at that point, 491 00:32:22,590 --> 00:32:24,497 they have the same height here, right? 492 00:32:27,120 --> 00:32:31,820 So the answer is actually this term, 493 00:32:31,820 --> 00:32:35,960 because this is alpha i and h i. 494 00:32:35,960 --> 00:32:38,920 So this term should be 0. 495 00:32:38,920 --> 00:32:42,860 Because as I just described, h i should 496 00:32:42,860 --> 00:32:48,470 be independent on alpha object, right? 497 00:32:48,470 --> 00:32:52,460 So if I do the math, then this is 1 over-- 498 00:32:52,460 --> 00:32:54,920 I just divide by s o and si. 499 00:32:54,920 --> 00:33:00,430 So this one is 1 over s o plus 1 over si minus 1 over f. 500 00:33:00,430 --> 00:33:07,470 It should be 0, which is, again, the lens law. 501 00:33:13,950 --> 00:33:17,770 Yeah, so that's the [INAUDIBLE] I described. 502 00:33:17,770 --> 00:33:27,620 And if I plug in this equation in this matrix, 503 00:33:27,620 --> 00:33:33,740 finally I get these matrices So if I continue at this occasion 504 00:33:33,740 --> 00:33:43,010 then minus x over F1 of them zero minus x I 505 00:33:43,010 --> 00:33:52,350 over f OK so the upper right on is 506 00:33:52,350 --> 00:33:55,650 we still have a negative on about f 507 00:33:55,650 --> 00:33:59,130 which is our last power or optical power 508 00:33:59,130 --> 00:34:03,710 and what is this time the upper limit 509 00:34:03,710 --> 00:34:14,500 Yeah this the last time negative x I over f anyone 510 00:34:14,500 --> 00:34:16,576 and there It's easy one. 511 00:34:21,091 --> 00:34:22,133 Press the button, please. 512 00:34:24,550 --> 00:34:25,550 AUDIENCE: Magnification? 513 00:34:25,550 --> 00:34:26,449 SE BAEK OH: Yes. 514 00:34:26,449 --> 00:34:29,510 Since this time is 0, so if you think about the second row 515 00:34:29,510 --> 00:34:34,850 here, then you have the h i is just this guy 516 00:34:34,850 --> 00:34:36,580 multiplied by ho, right? 517 00:34:39,560 --> 00:34:42,480 So if you just think about the second element here, 518 00:34:42,480 --> 00:34:50,020 then h i is negative xi over f, which is ho or object height. 519 00:34:50,020 --> 00:34:52,889 So this time actually tells you the relation 520 00:34:52,889 --> 00:34:56,100 between the object height and image height, 521 00:34:56,100 --> 00:34:58,516 which is the magnification. 522 00:34:58,516 --> 00:35:00,860 So I should say the lateral magnification, 523 00:35:00,860 --> 00:35:02,540 because we are talking about the size. 524 00:35:02,540 --> 00:35:04,570 So this term is magnification. 525 00:35:04,570 --> 00:35:13,160 And it turns out that the upper left term, this term, we 526 00:35:13,160 --> 00:35:14,780 call the angular magnification. 527 00:35:14,780 --> 00:35:19,250 Because there is related with the alpha i and alpha o. 528 00:35:19,250 --> 00:35:22,070 To be more precise, actually angular magnification 529 00:35:22,070 --> 00:35:26,510 is defined by the ratio of change 530 00:35:26,510 --> 00:35:30,210 in the image angle and object angle. 531 00:35:30,210 --> 00:35:34,520 And if you do the math, then we finally get this term, 532 00:35:34,520 --> 00:35:36,770 negative xo over f. 533 00:35:36,770 --> 00:35:41,970 And it turns out that the angular magnification is 534 00:35:41,970 --> 00:35:44,286 1 over lateral magnification. 535 00:35:53,230 --> 00:35:53,780 Yes. 536 00:35:53,780 --> 00:35:58,310 AUDIENCE: Yeah, what's the idea of angular magnification? 537 00:35:58,310 --> 00:36:00,530 We understand that lateral magnification means 538 00:36:00,530 --> 00:36:03,086 how much the object is scaled. 539 00:36:03,086 --> 00:36:04,310 Yes. 540 00:36:04,310 --> 00:36:09,730 But in the case of imaging, what does it mean? 541 00:36:09,730 --> 00:36:11,700 SE BAEK OH: That's actually a good question. 542 00:36:11,700 --> 00:36:14,858 So actually, if you see the definition of the angular 543 00:36:14,858 --> 00:36:17,150 magnification, it's actually there is the delta, right? 544 00:36:17,150 --> 00:36:23,060 So this delta alpha change in image angle 545 00:36:23,060 --> 00:36:27,740 over change in object angle, which means let's 546 00:36:27,740 --> 00:36:30,420 think about us those rays here and here. 547 00:36:30,420 --> 00:36:34,610 So you have the ray angle in object space 548 00:36:34,610 --> 00:36:36,650 and another ray in image space. 549 00:36:36,650 --> 00:36:39,230 If you change this angle in object space, 550 00:36:39,230 --> 00:36:43,120 then you're going to also change the angle in ray, 551 00:36:43,120 --> 00:36:45,720 I mean in this side, the image space. 552 00:36:45,720 --> 00:36:47,690 So actually, angular magnification 553 00:36:47,690 --> 00:36:49,740 tells you how they are related. 554 00:36:49,740 --> 00:36:57,140 So if you change this much, then what do you get in this side? 555 00:36:57,140 --> 00:37:00,840 How much change you get in image space? 556 00:37:00,840 --> 00:37:04,160 So I guess that's the proper interpretation 557 00:37:04,160 --> 00:37:07,155 of angular magnification. 558 00:37:07,155 --> 00:37:08,530 It's the answer to your question? 559 00:37:14,362 --> 00:37:15,320 AUDIENCE: Yeah, thanks. 560 00:37:15,320 --> 00:37:16,028 SE BAEK OH: Yeah. 561 00:37:16,028 --> 00:37:18,920 AUDIENCE: And does it relate to numerical aperture 562 00:37:18,920 --> 00:37:19,820 in some sense? 563 00:37:23,530 --> 00:37:24,292 SE BAEK OH: Sure. 564 00:37:24,292 --> 00:37:25,750 Actually, the angular magnification 565 00:37:25,750 --> 00:37:29,900 is xo over f, right? 566 00:37:29,900 --> 00:37:30,790 AUDIENCE: Yeah. 567 00:37:30,790 --> 00:37:32,200 SE BAEK OH: Not really. 568 00:37:32,200 --> 00:37:35,080 Yeah, it just depend on the-- 569 00:37:35,080 --> 00:37:37,600 you know, in this case we don't have the notion 570 00:37:37,600 --> 00:37:39,020 of the size of the lens here. 571 00:37:39,020 --> 00:37:39,290 AUDIENCE: Yeah. 572 00:37:39,290 --> 00:37:40,623 SE BAEK OH: So it's not related. 573 00:37:40,623 --> 00:37:41,660 Yeah. 574 00:37:41,660 --> 00:37:42,670 AUDIENCE: Yeah, thanks. 575 00:37:45,220 --> 00:37:46,470 SE BAEK OH: Any more question? 576 00:37:52,720 --> 00:37:55,922 I'm supposed to go very slowly, but there's no questions. 577 00:38:02,240 --> 00:38:09,470 Then let's talk about the next topic, so thick lens. 578 00:38:09,470 --> 00:38:11,860 So, so far, we just think about just thin lens. 579 00:38:11,860 --> 00:38:15,490 All these were ray transfer matrices or imaging condition. 580 00:38:15,490 --> 00:38:18,880 We just consider the thin lens, which has the two curvature. 581 00:38:18,880 --> 00:38:23,210 But we didn't really account for the thickness of the lens. 582 00:38:23,210 --> 00:38:28,080 But if you think about the real lens we've just seen, 583 00:38:28,080 --> 00:38:31,390 the biconvex lens, actually they have finite thickness, 584 00:38:31,390 --> 00:38:32,090 like this. 585 00:38:32,090 --> 00:38:34,720 So you have the first surface and second surface, 586 00:38:34,720 --> 00:38:36,830 but it has the finite thickness. 587 00:38:36,830 --> 00:38:41,110 So what is the more accurate or, I should say, 588 00:38:41,110 --> 00:38:46,615 more rigorous way to model, to make a model for this lens? 589 00:38:46,615 --> 00:38:48,880 This answer is obvious, right? 590 00:38:48,880 --> 00:38:53,680 So you just first take the refraction at first surface 591 00:38:53,680 --> 00:38:58,360 and just propagate the array inside the glass, right? 592 00:38:58,360 --> 00:39:01,060 And then take the second refraction 593 00:39:01,060 --> 00:39:02,620 at this second surface. 594 00:39:02,620 --> 00:39:08,420 So that's, you know, the proper way to describe. 595 00:39:08,420 --> 00:39:10,800 So I can do the ray transfer matrix here. 596 00:39:13,720 --> 00:39:16,480 Yeah. 597 00:39:16,480 --> 00:39:19,540 So we start with the alpha 1 and x1, 598 00:39:19,540 --> 00:39:24,430 which is the angle and height in left side and alpha 2 and x2. 599 00:39:27,470 --> 00:39:34,320 So it's alpha 2 and x2 and alpha 1 and x1. 600 00:39:34,320 --> 00:39:38,010 And the first matrix should be the refraction 601 00:39:38,010 --> 00:39:40,110 at this first surface. 602 00:39:40,110 --> 00:39:54,800 So it should be one negative left to right and R1 1 0. 603 00:39:54,800 --> 00:39:58,490 By the way, is R1 positive or negative? 604 00:39:58,490 --> 00:40:00,672 So R1 is the curvature, radius of 605 00:40:00,672 --> 00:40:01,880 curvature this first surface. 606 00:40:05,770 --> 00:40:07,160 We talked about that last time. 607 00:40:07,160 --> 00:40:10,740 If the center of the radius curvature is that way, I mean, 608 00:40:10,740 --> 00:40:14,285 which is the positive way, then this radius curvature 609 00:40:14,285 --> 00:40:16,410 is positive. 610 00:40:16,410 --> 00:40:18,740 So actually R1 is positive. 611 00:40:18,740 --> 00:40:23,180 And next matrix should be propagation from first surface 612 00:40:23,180 --> 00:40:32,730 to the second surface, which is 1 0 d over n. 613 00:40:32,730 --> 00:40:36,130 So don't forget n in denominator, because it's not 614 00:40:36,130 --> 00:40:36,930 [INAUDIBLE]. 615 00:40:36,930 --> 00:40:42,130 The ray is propagating inside the glass. 616 00:40:42,130 --> 00:40:54,180 And the last matrix should be 1 and minus negative R 617 00:40:54,180 --> 00:41:00,330 left to right and radius curvature 1 0. 618 00:41:00,330 --> 00:41:05,480 So these three matrices describe this thick lens, right? 619 00:41:05,480 --> 00:41:10,130 So we just consider the two reflection and the propagation 620 00:41:10,130 --> 00:41:12,930 through the glass. 621 00:41:12,930 --> 00:41:15,590 And if I compute these matrices, then I 622 00:41:15,590 --> 00:41:22,710 get then actually M21 M22. 623 00:41:27,670 --> 00:41:32,944 So I'll get the four different elements, right, which is-- 624 00:41:32,944 --> 00:41:35,940 AUDIENCE: [INAUDIBLE] 625 00:41:36,260 --> 00:41:38,760 SE BAEK OH: So actually if you compute those three matrices, 626 00:41:38,760 --> 00:41:39,540 I get this one. 627 00:41:39,540 --> 00:41:43,230 But I just symbolize M11, and M12, and-- 628 00:41:43,230 --> 00:41:46,368 AUDIENCE: [INAUDIBLE] 629 00:41:46,753 --> 00:41:47,670 SE BAEK OH: Which one? 630 00:41:47,670 --> 00:41:49,265 AUDIENCE: [INAUDIBLE] 631 00:41:49,265 --> 00:41:50,140 SE BAEK OH: d over n. 632 00:41:50,140 --> 00:41:50,980 AUDIENCE: d over n. 633 00:41:50,980 --> 00:41:51,688 SE BAEK OH: Yeah. 634 00:41:51,688 --> 00:41:55,150 Because distance is d, but the reflective [INAUDIBLE] is n. 635 00:41:55,150 --> 00:41:56,930 So you need to divide by n. 636 00:42:15,870 --> 00:42:18,740 Because, previously, we had the thin lens, 637 00:42:18,740 --> 00:42:25,730 which is just thin lens like this and incoming ray. 638 00:42:25,730 --> 00:42:30,960 They converge at point like this. 639 00:42:30,960 --> 00:42:34,350 And this was focal length, right? 640 00:42:34,350 --> 00:42:37,830 And the ray transfer matrix for this thin lens 641 00:42:37,830 --> 00:42:43,980 was 1 negative 1 over f, 0 and 1, right? 642 00:42:43,980 --> 00:42:45,970 So we get the-- 643 00:42:45,970 --> 00:42:46,470 yes? 644 00:42:46,470 --> 00:42:49,470 AUDIENCE: [INAUDIBLE] 645 00:42:55,193 --> 00:42:56,110 SE BAEK OH: Oh, where? 646 00:43:01,302 --> 00:43:02,730 Oh. 647 00:43:02,730 --> 00:43:03,727 [INAUDIBLE] 648 00:43:07,840 --> 00:43:10,970 I'm sorry, yes. 649 00:43:10,970 --> 00:43:17,710 All right, so it should be n minus 1 and 1 minus n. 650 00:43:17,710 --> 00:43:21,240 Yeah, it's confusing. 651 00:43:21,240 --> 00:43:25,675 Actually, the way I remember is the reflective index 652 00:43:25,675 --> 00:43:28,960 at left side minus the reflective index right side. 653 00:43:28,960 --> 00:43:31,410 But there was negative sign, so yeah. 654 00:43:31,410 --> 00:43:32,160 I got [INAUDIBLE]. 655 00:43:32,160 --> 00:43:32,890 Yeah. 656 00:43:32,890 --> 00:43:33,390 Thank you. 657 00:43:37,920 --> 00:43:39,460 Sorry. 658 00:43:39,460 --> 00:43:40,490 Yeah. 659 00:43:40,490 --> 00:43:42,650 So what I was going to talk about 660 00:43:42,650 --> 00:43:45,500 is if we have the thin lens, then 661 00:43:45,500 --> 00:43:50,570 the ray transfer matrix it was the 1 negative 1 over f 662 00:43:50,570 --> 00:43:51,590 and 1 0. 663 00:43:51,590 --> 00:43:53,270 But now, we have the thick lens. 664 00:43:53,270 --> 00:43:56,230 That's why we have complicated these four terms. 665 00:43:56,230 --> 00:43:58,340 But we get the same analogy of distance, 666 00:43:58,340 --> 00:44:01,300 because distance describe how much ray 667 00:44:01,300 --> 00:44:04,320 bend, right, the optical power or lens power. 668 00:44:04,320 --> 00:44:06,470 So we get the same thing here, which 669 00:44:06,470 --> 00:44:16,480 is actually this complicated term, this term. 670 00:44:16,480 --> 00:44:21,310 And since it is a thick lens, we define a new quantity which 671 00:44:21,310 --> 00:44:23,500 is effective focal length. 672 00:44:23,500 --> 00:44:29,530 So we consider that is a single quantity which was negative 1 673 00:44:29,530 --> 00:44:31,240 over effective focal length. 674 00:44:31,240 --> 00:44:33,070 So effective focal length is actually 675 00:44:33,070 --> 00:44:38,710 the quantity inside the bracket, so n minus 1 and 1 676 00:44:38,710 --> 00:44:40,840 over R1 minus 1 over R2. 677 00:44:40,840 --> 00:44:42,200 And we have extra term. 678 00:44:42,200 --> 00:44:46,190 So what is this term, the n minus 1 and 1 over R1 minus 1 679 00:44:46,190 --> 00:44:46,690 over R2? 680 00:44:57,110 --> 00:44:57,670 Yeah. 681 00:44:57,670 --> 00:44:59,760 Actually, that's what I described 682 00:44:59,760 --> 00:45:01,560 at the very first slide, right? 683 00:45:01,560 --> 00:45:04,860 So that's the lens maker's equation. 684 00:45:04,860 --> 00:45:07,340 So focal length of thin lens and you 685 00:45:07,340 --> 00:45:09,990 can compute the focal length from the reflective index 686 00:45:09,990 --> 00:45:11,550 and radius curvature, right? 687 00:45:11,550 --> 00:45:13,320 But now we have thick lens, so we 688 00:45:13,320 --> 00:45:16,360 have extra term, this function of the d, 689 00:45:16,360 --> 00:45:18,420 the distance from the first and second surface. 690 00:45:21,970 --> 00:45:25,210 So if you consider a thick lens, then the effective focal length 691 00:45:25,210 --> 00:45:27,267 is not same as the focal length, right? 692 00:45:30,250 --> 00:45:31,290 So we just find the-- 693 00:45:31,290 --> 00:45:33,820 AUDIENCE: Where is the focal length measured from? 694 00:45:33,820 --> 00:45:34,730 Is it from the middle of the lens? 695 00:45:34,730 --> 00:45:36,440 SE BAEK OH: That's what I was going to talk about, yeah. 696 00:45:36,440 --> 00:45:37,170 AUDIENCE: OK. 697 00:45:37,170 --> 00:45:39,420 SE BAEK OH: So we just find the effective focal length 698 00:45:39,420 --> 00:45:40,350 of the thick lens. 699 00:45:40,350 --> 00:45:45,730 But, yeah, the exactly, where the focus will be? 700 00:45:45,730 --> 00:45:47,550 That's the next question, right? 701 00:45:47,550 --> 00:45:50,760 Because we didn't define any planes yet. 702 00:45:50,760 --> 00:45:53,460 So let's think about it. 703 00:45:53,460 --> 00:45:55,650 So first one is back focal plane. 704 00:45:55,650 --> 00:45:59,250 So we have an object at infinity. 705 00:45:59,250 --> 00:46:02,550 And so we have the ray parallel to the optical axis. 706 00:46:02,550 --> 00:46:06,150 And they bend twice, here and here. 707 00:46:06,150 --> 00:46:09,360 And finally, they want to make our focus at here. 708 00:46:09,360 --> 00:46:11,100 So this is focal plane. 709 00:46:11,100 --> 00:46:15,470 And we can define the focal length from this point, OK? 710 00:46:19,590 --> 00:46:21,230 To find that point-- 711 00:46:21,230 --> 00:46:23,880 actually, this distance, right? 712 00:46:23,880 --> 00:46:28,380 So actually, we defined this distance 713 00:46:28,380 --> 00:46:32,490 as back focal plane, so from the second surface of the lens 714 00:46:32,490 --> 00:46:35,220 to this back focal plane. 715 00:46:35,220 --> 00:46:39,030 And then what I'm going to do is find the distance 716 00:46:39,030 --> 00:46:40,340 by ray transfer matrices. 717 00:46:43,190 --> 00:46:58,120 So what I do is, so same as before, alpha 2 and x2, 718 00:46:58,120 --> 00:47:00,010 which is here. 719 00:47:00,010 --> 00:47:03,910 But you know, the x2 is 0, because it 720 00:47:03,910 --> 00:47:06,850 is on the optical axis, right? 721 00:47:06,850 --> 00:47:09,960 So it is actually 0. 722 00:47:09,960 --> 00:47:18,770 And input is alpha 1 and x1, this one, so this x1 and angle. 723 00:47:18,770 --> 00:47:22,390 But since it is parallel to the optical axis, the alpha 1 is 0. 724 00:47:26,130 --> 00:47:30,450 And I just derived the ray transfer matrix 725 00:47:30,450 --> 00:47:32,930 of the thick lens, this guy. 726 00:47:32,930 --> 00:47:35,070 I mean this whole guy. 727 00:47:35,070 --> 00:47:45,370 So I have M11, M12, M21, M22. 728 00:47:45,370 --> 00:47:47,620 And it's not the end, right? 729 00:47:47,620 --> 00:47:49,930 So we have to propagate again from here 730 00:47:49,930 --> 00:47:53,510 to here by distance zb. 731 00:47:53,510 --> 00:47:59,120 So it's going to be 1 0 zb 1. 732 00:48:05,210 --> 00:48:09,930 So if you solve this equation, then-- 733 00:48:09,930 --> 00:48:14,010 so this is just what I've written. 734 00:48:14,010 --> 00:48:16,010 So we have the 1 0, zb 1. 735 00:48:16,010 --> 00:48:18,792 And this is our M matrices. 736 00:48:18,792 --> 00:48:22,200 And if you solve this equation, then we get two [INAUDIBLE],, 737 00:48:22,200 --> 00:48:22,700 right? 738 00:48:22,700 --> 00:48:24,990 We had the two equations. 739 00:48:24,990 --> 00:48:29,630 So one is alpha 2 is negative x1 and effective focal length. 740 00:48:29,630 --> 00:48:34,470 So this sign means this alpha 2 is heading downward. 741 00:48:34,470 --> 00:48:39,770 So the amplitude means x1 over effective focal length. 742 00:48:39,770 --> 00:48:45,010 And zb is actually effective focal length 743 00:48:45,010 --> 00:48:47,380 times 1 minus this guy. 744 00:48:47,380 --> 00:48:51,703 So in this case, actually the zb is 745 00:48:51,703 --> 00:48:53,120 bigger than effective focal length 746 00:48:53,120 --> 00:48:55,102 or smaller than effective focal length. 747 00:49:06,690 --> 00:49:09,470 You know, in this case, n is bigger than 1. 748 00:49:09,470 --> 00:49:13,090 So this guy is positive. 749 00:49:13,090 --> 00:49:17,506 So zb is actually smaller than effective focal length, right? 750 00:49:17,506 --> 00:49:18,480 Wake up, guys. 751 00:49:24,310 --> 00:49:28,720 So we define this distance zb as a back focal length. 752 00:49:28,720 --> 00:49:31,300 And we just talk about the effective focal length, 753 00:49:31,300 --> 00:49:33,520 the quantity in the bracket. 754 00:49:33,520 --> 00:49:35,725 And the 1 over effective focal length 755 00:49:35,725 --> 00:49:39,940 is power, the lens power or optical power 756 00:49:39,940 --> 00:49:42,680 of this thick lens. 757 00:49:42,680 --> 00:49:46,250 So this distance is the effective focal length. 758 00:49:46,250 --> 00:49:49,280 This is the answer to your question. 759 00:49:49,280 --> 00:49:52,520 And we can do the same thing in the other side. 760 00:49:57,870 --> 00:50:00,270 So we start from the point. 761 00:50:00,270 --> 00:50:04,200 We don't know where it is yet, but the focal point in front 762 00:50:04,200 --> 00:50:07,800 of the lens, which is the front focal plane, front focal point. 763 00:50:07,800 --> 00:50:09,480 And they bend twice. 764 00:50:09,480 --> 00:50:11,610 And finally, they get collimated, 765 00:50:11,610 --> 00:50:17,170 because it's going to the image at infinity. 766 00:50:17,170 --> 00:50:27,720 So the ray matrices, in this case, are alpha 2 and x2 767 00:50:27,720 --> 00:50:30,630 and alpha 1 and x1. 768 00:50:30,630 --> 00:50:34,480 But now, we start from the point on the optical axis. 769 00:50:34,480 --> 00:50:36,630 So x1 should be 0. 770 00:50:39,450 --> 00:50:44,520 And at the end, we are going to have the x2, but alpha 2 771 00:50:44,520 --> 00:50:46,670 equals 0. 772 00:50:46,670 --> 00:50:49,280 So this should be 0. 773 00:50:49,280 --> 00:50:52,820 And first matrices we should consider 774 00:50:52,820 --> 00:50:56,030 is this propagation by the zf, right? 775 00:50:56,030 --> 00:51:02,970 So it's going to be 1 0 zf 1. 776 00:51:02,970 --> 00:51:13,310 And then we have the thick lens, so M11, M12, M21, M22. 777 00:51:13,310 --> 00:51:16,430 And if you solve this equation, then we also 778 00:51:16,430 --> 00:51:20,840 get the 2 [INAUDIBLE],, which is the front focal length, which 779 00:51:20,840 --> 00:51:24,240 is zf from here to here. 780 00:51:24,240 --> 00:51:25,300 And this is what you get. 781 00:51:27,870 --> 00:51:33,688 And the second in x2 is alpha 1 times effective focal length. 782 00:51:42,170 --> 00:51:42,670 Question? 783 00:51:51,640 --> 00:51:54,110 I guess it's time to break. 784 00:51:54,110 --> 00:51:55,510 Yeah. 785 00:51:55,510 --> 00:51:57,090 Let's take a break here. 786 00:51:57,090 --> 00:52:00,515 So next time, I'm going to continue 787 00:52:00,515 --> 00:52:02,890 to explain these front focal length and back focal length 788 00:52:02,890 --> 00:52:04,420 and how they are related. 789 00:52:04,420 --> 00:52:07,320 And meantime, we had the demo set up here. 790 00:52:07,320 --> 00:52:11,425 So you're welcome to come and see. 791 00:52:11,425 --> 00:52:16,130 And what we have here is actually the imaging set up. 792 00:52:16,130 --> 00:52:19,380 We have a single lens here and object, 793 00:52:19,380 --> 00:52:20,780 which is the resolution target. 794 00:52:20,780 --> 00:52:22,470 And we have the screen here. 795 00:52:22,470 --> 00:52:24,860 So if you move this screen back and forth 796 00:52:24,860 --> 00:52:28,690 or lens and the image-- 797 00:52:28,690 --> 00:52:29,990 we cannot move the object. 798 00:52:29,990 --> 00:52:33,830 So basically we're going to demonstrate the imaging 799 00:52:33,830 --> 00:52:34,700 condition. 800 00:52:34,700 --> 00:52:39,110 So if the distance is properly located, 801 00:52:39,110 --> 00:52:41,690 then we are going to see the very nice image. 802 00:52:41,690 --> 00:52:44,000 But if not, then the image looks blurry. 803 00:52:49,860 --> 00:52:52,830 GUEST SPEAKER: So before we continue with all the math, 804 00:52:52,830 --> 00:52:54,400 some of you came to see the demo. 805 00:52:54,400 --> 00:52:56,550 And for the ones that didn't come, 806 00:52:56,550 --> 00:52:58,320 I suggest you to come after class. 807 00:52:58,320 --> 00:53:01,140 It's easier to see the image we try to form, 808 00:53:01,140 --> 00:53:02,940 because we don't have the dynamic range 809 00:53:02,940 --> 00:53:05,070 problem that any camera has. 810 00:53:05,070 --> 00:53:06,800 But anyways, the main idea of this demo 811 00:53:06,800 --> 00:53:08,550 is to show what we've been learning about, 812 00:53:08,550 --> 00:53:11,290 an imaging of a single lens, right? 813 00:53:11,290 --> 00:53:12,780 So if you can summarize this points 814 00:53:12,780 --> 00:53:15,450 so far what we've learned, we've learned the thin lenses, 815 00:53:15,450 --> 00:53:17,100 thick lenses, right? 816 00:53:17,100 --> 00:53:18,600 So it's just a refractive element 817 00:53:18,600 --> 00:53:22,050 that is capable of forming an image from a given point, 818 00:53:22,050 --> 00:53:24,750 either at infinity or a close distance, to another plane. 819 00:53:24,750 --> 00:53:26,130 That's what we learned. 820 00:53:26,130 --> 00:53:28,980 Another important point that we've learned today 821 00:53:28,980 --> 00:53:31,800 is the imaging condition, right? 822 00:53:31,800 --> 00:53:35,010 Imaging condition is just depending 823 00:53:35,010 --> 00:53:38,520 on three variables, the distance from the lens 824 00:53:38,520 --> 00:53:41,160 to the image plane, si, the distance 825 00:53:41,160 --> 00:53:43,020 from the lens to the object plane, 826 00:53:43,020 --> 00:53:45,722 s o, and the focal length, right? 827 00:53:45,722 --> 00:53:47,430 This is one of the most important things. 828 00:53:47,430 --> 00:53:50,160 Because basically this tells you, 829 00:53:50,160 --> 00:53:53,850 if I want to have an in-focus very sharp, nice image, 830 00:53:53,850 --> 00:53:57,440 I can either play with two of variables, keep one constant. 831 00:53:57,440 --> 00:53:59,640 So for example, in these demo what I'm going to show 832 00:53:59,640 --> 00:54:02,100 you is how a single lens, a positive lens, 833 00:54:02,100 --> 00:54:05,520 performs imaging of a thin transparency. 834 00:54:05,520 --> 00:54:07,230 So in this case, I'm going to start 835 00:54:07,230 --> 00:54:10,030 showing here how I'm illuminating this transparency, 836 00:54:10,030 --> 00:54:10,780 which is here. 837 00:54:10,780 --> 00:54:14,010 It's just a piece of glass that has some dark coded 838 00:54:14,010 --> 00:54:15,870 lines of different sizes. 839 00:54:15,870 --> 00:54:18,060 It's called a resolution target. 840 00:54:18,060 --> 00:54:21,160 And we're illuminating these with white light from the back. 841 00:54:21,160 --> 00:54:25,080 So it's just like transparency for an overhead projector 842 00:54:25,080 --> 00:54:26,320 you can think of. 843 00:54:26,320 --> 00:54:28,940 Then this is a positive lens here 844 00:54:28,940 --> 00:54:32,250 that will basically form an image at another screen 845 00:54:32,250 --> 00:54:33,480 here, right? 846 00:54:33,480 --> 00:54:36,900 So now, let's look at these quantities physically 847 00:54:36,900 --> 00:54:38,850 that we've learned in the math here. 848 00:54:38,850 --> 00:54:41,960 This distance from here to here is the object distance. 849 00:54:41,960 --> 00:54:44,580 That's the s o from the equation. 850 00:54:44,580 --> 00:54:47,550 This lens has a fixed focal length, which I cannot change. 851 00:54:47,550 --> 00:54:50,490 It's just a piece of glass curved in a given way. 852 00:54:50,490 --> 00:54:55,270 So this distance here is the distance to the image plane. 853 00:54:55,270 --> 00:54:58,410 So these two distances I really can change, A, 854 00:54:58,410 --> 00:55:01,740 to get a sharp focus to make sure that my image is exactly 855 00:55:01,740 --> 00:55:06,390 on my screen, and/or if I want to play with a magnification. 856 00:55:06,390 --> 00:55:08,310 Because remember from the math, if you 857 00:55:08,310 --> 00:55:12,270 can see the notes before, that the lateral magnification 858 00:55:12,270 --> 00:55:16,920 depends on the ratio of minus si, which 859 00:55:16,920 --> 00:55:21,390 is these distance, over s o, which is this distance, right? 860 00:55:21,390 --> 00:55:23,100 So let's lower the exposure here just 861 00:55:23,100 --> 00:55:26,438 to see the image that we have here, please. 862 00:55:26,438 --> 00:55:28,230 All right, so we lowered the exposure again 863 00:55:28,230 --> 00:55:32,590 for the same reasons of dynamic range. 864 00:55:32,590 --> 00:55:35,290 So I'm going to try to focus here on the image. 865 00:55:35,290 --> 00:55:39,430 So this is the image that we are forming on the screen. 866 00:55:39,430 --> 00:55:46,180 And as you can see, so there is a bunch of lines, stripes, 867 00:55:46,180 --> 00:55:48,840 and squares with numbers. 868 00:55:48,840 --> 00:55:51,750 And it's very sharply in focus. 869 00:55:51,750 --> 00:55:55,050 So now what I'm going to do, and hopefully we 870 00:55:55,050 --> 00:55:57,450 can see it with a camera, is that I'm 871 00:55:57,450 --> 00:56:00,640 going to change the ratio between these two distances. 872 00:56:00,640 --> 00:56:06,330 So what if, for example, I want to demagnify my image? 873 00:56:06,330 --> 00:56:09,780 So the magnification quantities I use describe si over s o. 874 00:56:09,780 --> 00:56:11,040 Forget about the minus sign. 875 00:56:11,040 --> 00:56:14,630 The minus sign just tells you that it's an inverted image. 876 00:56:14,630 --> 00:56:17,352 si over s o, I want that quantity smaller. 877 00:56:17,352 --> 00:56:18,060 What should I do? 878 00:56:32,840 --> 00:56:35,480 I'm going to repeat the question one more time. 879 00:56:35,480 --> 00:56:38,360 Magnification equal to 1, I want magnification, say, 880 00:56:38,360 --> 00:56:39,770 less than 1. 881 00:56:39,770 --> 00:56:42,680 How can I reduce that M number? 882 00:56:42,680 --> 00:56:46,150 M equals minus si over s o. 883 00:56:49,790 --> 00:56:51,230 AUDIENCE: [INAUDIBLE] 884 00:56:51,230 --> 00:56:52,670 GUEST SPEAKER: What? 885 00:56:52,670 --> 00:56:55,550 AUDIENCE: [INAUDIBLE] 886 00:56:56,520 --> 00:56:57,510 GUEST SPEAKER: OK. 887 00:56:57,510 --> 00:56:59,635 Just push the button and repeat what you just said. 888 00:57:03,600 --> 00:57:05,920 AUDIENCE: Increase the distance s o, 889 00:57:05,920 --> 00:57:07,883 so you move it closer to the screen. 890 00:57:07,883 --> 00:57:10,300 GUEST SPEAKER: So if I move the lens closer to the screen, 891 00:57:10,300 --> 00:57:15,700 effectively I reduce si, the imaging distance. 892 00:57:15,700 --> 00:57:17,650 So let's try it. 893 00:57:17,650 --> 00:57:20,960 So I'm going to move these lens closer to this side. 894 00:57:20,960 --> 00:57:22,610 So s o increases, of course. 895 00:57:25,210 --> 00:57:32,110 And I can just look at the right position here for focus. 896 00:57:32,110 --> 00:57:34,060 So now, this distance is smaller. 897 00:57:34,060 --> 00:57:37,930 And it's hard to see with a webcam, 898 00:57:37,930 --> 00:57:40,150 but the image is still in focus. 899 00:57:40,150 --> 00:57:42,558 It's smaller, demagnified respect to the one 900 00:57:42,558 --> 00:57:43,600 that I showed you before. 901 00:57:46,160 --> 00:57:49,570 But yeah, that basically will accomplish this, right? 902 00:57:49,570 --> 00:57:51,880 So for this part, if you can come and play 903 00:57:51,880 --> 00:57:53,930 with these distances later after class, 904 00:57:53,930 --> 00:57:57,220 you will see how this relationship works, right? 905 00:57:57,220 --> 00:58:00,280 So in this case, we have these two variables, the s o and si 906 00:58:00,280 --> 00:58:01,450 that we're playing at. 907 00:58:01,450 --> 00:58:04,140 But as we'll see in a second, for the eye, 908 00:58:04,140 --> 00:58:05,980 it's a very different story. 909 00:58:05,980 --> 00:58:10,750 Because in the eye, the lens of the eye and the retina, 910 00:58:10,750 --> 00:58:12,635 so in this case would be your si, is fixed. 911 00:58:12,635 --> 00:58:13,510 You cannot change it. 912 00:58:13,510 --> 00:58:15,400 It's the shape of your eye. 913 00:58:15,400 --> 00:58:19,030 So how can the eye focus far distance objects 914 00:58:19,030 --> 00:58:22,130 or when you read nearby objects? 915 00:58:22,130 --> 00:58:24,100 So it has to do similar tricks playing 916 00:58:24,100 --> 00:58:26,380 in the imaging conditions, such that it always 917 00:58:26,380 --> 00:58:28,150 has a sharp image. 918 00:58:28,150 --> 00:58:31,060 The way the eye does it, and we'll see it in a second, 919 00:58:31,060 --> 00:58:32,750 is by changing the focal length. 920 00:58:32,750 --> 00:58:36,130 So now, the two variables become f and s o. 921 00:58:36,130 --> 00:58:38,900 And you can do the same trick. 922 00:58:38,900 --> 00:58:43,640 So this was a positive lens. 923 00:58:43,640 --> 00:58:47,520 We will learn about negative power lenses, 924 00:58:47,520 --> 00:58:50,040 so the ones are curved like this, right? 925 00:58:50,040 --> 00:58:52,320 So in these ones, we've learned that these 926 00:58:52,320 --> 00:58:57,630 generate these weird non-intuitive virtual images, 927 00:58:57,630 --> 00:58:58,535 right? 928 00:58:58,535 --> 00:58:59,910 So I was just asking the students 929 00:58:59,910 --> 00:59:03,090 that came here, what did they expect 930 00:59:03,090 --> 00:59:05,790 to see if I put this lens here? 931 00:59:05,790 --> 00:59:08,200 Anyone wants to guess other than the students that 932 00:59:08,200 --> 00:59:11,100 already answered the question? 933 00:59:11,100 --> 00:59:13,330 What do you think will-- 934 00:59:13,330 --> 00:59:14,710 let me put it in this way. 935 00:59:14,710 --> 00:59:16,760 Would I see an image and where? 936 00:59:16,760 --> 00:59:20,400 Or should I not see anything if I put this negative lens? 937 00:59:27,980 --> 00:59:28,850 Image or no image? 938 00:59:28,850 --> 00:59:32,220 Singapore? 939 00:59:32,220 --> 00:59:35,130 AUDIENCE: Unless you form the image with another lens, 940 00:59:35,130 --> 00:59:35,917 you don't see it. 941 00:59:35,917 --> 00:59:37,250 GUEST SPEAKER: OK, let's try it. 942 00:59:42,970 --> 00:59:45,480 I put the negative lens. 943 00:59:45,480 --> 00:59:48,760 Actually, I'm going to put it in this. 944 00:59:48,760 --> 00:59:51,040 Oh. 945 00:59:51,040 --> 00:59:51,880 We lost the video. 946 00:59:51,880 --> 00:59:52,880 Give me just one second. 947 01:00:02,110 --> 01:00:09,210 All right, so I put the negative lens. 948 01:00:09,210 --> 01:00:10,580 Let me move it back and forth. 949 01:00:10,580 --> 01:00:13,430 And yeah, you can see here I have just a bright patch 950 01:00:13,430 --> 01:00:16,380 of light, no image, right? 951 01:00:16,380 --> 01:00:19,860 So you said that, if we use another lens, 952 01:00:19,860 --> 01:00:22,910 we can make that image into a real image. 953 01:00:22,910 --> 01:00:26,330 What type of lens do you think we need to add and where? 954 01:00:35,720 --> 01:00:38,590 OK, I'll answer that one. 955 01:00:38,590 --> 01:00:39,090 OK. 956 01:00:39,090 --> 01:00:40,060 You can answer? 957 01:00:43,540 --> 01:00:46,900 AUDIENCE: A positive lens after the negative lens, 958 01:00:46,900 --> 01:00:49,620 before the screen? 959 01:00:49,620 --> 01:00:51,580 GUEST SPEAKER: Exactly. 960 01:00:51,580 --> 01:00:53,770 So essentially, physically what this is doing 961 01:00:53,770 --> 01:00:56,170 is that the light going out from the object 962 01:00:56,170 --> 01:00:59,930 gets even bent outwards more, right? 963 01:00:59,930 --> 01:01:02,470 So it basically essentially forms a virtual object 964 01:01:02,470 --> 01:01:03,498 behind the lens, right? 965 01:01:03,498 --> 01:01:05,290 So the positive lens, what it's going to do 966 01:01:05,290 --> 01:01:09,400 is grab these outward rays and focus them back into the screen 967 01:01:09,400 --> 01:01:10,733 to form an image. 968 01:01:10,733 --> 01:01:11,650 And let's just try it. 969 01:01:15,350 --> 01:01:17,090 Now, I have the two lenses. 970 01:01:19,715 --> 01:01:22,343 Just make sure that the exposure is-- 971 01:01:22,343 --> 01:01:23,510 We're reducing the exposure. 972 01:01:33,480 --> 01:01:37,290 Oh, it's hard to see here, but there's lines again, right? 973 01:01:37,290 --> 01:01:39,130 So then we have an image. 974 01:01:39,130 --> 01:01:41,790 So essentially, as I was mentioning before, 975 01:01:41,790 --> 01:01:44,100 this is what our eye would do for us 976 01:01:44,100 --> 01:01:46,020 when we see virtual images. 977 01:01:46,020 --> 01:01:48,330 We have a visual image, and our eye 978 01:01:48,330 --> 01:01:50,460 is the lens that focuses this light 979 01:01:50,460 --> 01:01:53,520 and converts this virtual image into a real image, right? 980 01:01:53,520 --> 01:01:56,950 We'll understand more how the eye works in a second. 981 01:01:56,950 --> 01:02:00,130 So I think we're going to switch back to the normal class mode. 982 01:02:00,130 --> 01:02:03,110 Thanks for the presentation. 983 01:02:24,680 --> 01:02:29,510 SE BAEK OH: OK, so we were talking about the thick lens. 984 01:02:29,510 --> 01:02:32,690 So by using ray transfer matrices, 985 01:02:32,690 --> 01:02:35,750 we just derived the effective focal length of a thick lens. 986 01:02:35,750 --> 01:02:39,860 And we defined the back focal plane, back focal length, 987 01:02:39,860 --> 01:02:42,070 and the front focal length, which is function 988 01:02:42,070 --> 01:02:44,450 of effective focal length. 989 01:02:44,450 --> 01:02:52,810 And let's see how they are related. 990 01:02:52,810 --> 01:02:57,350 So first one we have the infinite conjugate 991 01:02:57,350 --> 01:02:58,320 configuration. 992 01:02:58,320 --> 01:03:00,170 So we have an object at infinity. 993 01:03:00,170 --> 01:03:03,590 And at back focal plane, we have focus. 994 01:03:03,590 --> 01:03:05,570 And we just derived the two equations, 995 01:03:05,570 --> 01:03:09,680 which is alpha 2 is x1 over effective focal length. 996 01:03:09,680 --> 01:03:12,800 And that focal length is effective focal length 997 01:03:12,800 --> 01:03:15,570 times some extra factor. 998 01:03:15,570 --> 01:03:31,180 And what I'm going to do here is I just 999 01:03:31,180 --> 01:03:33,520 measure the effective focal length 1000 01:03:33,520 --> 01:03:36,040 from the back focal plane. 1001 01:03:36,040 --> 01:03:39,410 And since the back focal length it 1002 01:03:39,410 --> 01:03:44,098 means the focal plane to the second surface 1003 01:03:44,098 --> 01:03:45,890 is shorter than the effective focal length, 1004 01:03:45,890 --> 01:03:47,830 so actually in this case we are going 1005 01:03:47,830 --> 01:03:51,070 to have the plane, the virtual plane, inside of the glass. 1006 01:03:53,640 --> 01:03:58,880 And from that equation, which is alpha 2 and alpha 2 equal x1 1007 01:03:58,880 --> 01:04:01,330 over effective focal length, it turns out 1008 01:04:01,330 --> 01:04:07,510 that if you extend this ray over here and this ray over here 1009 01:04:07,510 --> 01:04:11,060 they actually meet at that plane. 1010 01:04:11,060 --> 01:04:13,930 So it's essentially you can think, 1011 01:04:13,930 --> 01:04:17,610 even though you have thick lens, but you have thin lens there. 1012 01:04:17,610 --> 01:04:24,400 So ray just-- propagating from straight and at this plane 1013 01:04:24,400 --> 01:04:27,460 and bend and make a focus there. 1014 01:04:27,460 --> 01:04:30,800 So we call this plane a second principal plane, 1015 01:04:30,800 --> 01:04:32,800 because it's associated with a back focal plane. 1016 01:04:32,800 --> 01:04:37,140 So it is a second principal plane. 1017 01:04:37,140 --> 01:04:41,370 And you can do the same thing in the other side, of course. 1018 01:04:41,370 --> 01:04:44,520 So we had different focal plane. 1019 01:04:44,520 --> 01:04:48,360 And I measure from here to here by effective focal length. 1020 01:04:48,360 --> 01:04:50,160 And effective focal length is actually 1021 01:04:50,160 --> 01:04:54,880 longer than the front focal plane, zf, from here to there. 1022 01:04:54,880 --> 01:04:57,940 So it's still inside the glass. 1023 01:04:57,940 --> 01:05:00,030 And if you extend out those rays, 1024 01:05:00,030 --> 01:05:03,540 actually they meet at this plane. 1025 01:05:03,540 --> 01:05:05,390 So we call this first principal plane. 1026 01:05:08,720 --> 01:05:12,270 So I just put these two figures together. 1027 01:05:12,270 --> 01:05:14,200 So I have thick lens. 1028 01:05:14,200 --> 01:05:16,610 And we have different focal point. 1029 01:05:16,610 --> 01:05:20,060 And this distance [INAUDIBLE] the surface of the lens 1030 01:05:20,060 --> 01:05:21,830 is front focal length. 1031 01:05:21,830 --> 01:05:23,940 And we defined the same thing here. 1032 01:05:23,940 --> 01:05:26,210 So we have the back focal point. 1033 01:05:26,210 --> 01:05:29,840 And we defined the back focal length from here to here. 1034 01:05:29,840 --> 01:05:34,700 And from the ray transfer matrix, 1035 01:05:34,700 --> 01:05:39,050 we defined the effective focal length of this thick lens. 1036 01:05:39,050 --> 01:05:41,270 So we defined the first principal plane 1037 01:05:41,270 --> 01:05:42,560 and second principal plane. 1038 01:05:42,560 --> 01:05:46,870 And that's the effective focal length. 1039 01:05:46,870 --> 01:05:57,840 And so conceptually, these thick lens can be assumed. 1040 01:05:57,840 --> 01:06:00,880 We already computed ray transfer matrices, right? 1041 01:06:00,880 --> 01:06:05,610 So we can conceptually think we have the thin lens, 1042 01:06:05,610 --> 01:06:09,540 but it's the first surface in a infinite thin lens. 1043 01:06:09,540 --> 01:06:11,220 The first surface and second surface 1044 01:06:11,220 --> 01:06:13,080 is actually the first principal plane 1045 01:06:13,080 --> 01:06:14,800 and the second principal plane. 1046 01:06:14,800 --> 01:06:20,610 And if you remember the infinite conjugate configuration, 1047 01:06:20,610 --> 01:06:24,070 if ray from the object at infinity, 1048 01:06:24,070 --> 01:06:27,850 so it's propagating parallel to the optical axis, 1049 01:06:27,850 --> 01:06:30,880 then it bends at the second principal plane 1050 01:06:30,880 --> 01:06:35,340 and make focus at back focal plane. 1051 01:06:35,340 --> 01:06:38,280 And same thing here if you have the point 1052 01:06:38,280 --> 01:06:41,580 object at the different focal plane. 1053 01:06:41,580 --> 01:06:44,460 And it bends at the first principal plane, 1054 01:06:44,460 --> 01:06:46,780 and collinate it, and goes to the infinity. 1055 01:06:51,840 --> 01:06:53,860 So actually reason why we introduced 1056 01:06:53,860 --> 01:06:55,570 this concept, the principal plane 1057 01:06:55,570 --> 01:07:00,060 and effective focal length is actually pretty simple. 1058 01:07:00,060 --> 01:07:02,950 Because we start with the thin lens, but now 1059 01:07:02,950 --> 01:07:04,400 we had the thick lens. 1060 01:07:04,400 --> 01:07:07,420 So what if we have multiple lenses, like thick lenses? 1061 01:07:07,420 --> 01:07:10,120 So no matter how complicated the optical system is, 1062 01:07:10,120 --> 01:07:13,030 we can always find the effective focal length 1063 01:07:13,030 --> 01:07:15,820 and this first and second principal plane. 1064 01:07:15,820 --> 01:07:20,220 So once we have this first and the second principal plane 1065 01:07:20,220 --> 01:07:23,560 and effective focal length, f here, then we 1066 01:07:23,560 --> 01:07:27,130 can treat this whole system as one thin lens. 1067 01:07:27,130 --> 01:07:36,920 So for example-- come on. 1068 01:07:36,920 --> 01:07:39,740 So we have the object in object space. 1069 01:07:39,740 --> 01:07:44,810 And ray, it's exactly the same as a thin lens. 1070 01:07:44,810 --> 01:07:46,460 We choose two rays, right? 1071 01:07:46,460 --> 01:07:49,700 So the first one is bent at the second principal plane. 1072 01:07:49,700 --> 01:07:52,370 And it's passed through the back focal plane-- 1073 01:07:52,370 --> 01:07:54,350 back focal point, sorry. 1074 01:07:54,350 --> 01:08:02,240 And the second ray goes through the front focal point 1075 01:08:02,240 --> 01:08:05,910 and it bend at the first principal plane. 1076 01:08:05,910 --> 01:08:07,130 And it's collimated. 1077 01:08:07,130 --> 01:08:08,780 And they meet at some point. 1078 01:08:08,780 --> 01:08:11,960 So you can easily find the image even though your system 1079 01:08:11,960 --> 01:08:13,410 is pretty complicated. 1080 01:08:13,410 --> 01:08:15,890 But once you find these two principal 1081 01:08:15,890 --> 01:08:17,510 plane and effective focal length, 1082 01:08:17,510 --> 01:08:24,670 then you can still use the same equation as a thin lens. 1083 01:08:30,939 --> 01:08:31,770 Come on. 1084 01:08:31,770 --> 01:08:33,050 Yeah, all these equations. 1085 01:08:33,050 --> 01:08:37,064 So you can define the same thing, xo and s 1086 01:08:37,064 --> 01:08:40,350 o, the image distance and object distance like this. 1087 01:08:40,350 --> 01:08:42,350 And you can use the same equation, 1088 01:08:42,350 --> 01:08:46,510 so Newton's form, xo times xi equals to f squared. 1089 01:08:46,510 --> 01:08:49,359 And the lens law, 1 over object distance plus 1 1090 01:08:49,359 --> 01:08:51,569 over image distance, should be 1 over f. 1091 01:08:51,569 --> 01:08:54,830 So f is effective focal length in this case. 1092 01:08:54,830 --> 01:08:59,270 And the lateral magnification and angular magnification, 1093 01:08:59,270 --> 01:09:02,520 they're defined the same way. 1094 01:09:02,520 --> 01:09:05,122 And I just want to mention that the-- yes? 1095 01:09:08,439 --> 01:09:10,862 AUDIENCE: Where is [INAUDIBLE] on that picture? 1096 01:09:10,862 --> 01:09:13,820 Because the effective focal length you talked about depends 1097 01:09:13,820 --> 01:09:19,715 on the [INAUDIBLE] between the first [INAUDIBLE].. 1098 01:09:19,715 --> 01:09:21,840 SE BAEK OH: So actually, the effective focal length 1099 01:09:21,840 --> 01:09:25,380 depend on the stuff inside of the neuro-optical system. 1100 01:09:25,380 --> 01:09:27,510 So the thick lens we just consider 1101 01:09:27,510 --> 01:09:30,870 one thick lens-- so one, the first surface, 1102 01:09:30,870 --> 01:09:32,729 and lens, and second surface. 1103 01:09:32,729 --> 01:09:36,700 But I'm going to actually talk about that later. 1104 01:09:36,700 --> 01:09:38,460 But what if we have two lens? 1105 01:09:38,460 --> 01:09:41,729 So we first consider first lens and propagation 1106 01:09:41,729 --> 01:09:42,859 and the second lens. 1107 01:09:42,859 --> 01:09:48,689 So you can define the effective focal length the same way, OK? 1108 01:09:48,689 --> 01:09:51,120 So in this case, the effective focal length 1109 01:09:51,120 --> 01:09:54,600 is not related to the aperture or whatever. 1110 01:09:54,600 --> 01:09:59,490 It just depend on the reflective index and distance 1111 01:09:59,490 --> 01:10:02,560 between the optical element. 1112 01:10:02,560 --> 01:10:04,480 AUDIENCE: But in the effective focal length 1113 01:10:04,480 --> 01:10:07,880 you've got the parameter b, [INAUDIBLE].. 1114 01:10:07,880 --> 01:10:10,520 SE BAEK OH: Yeah, distance between the elements, right? 1115 01:10:10,520 --> 01:10:12,300 AUDIENCE: OK, so that's width of the lens? 1116 01:10:12,300 --> 01:10:12,967 SE BAEK OH: Yes. 1117 01:10:15,717 --> 01:10:16,300 AUDIENCE: So-- 1118 01:10:16,300 --> 01:10:17,008 SE BAEK OH: Yeah? 1119 01:10:17,008 --> 01:10:17,590 Yeah. 1120 01:10:17,590 --> 01:10:20,240 AUDIENCE: Over here we have this duality between x object 1121 01:10:20,240 --> 01:10:22,432 and x image, but we always have 1f. 1122 01:10:22,432 --> 01:10:23,890 Is that only because we're assuming 1123 01:10:23,890 --> 01:10:25,600 that the lens has the same radius of curvature 1124 01:10:25,600 --> 01:10:26,510 on either side for now? 1125 01:10:26,510 --> 01:10:26,710 SE BAEK OH: No, no. 1126 01:10:26,710 --> 01:10:28,660 AUDIENCE: Or is it always just 1f? 1127 01:10:28,660 --> 01:10:29,830 SE BAEK OH: No, no. 1128 01:10:29,830 --> 01:10:35,330 So effective focal length is just function of-- 1129 01:10:38,192 --> 01:10:42,020 yeah, maybe it's confusing, but the-- 1130 01:10:48,290 --> 01:10:50,780 so in this thick lens, the effective focal length 1131 01:10:50,780 --> 01:10:54,210 is just function of the radius curvature and reflective index 1132 01:10:54,210 --> 01:10:56,890 and d, right? 1133 01:10:56,890 --> 01:10:59,370 So the concept of this effective focal length 1134 01:10:59,370 --> 01:11:01,740 and principal plane, we treat the whole system 1135 01:11:01,740 --> 01:11:03,150 as one thing lens. 1136 01:11:03,150 --> 01:11:06,420 And one thing lens has the same focal length in front side 1137 01:11:06,420 --> 01:11:07,560 and rear side, right? 1138 01:11:07,560 --> 01:11:09,060 So effective focal length is already 1139 01:11:09,060 --> 01:11:13,410 same in front side and the back side of the lens. 1140 01:11:13,410 --> 01:11:15,360 But it depends on the system. 1141 01:11:15,360 --> 01:11:18,520 Because right now, I just talk about this thick lens. 1142 01:11:18,520 --> 01:11:22,750 So that's why we have only, 1, 2, 3, 4 parameter here. 1143 01:11:22,750 --> 01:11:25,660 But if I have another thick lens as [INAUDIBLE] here, 1144 01:11:25,660 --> 01:11:28,390 then effective focal length is more complicated, right? 1145 01:11:28,390 --> 01:11:31,950 So it's also a function of the reflective index, and distance, 1146 01:11:31,950 --> 01:11:35,432 and the curvature of the second lens, OK? 1147 01:11:35,432 --> 01:11:36,390 Now, we'll talk about-- 1148 01:11:36,390 --> 01:11:40,810 I mean, actually I'll show you [INAUDIBLE].. 1149 01:11:40,810 --> 01:11:42,380 AUDIENCE: So for one lens, you always 1150 01:11:42,380 --> 01:11:45,080 have one effective focal length to characterize 1151 01:11:45,080 --> 01:11:45,760 the entire lens? 1152 01:11:45,760 --> 01:11:46,250 SE BAEK OH: Yeah. 1153 01:11:46,250 --> 01:11:47,565 AUDIENCE: No matter what the sides are? 1154 01:11:47,565 --> 01:11:47,820 SE BAEK OH: Yeah. 1155 01:11:47,820 --> 01:11:49,890 So let's say if you have the 100 length. 1156 01:11:49,890 --> 01:11:53,084 But you can always find the one effective focal length. 1157 01:11:53,084 --> 01:11:53,584 Yeah. 1158 01:11:58,020 --> 01:12:00,620 So actually, if you have a digital camera, then 1159 01:12:00,620 --> 01:12:03,650 typically you have multiple lens, or three or four or five. 1160 01:12:03,650 --> 01:12:06,440 But you only have the one focal length in it. 1161 01:12:06,440 --> 01:12:08,640 I mean, they only specify one focal length, right? 1162 01:12:08,640 --> 01:12:10,880 So that is actually effective focal length. 1163 01:12:10,880 --> 01:12:13,459 So they already compute this whole thing, OK? 1164 01:12:28,440 --> 01:12:34,280 So that's the reason why we introduced this concept. 1165 01:12:34,280 --> 01:12:38,090 And I just want to mention the center ray which 1166 01:12:38,090 --> 01:12:41,240 is starting from the object point, 1167 01:12:41,240 --> 01:12:46,000 but is incident on the center at the first principal plane. 1168 01:12:46,000 --> 01:12:51,770 And if you remind the thin lens case, then at the thin lens 1169 01:12:51,770 --> 01:12:55,890 that ray actually just pass through the center of the ray, 1170 01:12:55,890 --> 01:12:56,390 right? 1171 01:12:56,390 --> 01:13:02,237 So the same here, so that ray is starting again 1172 01:13:02,237 --> 01:13:04,070 at the second principal plane, at the center 1173 01:13:04,070 --> 01:13:05,320 of the second principal plane. 1174 01:13:05,320 --> 01:13:08,270 And it goes to the image. 1175 01:13:08,270 --> 01:13:15,680 And of course, if you have the same medium 1176 01:13:15,680 --> 01:13:19,140 in front of the principal plane and behind the principal plane, 1177 01:13:19,140 --> 01:13:25,790 then this angle and this angle are same, right? 1178 01:13:25,790 --> 01:13:27,610 Because you know, at the center you 1179 01:13:27,610 --> 01:13:29,130 will just have a piece of glass. 1180 01:13:29,130 --> 01:13:31,860 So by the [INAUDIBLE] law, they should be parallel. 1181 01:13:37,210 --> 01:13:40,990 OK, actually, that's about it. 1182 01:13:40,990 --> 01:13:43,120 So the take home message is we just talk 1183 01:13:43,120 --> 01:13:46,307 about the imaging condition. 1184 01:13:46,307 --> 01:13:47,890 Anyway, by the way, he's going to talk 1185 01:13:47,890 --> 01:13:49,910 about the human visual system. 1186 01:13:49,910 --> 01:13:51,993 So take home message of my part is we 1187 01:13:51,993 --> 01:13:53,410 just talk about imaging condition, 1188 01:13:53,410 --> 01:13:57,172 which is 1 over s o and plus 1 over si is 1 over f. 1189 01:13:57,172 --> 01:13:58,630 And there are some mathematical way 1190 01:13:58,630 --> 01:14:02,570 to find or to write the condition, OK, which 1191 01:14:02,570 --> 01:14:04,180 is the ray transfer matrices. 1192 01:14:04,180 --> 01:14:10,390 And we just introduced the front focal length and back 1193 01:14:10,390 --> 01:14:12,310 focal length and principal planes. 1194 01:14:12,310 --> 01:14:14,740 But I didn't really talk about how 1195 01:14:14,740 --> 01:14:19,330 to find this principal place OK so let 1196 01:14:19,330 --> 01:14:23,590 me finish we are hard to find the principal place if you have 1197 01:14:23,590 --> 01:14:27,700 multiple elements which he was the of course we have the two 1198 01:14:27,700 --> 01:14:29,920 example of two lenses 1199 01:14:29,920 --> 01:14:35,310 so that completes so initially we 1200 01:14:35,310 --> 01:14:41,940 had the example that two lens which has focal length 1201 01:14:41,940 --> 01:14:46,110 is 10, 10. 1202 01:14:46,110 --> 01:14:49,730 And distance is 5 millimeter. 1203 01:14:49,730 --> 01:14:55,300 And the object was also 5 [INAUDIBLE].. 1204 01:14:55,300 --> 01:14:57,870 By the way, Professor Barbastathis, 1205 01:14:57,870 --> 01:15:03,990 he posted a different way to do it, to find where the image is, 1206 01:15:03,990 --> 01:15:06,820 or how big it is, and where is the principal plane, 1207 01:15:06,820 --> 01:15:08,340 and what's the effective length. 1208 01:15:08,340 --> 01:15:12,270 He summarized all these different method, 1209 01:15:12,270 --> 01:15:13,990 and he posted on a [INAUDIBLE] website 1210 01:15:13,990 --> 01:15:15,300 in a supplement material. 1211 01:15:15,300 --> 01:15:20,670 So please go to the website and review it. 1212 01:15:20,670 --> 01:15:21,990 And it looks complicated. 1213 01:15:21,990 --> 01:15:24,510 But once [INAUDIBLE],, then it's pretty straightforward. 1214 01:15:24,510 --> 01:15:26,520 And you will never forget. 1215 01:15:26,520 --> 01:15:27,660 You're not going to forget. 1216 01:15:27,660 --> 01:15:30,250 So please do it. 1217 01:15:30,250 --> 01:15:34,050 I strongly suggest you. 1218 01:15:34,050 --> 01:15:37,115 So let's continue how to find the principal planes here. 1219 01:15:37,115 --> 01:15:38,740 So there are a bunch of different ways. 1220 01:15:38,740 --> 01:15:41,860 So I'm going to do the first one the easy way. 1221 01:15:41,860 --> 01:15:49,193 So let's first find the back focal plane first, 1222 01:15:49,193 --> 01:15:49,860 because we know. 1223 01:15:53,310 --> 01:15:55,440 The definition of the focal plane, 1224 01:15:55,440 --> 01:15:59,960 if you remind the thin lens, like this, then 1225 01:15:59,960 --> 01:16:05,680 these incoming rays, they converged at one point, right? 1226 01:16:05,680 --> 01:16:10,870 So in this case, let's first assume 1227 01:16:10,870 --> 01:16:16,390 I have the ray coming from infinity like this. 1228 01:16:16,390 --> 01:16:19,940 And I do the cascade method. 1229 01:16:19,940 --> 01:16:22,120 So I just consider first lens here. 1230 01:16:22,120 --> 01:16:28,096 And where is my image? 1231 01:16:28,096 --> 01:16:31,960 Actually, we already computed, like, it's already computed. 1232 01:16:38,020 --> 01:16:43,030 So this focal length is distance 10, right, so distance f. 1233 01:16:43,030 --> 01:16:50,930 So by the first lens, I draw only one ray here. 1234 01:16:50,930 --> 01:16:52,670 This is parallel to the optical axis. 1235 01:16:52,670 --> 01:16:58,860 So third ray actually goes to the focal point 1236 01:16:58,860 --> 01:17:06,010 of the first lens, which is 10, right? 1237 01:17:06,010 --> 01:17:07,840 But we do have the second lens here. 1238 01:17:10,350 --> 01:17:14,720 So if you do the lens equation, then actually it bends more. 1239 01:17:14,720 --> 01:17:21,600 So finally, what you get is it coming in, bend like this. 1240 01:17:21,600 --> 01:17:26,260 It's supposed to go like this, but it bend more like this. 1241 01:17:26,260 --> 01:17:35,140 So this point is back focal point of these two lens system. 1242 01:17:35,140 --> 01:17:40,270 And if you do the same thing, so you extend the [INAUDIBLE] ray 1243 01:17:40,270 --> 01:17:45,100 like this, and if you extend like this, then where 1244 01:17:45,100 --> 01:17:51,370 they meet, actually that's the position 1245 01:17:51,370 --> 01:17:52,620 of the second principal plane. 1246 01:17:55,280 --> 01:17:56,800 Because you have all the numbers, 1247 01:17:56,800 --> 01:17:59,930 you can easily find the position of this guy. 1248 01:17:59,930 --> 01:18:06,070 And so this distance is actually the effective focal length. 1249 01:18:06,070 --> 01:18:11,730 And the distance from the second lens to the back focal point 1250 01:18:11,730 --> 01:18:15,010 is actually back focal length. 1251 01:18:15,010 --> 01:18:19,700 So we just find the second principal plane here, 1252 01:18:19,700 --> 01:18:22,570 second principal plane. 1253 01:18:22,570 --> 01:18:24,610 And you can do the same thing in object side. 1254 01:18:24,610 --> 01:18:36,090 You start with the point source on optical axis. 1255 01:18:36,090 --> 01:18:40,890 And at the end, you're going to get the collimated light. 1256 01:18:40,890 --> 01:18:45,840 So since it is symmetric, so it's actually 1257 01:18:45,840 --> 01:18:49,450 you're going to put the ray like this and bend like this. 1258 01:18:49,450 --> 01:18:50,970 And it's finally collimated. 1259 01:18:50,970 --> 01:18:53,200 So if you do the same thing, then you're 1260 01:18:53,200 --> 01:18:56,760 going to get the first principal plane here. 1261 01:18:56,760 --> 01:19:01,660 And this is effective focal length, 1262 01:19:01,660 --> 01:19:03,140 which is same as before. 1263 01:19:03,140 --> 01:19:11,010 And you can find the front focal plane, front focal length. 1264 01:19:11,010 --> 01:19:14,610 So that's the just conceptual way 1265 01:19:14,610 --> 01:19:17,730 to find the principal plane and effective focal length. 1266 01:19:17,730 --> 01:19:21,130 But if you want to be accurate or precise, 1267 01:19:21,130 --> 01:19:25,200 then you can always use the ray transfer matrix. 1268 01:19:25,200 --> 01:19:28,170 So let me do this. 1269 01:19:34,590 --> 01:19:37,430 We have two lens, focal length f. 1270 01:19:41,520 --> 01:19:46,440 So let's start with actually this interface 1271 01:19:46,440 --> 01:19:49,400 at the end of the second lens. 1272 01:19:49,400 --> 01:19:58,570 So we have here alpha o and xo and here alpha i and xi. 1273 01:19:58,570 --> 01:20:05,550 So I have alpha i xi, alpha o and xo. 1274 01:20:05,550 --> 01:20:08,240 And I assume this lenses are thin lenses. 1275 01:20:08,240 --> 01:20:13,430 So first matrices should be 1 over 1 and negative 1 1276 01:20:13,430 --> 01:20:17,090 over f and 0 1. 1277 01:20:17,090 --> 01:20:21,390 And next one is the propagation from here to here. 1278 01:20:21,390 --> 01:20:24,070 So this should be 1 0. 1279 01:20:24,070 --> 01:20:26,620 Actually, this is 4 1, because-- 1280 01:20:26,620 --> 01:20:28,660 that's 5, 5. 1281 01:20:28,660 --> 01:20:33,190 And the second lens, it should be same as the first one, 1, 1 1282 01:20:33,190 --> 01:20:36,700 over negative f 0 1. 1283 01:20:36,700 --> 01:20:38,320 So if you could compute this one, 1284 01:20:38,320 --> 01:20:47,125 then you are going to get this is 1 minus 1 0 and 1 0, 5 1, 1285 01:20:47,125 --> 01:20:55,070 and 1 minus 1 10, 1 0, 0. 1286 01:20:55,070 --> 01:21:14,190 And you're getting, it should be, 1 over 2 negative 3 over 20 1287 01:21:14,190 --> 01:21:23,870 and 5 1 over 2 and alpha object and x object. 1288 01:21:23,870 --> 01:21:28,100 So I should remind the thin lens case, which is 1 minus 1 1289 01:21:28,100 --> 01:21:29,930 over f 0 1. 1290 01:21:29,930 --> 01:21:34,310 So actually this guy is 1 over effective focal length. 1291 01:21:34,310 --> 01:21:39,790 So in this case, effective focal length should be 20 over 3. 1292 01:21:47,870 --> 01:21:50,380 So this is how to find the effective focal length 1293 01:21:50,380 --> 01:21:53,560 by using ray transfer matrices. 1294 01:21:53,560 --> 01:21:56,590 And you can find the back focal length and front focal length. 1295 01:21:56,590 --> 01:21:59,180 Just cascade another propagation, 1296 01:21:59,180 --> 01:22:01,280 you know, just like what we did in class. 1297 01:22:01,280 --> 01:22:06,140 So here and here, you can find the back focal plane, back 1298 01:22:06,140 --> 01:22:10,250 focal plane, and front focal plane, and front focal length, 1299 01:22:10,250 --> 01:22:15,480 and, you know, first and second principal plane. 1300 01:22:15,480 --> 01:22:19,810 So since Professor posted the detailed material, 1301 01:22:19,810 --> 01:22:21,730 he actually derived four different rays. 1302 01:22:21,730 --> 01:22:27,050 So please visit the website and do it by yourself. 1303 01:22:27,050 --> 01:22:27,550 Thank you. 1304 01:22:54,480 --> 01:22:55,730 GUEST SPEAKER: OK. 1305 01:22:55,730 --> 01:22:58,370 So, so far, we've been learning about lenses 1306 01:22:58,370 --> 01:23:02,535 and some sort of imaging techniques and principles. 1307 01:23:02,535 --> 01:23:03,910 But more than that, we've learned 1308 01:23:03,910 --> 01:23:06,380 about some optical principles that 1309 01:23:06,380 --> 01:23:10,400 regulate how light propagates, namely refraction, reflection 1310 01:23:10,400 --> 01:23:13,200 so far, total internal reflection. 1311 01:23:13,200 --> 01:23:17,120 So now the question is, how does nature does it? 1312 01:23:17,120 --> 01:23:20,690 And how has it evolved over the past several, several years? 1313 01:23:20,690 --> 01:23:22,700 And it actually comes down, according 1314 01:23:22,700 --> 01:23:25,910 to these reference here, to eight 1315 01:23:25,910 --> 01:23:28,220 different possible configurations of eyes. 1316 01:23:28,220 --> 01:23:30,310 And just by the way, defining an eye 1317 01:23:30,310 --> 01:23:33,890 is more complicated than just a simple photoreceptor. 1318 01:23:33,890 --> 01:23:35,930 So an eye, it's a little bit more 1319 01:23:35,930 --> 01:23:40,220 evolved like some sort of forming either an image 1320 01:23:40,220 --> 01:23:43,640 or a shadow based system. 1321 01:23:43,640 --> 01:23:47,900 So these type of eyes can be broadly categorized or divided 1322 01:23:47,900 --> 01:23:51,140 into chamber eyes, the ones that I'm showing here, OK? 1323 01:23:51,140 --> 01:23:53,840 So let's look at these eyes here and see what principles apply 1324 01:23:53,840 --> 01:23:55,560 from what we've learned so far. 1325 01:23:55,560 --> 01:23:58,220 So in C and in D, we can see what? 1326 01:23:58,220 --> 01:23:59,570 Snell's law, right? 1327 01:23:59,570 --> 01:24:00,860 So this is refraction. 1328 01:24:00,860 --> 01:24:03,590 So these type of eyes, again, like our human eye, 1329 01:24:03,590 --> 01:24:04,970 focus the light and form an image 1330 01:24:04,970 --> 01:24:08,960 in some sort of photoreceptors located here, right? 1331 01:24:08,960 --> 01:24:11,600 Then we have also reflection based. 1332 01:24:11,600 --> 01:24:13,220 These lenses here-- 1333 01:24:13,220 --> 01:24:15,050 I'm sorry, this mirror base here where 1334 01:24:15,050 --> 01:24:17,520 the light gets reflected and forms an image 1335 01:24:17,520 --> 01:24:19,840 in a photoreceptor here. 1336 01:24:19,840 --> 01:24:23,000 And now, we also have another one that is an aperture based, 1337 01:24:23,000 --> 01:24:26,270 or you can think of these has been as a natural pin hole. 1338 01:24:26,270 --> 01:24:29,760 And these images form by shadows, right? 1339 01:24:29,760 --> 01:24:31,880 So you see the shadow difference. 1340 01:24:31,880 --> 01:24:34,130 So these are the four types of chamber eyes. 1341 01:24:34,130 --> 01:24:37,310 But even more older type of eyes, 1342 01:24:37,310 --> 01:24:41,410 we have the compound eye, as we said in the very first lecture. 1343 01:24:41,410 --> 01:24:45,040 They're made out of a segmented array of many apertures 1344 01:24:45,040 --> 01:24:46,680 or many elements. 1345 01:24:46,680 --> 01:24:48,530 You can think about like many lenses 1346 01:24:48,530 --> 01:24:52,550 for the case of our refractive based system. 1347 01:24:52,550 --> 01:24:54,620 Or for our reflective based system, 1348 01:24:54,620 --> 01:24:57,410 it's several apertures that reflect the light somewhere 1349 01:24:57,410 --> 01:25:02,360 here and also focus it into some photoreceptive sensor. 1350 01:25:02,360 --> 01:25:04,280 Or in this case, for instance, here, 1351 01:25:04,280 --> 01:25:08,720 each one of these segments sees a very tiny field of view 1352 01:25:08,720 --> 01:25:12,260 and integrates all that field of view into that photoreceptor. 1353 01:25:12,260 --> 01:25:14,627 So in reality, it's not like the type of images 1354 01:25:14,627 --> 01:25:15,710 that we're used to, right? 1355 01:25:15,710 --> 01:25:18,020 It's just sort of like a blurry version 1356 01:25:18,020 --> 01:25:21,680 of our images in this case. 1357 01:25:21,680 --> 01:25:26,610 But of course, of very important interest to us 1358 01:25:26,610 --> 01:25:27,900 is how the human eye works. 1359 01:25:27,900 --> 01:25:32,060 Because as we know, we've experienced-- we have eyes-- 1360 01:25:32,060 --> 01:25:36,228 it's an extremely robust and very elaborate optical system. 1361 01:25:36,228 --> 01:25:38,520 I just said one of the problems we've had with the demo 1362 01:25:38,520 --> 01:25:40,770 is the adaptive to dynamic range. 1363 01:25:40,770 --> 01:25:42,670 Our eyes can do that very well. 1364 01:25:42,670 --> 01:25:45,480 We can also go to read a book or just 1365 01:25:45,480 --> 01:25:48,300 look at something far away. 1366 01:25:48,300 --> 01:25:50,530 And we can focus pretty well, too, right? 1367 01:25:50,530 --> 01:25:53,070 So all these things and all these adaptations 1368 01:25:53,070 --> 01:25:56,760 regulate these optical principles that we presented 1369 01:25:56,760 --> 01:25:59,110 are actually what made a lot of researchers 1370 01:25:59,110 --> 01:26:01,740 to try to study the eye and how the eye perceives light. 1371 01:26:01,740 --> 01:26:06,630 So that's under the field of visual perception. 1372 01:26:06,630 --> 01:26:08,280 So this is the structure of the eye. 1373 01:26:08,280 --> 01:26:11,980 The eye, it's essentially a sphere. 1374 01:26:11,980 --> 01:26:15,680 And it's all covered by some white opaque 1375 01:26:15,680 --> 01:26:17,600 layer called the sclera. 1376 01:26:17,600 --> 01:26:20,360 And that basically blocks straight light going through. 1377 01:26:20,360 --> 01:26:24,680 The only transparent section of the eye is the cornea, here. 1378 01:26:24,680 --> 01:26:27,200 So in the cornea, the light can go through. 1379 01:26:27,200 --> 01:26:31,040 And the cornea is the first refractive element of the eye. 1380 01:26:31,040 --> 01:26:31,970 It's curved. 1381 01:26:31,970 --> 01:26:35,600 It has a refractive index of something like 1.37, 1382 01:26:35,600 --> 01:26:38,960 which basically is the largest bending of light. 1383 01:26:38,960 --> 01:26:42,915 Because it comes from air to this 1.37 element. 1384 01:26:42,915 --> 01:26:45,290 So that's why you can think of that when you are actually 1385 01:26:45,290 --> 01:26:47,660 swimming it's hard to see. 1386 01:26:47,660 --> 01:26:48,380 Why? 1387 01:26:48,380 --> 01:26:50,810 Because the index of refraction of water 1388 01:26:50,810 --> 01:26:54,360 is 1.33, very close to that of the cornea. 1389 01:26:54,360 --> 01:26:58,010 So then the bending of light that occurs in this first layer 1390 01:26:58,010 --> 01:27:00,230 is very minimal. 1391 01:27:00,230 --> 01:27:03,890 So after the cornea, we have some chamber 1392 01:27:03,890 --> 01:27:08,330 filled with a solution called aqueous humor, which basically 1393 01:27:08,330 --> 01:27:13,080 nourishes the eye, especially the cornea, keeps it alive. 1394 01:27:13,080 --> 01:27:15,480 That is very similar to water. 1395 01:27:15,480 --> 01:27:18,030 Now, we have then the iris. 1396 01:27:18,030 --> 01:27:21,085 The iris is the element that controls-- well, 1397 01:27:21,085 --> 01:27:23,460 it's functional purpose is to control the amount of light 1398 01:27:23,460 --> 01:27:24,780 that your eye receives. 1399 01:27:24,780 --> 01:27:27,390 So as we know, the iris expands and contracts 1400 01:27:27,390 --> 01:27:30,360 depending on the amount of light present in the environment. 1401 01:27:30,360 --> 01:27:32,050 And actually, it's very impressive. 1402 01:27:32,050 --> 01:27:34,740 It can go from, like, 2 millimeters in diameter 1403 01:27:34,740 --> 01:27:37,050 to 8 millimeters in diameter depending 1404 01:27:37,050 --> 01:27:39,150 on the light condition. 1405 01:27:39,150 --> 01:27:42,750 But it's also responsible for the nice color of the eyes 1406 01:27:42,750 --> 01:27:46,560 that we see, like blue eyes, green eyes, you know? 1407 01:27:46,560 --> 01:27:47,760 That's the one to blame. 1408 01:27:51,150 --> 01:27:55,560 The aperture or the hole that we have is what we call the pupil. 1409 01:27:55,560 --> 01:27:58,570 So after the iris, we have the second most-- yeah? 1410 01:27:58,570 --> 01:28:03,230 AUDIENCE: Does the color of the eye [INAUDIBLE]?? 1411 01:28:03,230 --> 01:28:03,980 GUEST SPEAKER: No. 1412 01:28:03,980 --> 01:28:07,200 It's due to-- and actually it's very interesting. 1413 01:28:07,200 --> 01:28:10,460 So no, it basically just blocks the light. 1414 01:28:10,460 --> 01:28:13,450 It acts like an aperture, like of the aperture of your camera. 1415 01:28:13,450 --> 01:28:17,960 So if you like, photography would control the speed 1416 01:28:17,960 --> 01:28:21,200 or the f number of your system. 1417 01:28:21,200 --> 01:28:25,460 But the light reflected from the eye 1418 01:28:25,460 --> 01:28:27,770 gets the color in a similar principle 1419 01:28:27,770 --> 01:28:28,915 to why the sky is blue. 1420 01:28:28,915 --> 01:28:31,040 And I'll just let you investigate, because actually 1421 01:28:31,040 --> 01:28:31,970 it's very interesting. 1422 01:28:31,970 --> 01:28:34,677 And we used to have that problem in the first p set. 1423 01:28:34,677 --> 01:28:35,510 Why the sky is blue? 1424 01:28:35,510 --> 01:28:37,510 Why clouds are white? 1425 01:28:37,510 --> 01:28:40,207 And I guess the physical phenomena of why that happens 1426 01:28:40,207 --> 01:28:41,040 is very interesting. 1427 01:28:41,040 --> 01:28:42,470 So you guys should read. 1428 01:28:42,470 --> 01:28:45,390 It's in Hecht. 1429 01:28:45,390 --> 01:28:48,210 OK, so after the iris, we have these 1430 01:28:48,210 --> 01:28:51,830 what is called the crystalline lens, this lens here. 1431 01:28:51,830 --> 01:28:54,890 This is the second optical component most important 1432 01:28:54,890 --> 01:28:56,750 in our eye. 1433 01:28:56,750 --> 01:29:01,700 It's basically multilayer fibrous mass element covered 1434 01:29:01,700 --> 01:29:05,000 by some elastic membrane. 1435 01:29:05,000 --> 01:29:06,830 It's transparent. 1436 01:29:06,830 --> 01:29:10,040 And it can contract and deform itself in such a way 1437 01:29:10,040 --> 01:29:12,540 that it changes the effective focal length of this lens. 1438 01:29:12,540 --> 01:29:14,075 But you can think about this element 1439 01:29:14,075 --> 01:29:18,050 as some transparent quasi-onion. 1440 01:29:18,050 --> 01:29:20,240 But in addition, it has very interesting properties. 1441 01:29:20,240 --> 01:29:22,760 Because these lens is actually a gradient refractive index 1442 01:29:22,760 --> 01:29:26,600 lens, is, what we learned in some classes, a green lens, 1443 01:29:26,600 --> 01:29:27,840 this element here. 1444 01:29:27,840 --> 01:29:31,670 It has a refractive index in the core something like 1.4. 1445 01:29:31,670 --> 01:29:35,960 And it decays all the way to something like 1.38 1446 01:29:35,960 --> 01:29:37,640 to the edges. 1447 01:29:37,640 --> 01:29:39,968 So the light gets basically-- 1448 01:29:39,968 --> 01:29:40,760 see the transition. 1449 01:29:40,760 --> 01:29:43,410 So this is similar to the p set one. 1450 01:29:43,410 --> 01:29:45,450 And it basically sees multiple layers. 1451 01:29:45,450 --> 01:29:46,910 So depending indices of refraction, 1452 01:29:46,910 --> 01:29:49,930 it starts bending accordingly. 1453 01:29:49,930 --> 01:29:55,160 OK, so this lens will, in conjunction with this cornea, 1454 01:29:55,160 --> 01:29:57,680 form what we call or we could model 1455 01:29:57,680 --> 01:30:01,700 this system as a dual or double lens optical system. 1456 01:30:01,700 --> 01:30:05,365 And combined, they have an optical power-- 1457 01:30:05,365 --> 01:30:06,740 and remember the optical power is 1458 01:30:06,740 --> 01:30:12,110 1 over the focal length, which it's measure in diopters-- 1459 01:30:12,110 --> 01:30:14,200 of equivalent of something like 59 diopters, 1460 01:30:14,200 --> 01:30:17,750 just so you get an idea for an unaccommodated eye 1461 01:30:17,750 --> 01:30:21,330 or a relaxed eye just looking at infinity. 1462 01:30:21,330 --> 01:30:23,840 So then after this lens, we have another chamber 1463 01:30:23,840 --> 01:30:26,540 with another fluid called vitreous humor. 1464 01:30:26,540 --> 01:30:29,810 And it's another fluid that basically gives support 1465 01:30:29,810 --> 01:30:31,280 to the eye. 1466 01:30:31,280 --> 01:30:34,070 And going back to our question, I think someone in Singapore 1467 01:30:34,070 --> 01:30:39,500 had in the very first lecture, this fluid 1468 01:30:39,500 --> 01:30:45,090 has a lot of little particles floating, debris. 1469 01:30:45,090 --> 01:30:46,980 And actually sometimes you can see them. 1470 01:30:46,980 --> 01:30:48,560 And maybe many of you have seen them. 1471 01:30:48,560 --> 01:30:50,550 If you see to the sky or you squint your eyes 1472 01:30:50,550 --> 01:30:53,130 and see a bright light source, you 1473 01:30:53,130 --> 01:30:57,570 see the shadows of these little particles that are freely 1474 01:30:57,570 --> 01:31:00,030 flowing in the vitreous humor. 1475 01:31:00,030 --> 01:31:02,400 And you can see the fringes if you look carefully 1476 01:31:02,400 --> 01:31:05,890 of the light refracting that. 1477 01:31:05,890 --> 01:31:07,780 OK, so after that, the light basically 1478 01:31:07,780 --> 01:31:09,700 gets focused into the retina. 1479 01:31:09,700 --> 01:31:13,600 We know the retina is composed of photoreceptors, 1480 01:31:13,600 --> 01:31:16,330 photoreceptive cells, cone and rods. 1481 01:31:16,330 --> 01:31:20,020 And I'm going to explain those in a couple of slides. 1482 01:31:20,020 --> 01:31:23,020 And then we can also identify two other points. 1483 01:31:23,020 --> 01:31:26,110 We identify here that each of these cells 1484 01:31:26,110 --> 01:31:27,550 are connected to optical nerves. 1485 01:31:27,550 --> 01:31:29,860 And they all basically come together 1486 01:31:29,860 --> 01:31:32,840 into this output that goes to the brain. 1487 01:31:32,840 --> 01:31:34,777 And this is what constitutes the blind spot. 1488 01:31:34,777 --> 01:31:35,860 And I also explained that. 1489 01:31:35,860 --> 01:31:38,860 And we have a fun exercise in a second. 1490 01:31:38,860 --> 01:31:41,920 And we also have this other region, 1491 01:31:41,920 --> 01:31:45,340 which is like a spot of 3 millimeters in diameter, 1492 01:31:45,340 --> 01:31:45,950 more or less. 1493 01:31:45,950 --> 01:31:46,950 It's like a yellow spot. 1494 01:31:46,950 --> 01:31:48,790 It's called the macula. 1495 01:31:48,790 --> 01:31:51,670 And it has the largest concentration of cones. 1496 01:31:51,670 --> 01:31:55,120 And I'll explain what is its role, but it is very important. 1497 01:31:55,120 --> 01:31:58,030 Just that section here accounts for 90% to 95% 1498 01:31:58,030 --> 01:32:01,480 of our visual perception. 1499 01:32:01,480 --> 01:32:06,280 So I talked about the ability of these crystalline lens 1500 01:32:06,280 --> 01:32:08,800 to accommodate, change the focal length. 1501 01:32:08,800 --> 01:32:11,200 And similar to this demo that we were changing 1502 01:32:11,200 --> 01:32:14,060 the distance between these guys, well, in this case, 1503 01:32:14,060 --> 01:32:17,307 as I said before, this isn't fixed, right, 1504 01:32:17,307 --> 01:32:19,390 unless you have some sort of disease that actually 1505 01:32:19,390 --> 01:32:20,810 changes the length of your eye. 1506 01:32:20,810 --> 01:32:23,960 And that actually happens. 1507 01:32:23,960 --> 01:32:25,700 We can think of as this fixed. 1508 01:32:25,700 --> 01:32:29,350 So if we want to focus objects other than infinity, 1509 01:32:29,350 --> 01:32:31,952 we need to play now with a focal length, right? 1510 01:32:31,952 --> 01:32:33,910 So now, this lens has to be capable of changing 1511 01:32:33,910 --> 01:32:36,550 the effective focal length in such a way 1512 01:32:36,550 --> 01:32:38,530 that it will conserve or preserve 1513 01:32:38,530 --> 01:32:40,760 the imaging distance here. 1514 01:32:40,760 --> 01:32:44,740 So here, this lens does it by contracting or expanding 1515 01:32:44,740 --> 01:32:47,920 the ciliary muscles that are connected 1516 01:32:47,920 --> 01:32:51,010 via some fibers to these lens, right? 1517 01:32:51,010 --> 01:32:55,030 So in a relaxed state, you see this case here. 1518 01:32:55,030 --> 01:32:58,280 The radius of curvature of this lens, it's very large, 1519 01:32:58,280 --> 01:33:01,330 like closer to infinity, say, like very flat. 1520 01:33:01,330 --> 01:33:04,660 And then it focuses nice into the retina, 1521 01:33:04,660 --> 01:33:09,670 like a plane wave, whereas, for nearby objects, 1522 01:33:09,670 --> 01:33:12,010 these muscles are stressed. 1523 01:33:12,010 --> 01:33:14,980 So then the radius of curvature of the lens changes. 1524 01:33:14,980 --> 01:33:16,870 The focal length changes. 1525 01:33:16,870 --> 01:33:22,900 Now, this image is focusing to, again, the retina. 1526 01:33:22,900 --> 01:33:27,580 So we can think about some of the conditions that 1527 01:33:27,580 --> 01:33:31,540 would affect the normal behavior of the lens of the eye. 1528 01:33:31,540 --> 01:33:35,570 And the two very important conditions that we have 1529 01:33:35,570 --> 01:33:38,510 is farsighted or nearsighted. 1530 01:33:38,510 --> 01:33:42,260 So in the farsighted case, for example, our eye 1531 01:33:42,260 --> 01:33:46,130 lost its ability to focus effectively. 1532 01:33:46,130 --> 01:33:50,060 And in a relaxed state, it will actually form a focal point. 1533 01:33:50,060 --> 01:33:53,990 So the back focal point, it will be far away behind our retina. 1534 01:33:53,990 --> 01:33:56,720 So actually what you see would be a blurry image. 1535 01:33:56,720 --> 01:33:59,270 In their myopia case, or nearsighted, 1536 01:33:59,270 --> 01:34:00,170 you see the opposite. 1537 01:34:00,170 --> 01:34:03,050 Now, the point is formed in front of the retina. 1538 01:34:03,050 --> 01:34:05,330 And again, you see a blurry signal. 1539 01:34:05,330 --> 01:34:08,870 And by the way, a far point for a normal healthy eye 1540 01:34:08,870 --> 01:34:11,910 it starts from something like 5 meters on. 1541 01:34:11,910 --> 01:34:14,190 So 5 meters, more or less, what you can see there 1542 01:34:14,190 --> 01:34:16,100 is still like a five point. 1543 01:34:16,100 --> 01:34:18,710 So for someone that suffers myopia, typically 1544 01:34:18,710 --> 01:34:21,980 they see close by objects pretty fine. 1545 01:34:21,980 --> 01:34:24,290 But far objects, let's say further than 1546 01:34:24,290 --> 01:34:27,180 the far point, something like 5 meters away, 1547 01:34:27,180 --> 01:34:29,250 they become blurry. 1548 01:34:29,250 --> 01:34:32,990 And the near point, which is the counterpart of the far point, 1549 01:34:32,990 --> 01:34:34,640 is how close can we see. 1550 01:34:34,640 --> 01:34:36,920 That's a point that also varies with age. 1551 01:34:36,920 --> 01:34:39,695 Normally, teenagers the closer they can see 1552 01:34:39,695 --> 01:34:41,590 is something like 7 centimeters. 1553 01:34:41,590 --> 01:34:43,910 For us, maybe it's around 10 to 12-- 1554 01:34:43,910 --> 01:34:45,830 you can try later by just trying to focus 1555 01:34:45,830 --> 01:34:47,870 your notebook, centimeters. 1556 01:34:47,870 --> 01:34:50,130 And then if you are over 60 years old, 1557 01:34:50,130 --> 01:34:53,970 it goes up to 100 centimeters. 1558 01:34:53,970 --> 01:34:55,670 So basically, you can see how the eye 1559 01:34:55,670 --> 01:34:59,240 starts decaying in its ability to modify 1560 01:34:59,240 --> 01:35:01,580 this crystalline lens. 1561 01:35:01,580 --> 01:35:06,670 So to correct for these conditions, 1562 01:35:06,670 --> 01:35:09,360 we can use what we've learned so far, positive 1563 01:35:09,360 --> 01:35:11,370 and negative lenses, right? 1564 01:35:11,370 --> 01:35:12,660 So let's think about it. 1565 01:35:12,660 --> 01:35:16,170 In this case, the rays are not focusing enough, 1566 01:35:16,170 --> 01:35:18,150 are not bending enough, right? 1567 01:35:18,150 --> 01:35:20,760 Because they are basically focusing behind that. 1568 01:35:20,760 --> 01:35:24,000 So I want to help the rays to focus a little bit more. 1569 01:35:24,000 --> 01:35:29,310 So a positive power lens or a positive lens, like this one, 1570 01:35:29,310 --> 01:35:32,870 allows me to bend the rays inward more, right? 1571 01:35:32,870 --> 01:35:34,710 And this essentially what this is happening. 1572 01:35:34,710 --> 01:35:38,730 The positive power bends these parallel rays more and then 1573 01:35:38,730 --> 01:35:45,810 assures that this focuses in the retina. 1574 01:35:45,810 --> 01:35:47,640 So let me ask a question. 1575 01:35:47,640 --> 01:35:51,570 What do you think happens with the magnification 1576 01:35:51,570 --> 01:35:55,010 for this case? 1577 01:35:55,010 --> 01:35:56,260 Any idea? 1578 01:35:56,260 --> 01:35:57,830 For those of you that wear glasses, 1579 01:35:57,830 --> 01:36:02,750 do you guys see the world larger, magnified? 1580 01:36:02,750 --> 01:36:03,610 No? 1581 01:36:03,610 --> 01:36:05,880 There is shaking head, no. 1582 01:36:05,880 --> 01:36:07,390 Why do you think it's not the case? 1583 01:36:21,920 --> 01:36:25,240 OK-- so the power of the optical system, 1584 01:36:25,240 --> 01:36:26,840 the compound optical system. 1585 01:36:26,840 --> 01:36:31,450 So if you work out actually the power of the cornea 1586 01:36:31,450 --> 01:36:33,490 plus crystalline lens-- which I said 1587 01:36:33,490 --> 01:36:36,220 is something like 59 for a healthy eye. 1588 01:36:36,220 --> 01:36:38,650 But in reality when it's unhealthy, it changes. 1589 01:36:38,650 --> 01:36:45,020 And if you consider the power added by this element here, 1590 01:36:45,020 --> 01:36:48,470 it basically comes down to the same power as the healthy eye. 1591 01:36:48,470 --> 01:36:52,670 So therefore, you don't add or subtract any power. 1592 01:36:52,670 --> 01:36:55,310 So therefore, the magnification stays the same. 1593 01:36:55,310 --> 01:36:57,630 For the myopia case, we can use the opposite. 1594 01:36:57,630 --> 01:36:59,840 We can use a negative lens, as shown here, 1595 01:36:59,840 --> 01:37:03,043 to actually bend the rays a little bit outwards, right? 1596 01:37:03,043 --> 01:37:04,460 So essentially this is interesting 1597 01:37:04,460 --> 01:37:08,300 because, again the myopia case you cannot you see far away 1598 01:37:08,300 --> 01:37:12,890 objects blurry right but some objects are closer than 1599 01:37:12,890 --> 01:37:15,740 the fire point you can see them fine so what the negative lens 1600 01:37:15,740 --> 01:37:16,590 is doing-- 1601 01:37:16,590 --> 01:37:18,770 and again, going back to these virtual images-- 1602 01:37:18,770 --> 01:37:23,450 is bringing a far away object into a near distance closer 1603 01:37:23,450 --> 01:37:24,770 to the far point. 1604 01:37:24,770 --> 01:37:28,310 As you can see, this appears to come from some virtual point 1605 01:37:28,310 --> 01:37:30,770 here that is closer from a region 1606 01:37:30,770 --> 01:37:32,840 that you can see naturally with your eye. 1607 01:37:32,840 --> 01:37:34,670 So therefore, intuitively this is 1608 01:37:34,670 --> 01:37:38,825 how this ray makes this lens still project 1609 01:37:38,825 --> 01:37:40,910 the image into the retina. 1610 01:37:40,910 --> 01:37:43,260 But as a side effect, the near point-- yup? 1611 01:37:43,260 --> 01:37:45,730 AUDIENCE: So can people [INAUDIBLE] 1612 01:37:45,730 --> 01:37:49,190 focal point closer than [INAUDIBLE]?? 1613 01:37:49,190 --> 01:37:49,980 GUEST SPEAKER: No. 1614 01:37:49,980 --> 01:37:52,800 And actually, yeah, that was the second point 1615 01:37:52,800 --> 01:37:54,390 I was going to say. 1616 01:37:54,390 --> 01:37:58,243 As a consequence of this, your near point, 1617 01:37:58,243 --> 01:37:59,910 which I said that for like a healthy eye 1618 01:37:59,910 --> 01:38:04,440 would be something like 12 centimeters, becomes larger. 1619 01:38:04,440 --> 01:38:05,790 So people that have myopia-- 1620 01:38:05,790 --> 01:38:07,290 I don't know if there's anyone here. 1621 01:38:07,290 --> 01:38:10,035 But probably you know that sometimes, 1622 01:38:10,035 --> 01:38:11,910 if you want to read a very close by document, 1623 01:38:11,910 --> 01:38:13,698 you need to remove your glasses, right? 1624 01:38:13,698 --> 01:38:15,240 And people adjust OK for small print. 1625 01:38:15,240 --> 01:38:16,890 They get out their glasses. 1626 01:38:16,890 --> 01:38:19,860 And for far away objects, they put their glasses on and see. 1627 01:38:24,640 --> 01:38:29,348 All right, so any other questions? 1628 01:38:34,610 --> 01:38:37,850 OK, so the retina, the retina has a bunch 1629 01:38:37,850 --> 01:38:40,550 of cells that are photoreceptive cells that 1630 01:38:40,550 --> 01:38:45,920 can be classified into two types, rods and cones, right? 1631 01:38:45,920 --> 01:38:49,295 And we can see here rods and cones. 1632 01:38:49,295 --> 01:38:50,920 For those of you that like photography, 1633 01:38:50,920 --> 01:38:53,920 you can think about the rods being equivalent 1634 01:38:53,920 --> 01:38:57,913 of a high speed black and white film. 1635 01:38:57,913 --> 01:38:59,080 What is the meaning of that? 1636 01:38:59,080 --> 01:39:02,050 It basically means that is very, very sensitive to light, OK? 1637 01:39:02,050 --> 01:39:05,770 For very low levels of light, you can detect them very fine. 1638 01:39:05,770 --> 01:39:09,240 But it's insensitive to color and gives you 1639 01:39:09,240 --> 01:39:11,190 images that are not really good quality, 1640 01:39:11,190 --> 01:39:15,450 sort of like blurry type of images, right? 1641 01:39:15,450 --> 01:39:17,040 The cones, on the other hand, can 1642 01:39:17,040 --> 01:39:24,160 be thought of as low contrast or low speed color film. 1643 01:39:24,160 --> 01:39:27,660 So the cones have cells that are sensitive to red, green, blue, 1644 01:39:27,660 --> 01:39:30,230 are responsible for the colors that we see 1645 01:39:30,230 --> 01:39:34,540 and are also responsible of the nice, sharp images. 1646 01:39:34,540 --> 01:39:39,030 So all around the retina, we have 1647 01:39:39,030 --> 01:39:40,320 sort of a combination of both. 1648 01:39:40,320 --> 01:39:44,520 Although as you can see here in the density plot shown here, 1649 01:39:44,520 --> 01:39:47,130 there is a region that is called the macula. 1650 01:39:47,130 --> 01:39:49,530 And inside the macula, there is even a smaller region 1651 01:39:49,530 --> 01:39:51,390 of something like 300 micron. 1652 01:39:51,390 --> 01:39:52,500 That's called the fovea. 1653 01:39:52,500 --> 01:39:55,807 That has the highest concentration of cones, again, 1654 01:39:55,807 --> 01:39:58,140 those responsible for the color vision-- as you can see, 1655 01:39:58,140 --> 01:39:59,400 the plot just peaks here-- 1656 01:39:59,400 --> 01:40:02,520 and almost no rods, right? 1657 01:40:02,520 --> 01:40:04,380 This is called the fovea centralis. 1658 01:40:04,380 --> 01:40:07,530 And that's responsible of the central vision. 1659 01:40:07,530 --> 01:40:09,030 And basically, that's the one that I 1660 01:40:09,030 --> 01:40:11,700 was saying that's responsible for 90% to 95% 1661 01:40:11,700 --> 01:40:14,050 of the visual perception that we have. 1662 01:40:14,050 --> 01:40:15,780 So it's interesting to note that, 1663 01:40:15,780 --> 01:40:20,605 in contrast to a normal camera, there sampling of these 1664 01:40:20,605 --> 01:40:22,980 photoreceptor elements-- so you can think of it as, like, 1665 01:40:22,980 --> 01:40:24,960 pixels-- 1666 01:40:24,960 --> 01:40:26,160 it's different. 1667 01:40:26,160 --> 01:40:30,270 Outside the macula, they are large and course. 1668 01:40:30,270 --> 01:40:33,390 As you can see, these rods are just 1669 01:40:33,390 --> 01:40:37,980 responsible for the peripheral vision and black and white. 1670 01:40:37,980 --> 01:40:41,070 But in this macula, they are very concentrated and dense. 1671 01:40:41,070 --> 01:40:44,670 And as a matter of fact, the cones inside this region, 1672 01:40:44,670 --> 01:40:48,270 so when they are here, they have a different diameter 1673 01:40:48,270 --> 01:40:50,545 than the ones outside. 1674 01:40:50,545 --> 01:40:52,170 There is something like a factor of two 1675 01:40:52,170 --> 01:40:53,253 that are actually thinner. 1676 01:40:53,253 --> 01:40:56,570 So they are very close packed together. 1677 01:40:56,570 --> 01:40:58,960 So you can see very sharp images here. 1678 01:41:01,780 --> 01:41:06,250 As I mentioned before, each of these photoreceptors 1679 01:41:06,250 --> 01:41:08,260 is connected to these nerves that all 1680 01:41:08,260 --> 01:41:12,170 bundle up together and go to the blindspot, shown here. 1681 01:41:12,170 --> 01:41:17,130 Now, have you guys been bothered by a blind spot all your lives? 1682 01:41:17,130 --> 01:41:18,100 Not really. 1683 01:41:18,100 --> 01:41:18,600 Why? 1684 01:41:18,600 --> 01:41:20,142 Because as you can see, it's actually 1685 01:41:20,142 --> 01:41:22,650 just blocking a very small portion of your vision. 1686 01:41:22,650 --> 01:41:26,400 As I said, a lot of the vision or visual perception 1687 01:41:26,400 --> 01:41:27,887 happens in this region, right? 1688 01:41:27,887 --> 01:41:29,470 This is not true if you have a camera. 1689 01:41:29,470 --> 01:41:32,700 If I have a camera and we have a bunch of bad pixels like that, 1690 01:41:32,700 --> 01:41:33,930 it might corrupt our system. 1691 01:41:33,930 --> 01:41:34,763 And then we're done. 1692 01:41:34,763 --> 01:41:37,050 Like, if a microscope experiment, for example, 1693 01:41:37,050 --> 01:41:37,940 forget about it. 1694 01:41:37,940 --> 01:41:39,750 We lose a lot of pixels, and then the image 1695 01:41:39,750 --> 01:41:41,430 gets really corrupted. 1696 01:41:41,430 --> 01:41:43,683 So I brought a little card. 1697 01:41:43,683 --> 01:41:44,850 I'm going to pass it around. 1698 01:41:44,850 --> 01:41:46,365 I have actually multiple of these. 1699 01:41:46,365 --> 01:41:49,110 So this is a fun experiment. 1700 01:41:49,110 --> 01:41:53,400 It has, in the top part, a little cross 1701 01:41:53,400 --> 01:41:55,980 and a little black circle. 1702 01:41:55,980 --> 01:41:57,510 In the bottom part-- another cross 1703 01:41:57,510 --> 01:42:00,295 and a line that is basically truncated, right? 1704 01:42:00,295 --> 01:42:01,920 So what you're going to do when you get 1705 01:42:01,920 --> 01:42:06,900 it is that you're going to have the cross to your right side. 1706 01:42:06,900 --> 01:42:09,750 And you're going to close your right eye. 1707 01:42:09,750 --> 01:42:12,390 And then you're going to just play with this distance 1708 01:42:12,390 --> 01:42:13,380 staring at the cross. 1709 01:42:13,380 --> 01:42:16,950 So you're going to focus your left eye at the cross. 1710 01:42:16,950 --> 01:42:19,920 And you're going to find a position here 1711 01:42:19,920 --> 01:42:22,380 in which the circle will disappear, right? 1712 01:42:22,380 --> 01:42:24,210 Because the circle essentially will 1713 01:42:24,210 --> 01:42:27,880 be imaged into this blind spot, and we're not going to see it. 1714 01:42:27,880 --> 01:42:30,060 But the second one is more interesting. 1715 01:42:30,060 --> 01:42:34,500 Because you do the same thing, and the hole here disappears. 1716 01:42:34,500 --> 01:42:37,300 But not only disappears, it gets filled with a line. 1717 01:42:37,300 --> 01:42:39,275 So you'll see a continuous line. 1718 01:42:39,275 --> 01:42:41,400 And it's more shocking, because basically our brain 1719 01:42:41,400 --> 01:42:43,525 fills that missing information. 1720 01:42:43,525 --> 01:42:44,900 It's actually pretty interesting. 1721 01:42:44,900 --> 01:42:47,067 So I don't know if you can help me pass this around. 1722 01:43:13,328 --> 01:43:14,910 How do I go to the next one? 1723 01:43:19,420 --> 01:43:21,060 [INAUDIBLE] this one? 1724 01:43:24,006 --> 01:43:35,872 OK, takes forever. 1725 01:43:35,872 --> 01:43:37,830 OK. 1726 01:43:37,830 --> 01:43:44,660 So this is a simulation that it was done by a group in Caltech. 1727 01:43:44,660 --> 01:43:46,233 They were trying to simulate what 1728 01:43:46,233 --> 01:43:47,900 would be the image that our eye actually 1729 01:43:47,900 --> 01:43:49,530 is projecting at the retina. 1730 01:43:49,530 --> 01:43:51,650 What is exactly what we see? 1731 01:43:51,650 --> 01:43:53,600 And interestingly enough, compared 1732 01:43:53,600 --> 01:43:57,830 to a normal image of the same scene produced by a CCD camera, 1733 01:43:57,830 --> 01:44:00,470 as you can see, the image is really blurry 1734 01:44:00,470 --> 01:44:03,230 in the surroundings, very sharp in the center, 1735 01:44:03,230 --> 01:44:06,670 as we described due to the sampling, et cetera. 1736 01:44:06,670 --> 01:44:11,410 So the eye tries to take advantage of the fact 1737 01:44:11,410 --> 01:44:14,830 that it has a very small, very sharp region in focus 1738 01:44:14,830 --> 01:44:16,840 as much as it can. 1739 01:44:16,840 --> 01:44:21,190 And the way it does it is by jittering the eye, 1740 01:44:21,190 --> 01:44:25,420 moving it at a frequency of something like 30 to 70 Hertz, 1741 01:44:25,420 --> 01:44:28,540 to scan a given scene and try to collect as much information 1742 01:44:28,540 --> 01:44:31,722 to create the scene that we perceive in our brain. 1743 01:44:31,722 --> 01:44:33,430 And also, there is some interesting image 1744 01:44:33,430 --> 01:44:36,060 processing to try to account for this blurring. 1745 01:44:36,060 --> 01:44:37,810 Or you can think of that, for those of you 1746 01:44:37,810 --> 01:44:40,102 that are in signal processing, deep learning algorithms 1747 01:44:40,102 --> 01:44:41,860 embedded in our brains. 1748 01:44:41,860 --> 01:44:43,350 I think it's pretty interesting. 1749 01:44:43,350 --> 01:44:44,965 So the phenomena of moving of the eye, 1750 01:44:44,965 --> 01:44:46,675 it's called saccadic motion. 1751 01:44:51,820 --> 01:44:54,290 Also, the cones and the rods, as I said, 1752 01:44:54,290 --> 01:44:55,640 are connected with nerves. 1753 01:44:55,640 --> 01:45:01,150 But it was first proposed by studying the eye of a cat 1754 01:45:01,150 --> 01:45:03,190 and then for humans that the eye actually 1755 01:45:03,190 --> 01:45:07,812 has this type of responds to a light as stimulus, 1756 01:45:07,812 --> 01:45:09,770 that in some regions it's going to be positive. 1757 01:45:09,770 --> 01:45:12,320 Some regions it's going to be negative following what 1758 01:45:12,320 --> 01:45:15,860 is called a Mexican-hat trend. 1759 01:45:15,860 --> 01:45:19,200 And actually, this response is what 1760 01:45:19,200 --> 01:45:22,310 is responsible for many optical illusions 1761 01:45:22,310 --> 01:45:25,160 that we see, for example, this one. 1762 01:45:25,160 --> 01:45:26,240 So what do you guys see? 1763 01:45:29,602 --> 01:45:31,310 You've seen this one probably before, no? 1764 01:45:34,260 --> 01:45:36,500 So you see this flickering gray dots 1765 01:45:36,500 --> 01:45:38,128 that are really not there right 1766 01:45:38,128 --> 01:45:40,670 and if you try to focus your eye and if you are like as close 1767 01:45:40,670 --> 01:45:43,400 as I am to the projector and I'm focusing my eye 1768 01:45:43,400 --> 01:45:46,240 here I don't see anything of the at least at that point I don't 1769 01:45:46,240 --> 01:45:48,740 see any great does however if I focus in another point right 1770 01:45:48,740 --> 01:45:51,220 I'm also seeing this flicker.