1 00:00:01,168 --> 00:00:02,679 - Here's something confusing. 2 00:00:02,679 --> 00:00:04,489 If I showed you two lenses 3 00:00:04,489 --> 00:00:06,034 that had two different focal lengths. 4 00:00:06,034 --> 00:00:08,618 One had a little focal length, one had a big focal length, 5 00:00:08,618 --> 00:00:12,879 and asked you which one of these is more powerful. 6 00:00:12,879 --> 00:00:14,544 Which lens has the higher power? 7 00:00:14,544 --> 00:00:16,831 You might confused about what power means, 8 00:00:16,831 --> 00:00:18,548 but if you had to pick, I think a lot of people 9 00:00:18,548 --> 00:00:20,304 would probably pick this lens down here 10 00:00:20,304 --> 00:00:24,129 because we automatically think bigger means more powerful, 11 00:00:24,129 --> 00:00:27,539 so a bigger focal length means that it's more powerful. 12 00:00:27,539 --> 00:00:29,379 But that doesn't really make a lot of sense, 13 00:00:29,379 --> 00:00:31,301 because let me show you what happens if we send in 14 00:00:31,301 --> 00:00:33,974 parallel light rays into these lenses. 15 00:00:33,974 --> 00:00:36,088 Well, what do they do with these light rays? 16 00:00:36,088 --> 00:00:36,929 We know what they do. 17 00:00:36,929 --> 00:00:39,223 They send light rays to the focal point 18 00:00:39,223 --> 00:00:41,232 because that's what convex lenses do. 19 00:00:41,232 --> 00:00:43,112 So it'll look something like this. 20 00:00:43,112 --> 00:00:47,934 So this light ray gets sent there, that gets sent there, 21 00:00:47,934 --> 00:00:51,445 this one through here and this one through here. 22 00:00:51,445 --> 00:00:52,830 That's what happens with that lens. 23 00:00:52,830 --> 00:00:54,433 What happens down here? 24 00:00:54,433 --> 00:00:58,488 This lens isn't going to bend the light as much. 25 00:00:58,488 --> 00:01:01,630 If your focal length is farther away, look at, 26 00:01:01,630 --> 00:01:03,557 it's bending the light, yes, 27 00:01:03,557 --> 00:01:06,343 but the light has not been impacted. 28 00:01:06,343 --> 00:01:10,268 It's original trajectory has not been as influenced 29 00:01:10,268 --> 00:01:13,705 as the other lens up here with the smaller focal lengths. 30 00:01:13,705 --> 00:01:18,705 So it turns out, lenses that have a small focal length 31 00:01:19,149 --> 00:01:21,525 will actually have more a greater impact 32 00:01:21,525 --> 00:01:24,522 on the trajectory of the light 33 00:01:24,522 --> 00:01:26,673 than lenses do with a larger focal length. 34 00:01:26,673 --> 00:01:27,815 Imagine putting this focal length 35 00:01:27,815 --> 00:01:30,009 all the way out at infinity, 36 00:01:30,009 --> 00:01:31,964 well then it really wouldn't affect the light at all. 37 00:01:31,964 --> 00:01:33,655 The light would just continue straight through 38 00:01:33,655 --> 00:01:36,579 because the amount it's bending is hardly anything. 39 00:01:36,579 --> 00:01:41,232 So this is a little weird, but small focal length 40 00:01:41,232 --> 00:01:43,094 means a powerful lens. 41 00:01:43,094 --> 00:01:47,269 So rather than talk about focal length, 42 00:01:47,269 --> 00:01:51,113 optometrists and ophthalmologists often talk about 43 00:01:51,113 --> 00:01:56,113 lens power, so the lens power is just defined to be - 44 00:01:57,997 --> 00:01:59,974 this isn't power like jules per second - 45 00:01:59,974 --> 00:02:04,816 this is lens powers defined to be one over the focal length 46 00:02:04,816 --> 00:02:09,816 and so if you're using SI units, we'd have one over meters 47 00:02:11,105 --> 00:02:13,047 and that's given a special name. 48 00:02:13,047 --> 00:02:16,354 That's called diopters. 49 00:02:16,414 --> 00:02:19,591 So a one over a meter is called a diopter 50 00:02:19,591 --> 00:02:22,633 and this is what optometrists and ophthalmologists use 51 00:02:22,633 --> 00:02:25,888 to measure lens power in, it's represented with a D. 52 00:02:25,888 --> 00:02:27,060 This makes a little more sense 53 00:02:27,060 --> 00:02:30,623 because if your diopter measurement is large, 54 00:02:30,623 --> 00:02:32,342 that means powerful lens. 55 00:02:32,342 --> 00:02:33,953 And if your diopter measurement is small, 56 00:02:33,953 --> 00:02:36,772 that means not as powerful of a lens. 57 00:02:36,772 --> 00:02:39,770 And so in other words, if this focal length up here 58 00:02:39,770 --> 00:02:44,019 was 10 centimeters, well I'd have to convert it to meters, 59 00:02:44,019 --> 00:02:47,994 so 10 centimeters is .1 meters, and then to get 60 00:02:47,994 --> 00:02:51,323 the power, the power for this lens would be 61 00:02:51,323 --> 00:02:53,961 one over the focal length in meters, 62 00:02:53,961 --> 00:02:56,830 so I'd have one over .1 meters, 63 00:02:56,830 --> 00:03:01,154 and that would mean this is a 10 diopter lens. 64 00:03:01,168 --> 00:03:05,175 That's supposed to be a D, 10 diopter. 65 00:03:05,433 --> 00:03:10,433 And down here, if this one was more like 50 centimeters, 66 00:03:10,498 --> 00:03:14,170 I'd say that the power is one over f, 67 00:03:14,170 --> 00:03:18,769 I've got to convert to meters, so one over .5 meters, 68 00:03:18,769 --> 00:03:23,769 and I'd get two diopter, or two one over meters, 69 00:03:24,329 --> 00:03:28,954 so a diopter has units of one over meters, 70 00:03:28,954 --> 00:03:31,179 or meters to the negative one. 71 00:03:31,179 --> 00:03:33,292 Now I'm kind of lying a little bit. 72 00:03:33,292 --> 00:03:37,006 Spherical lenses don't actually send their light rays 73 00:03:37,006 --> 00:03:38,997 exactly through the focal point. 74 00:03:38,997 --> 00:03:42,073 Not all of them if you're sending parallel light rays 75 00:03:42,073 --> 00:03:44,701 like this through the whole face of the lens. 76 00:03:44,701 --> 00:03:46,738 Some of them are going to miss a little bit 77 00:03:46,738 --> 00:03:48,722 and it's called spherical aberration, 78 00:03:48,722 --> 00:03:50,468 so another thing that you'd be interested in 79 00:03:50,468 --> 00:03:53,114 if you're trying to craft precise lenses 80 00:03:53,114 --> 00:03:56,911 for a specific purpose is the idea of spherical aberration. 81 00:03:56,911 --> 00:03:58,227 Let me show you what that's all about. 82 00:03:58,227 --> 00:03:59,891 So let me hide these. 83 00:03:59,891 --> 00:04:02,569 So what's supposed to happen, parallel light rays 84 00:04:02,569 --> 00:04:06,296 are supposed to get sent exactly through the focal point, 85 00:04:06,296 --> 00:04:07,915 boom, right there. 86 00:04:07,915 --> 00:04:12,915 What actually happens is, parallel light rays get sent - 87 00:04:14,838 --> 00:04:17,778 the ones on top get bent a little bit more 88 00:04:17,778 --> 00:04:19,837 and they might focus around this point, 89 00:04:19,837 --> 00:04:22,077 and the ones closer into the center of the lens 90 00:04:22,077 --> 00:04:27,077 get sent over here, and so this spherical convex lens 91 00:04:27,980 --> 00:04:31,022 kind of focuses all the light to a point, 92 00:04:31,022 --> 00:04:33,731 but it creates a little bit of a blur here, 93 00:04:33,731 --> 00:04:37,411 so this is called spherical aberration 94 00:04:37,411 --> 00:04:42,411 and this is an inherit problem with spherical lenses. 95 00:04:43,061 --> 00:04:45,609 The light that gets sent through the top gets bent 96 00:04:45,609 --> 00:04:47,860 a little bit more than the light that gets sent more 97 00:04:47,860 --> 00:04:50,801 toward the middle, and so you've got this problem. 98 00:04:50,801 --> 00:04:53,158 This is a problem if you have a highly precise situation 99 00:04:53,158 --> 00:04:55,866 that you need to create an image for. 100 00:04:55,866 --> 00:04:57,116 It might get a little bit blurry 101 00:04:57,116 --> 00:04:58,997 because of spherical aberration. 102 00:04:58,997 --> 00:04:59,907 So you might wonder, 103 00:04:59,907 --> 00:05:02,318 why does this spherical aberration happen? 104 00:05:02,318 --> 00:05:03,614 It has to do with the fact that, 105 00:05:03,614 --> 00:05:06,296 you know how we're always calling these thin lenses, 106 00:05:06,296 --> 00:05:08,959 you might wonder, why are we always calling them thin? 107 00:05:08,959 --> 00:05:10,461 Why do they got to be thin? 108 00:05:10,461 --> 00:05:14,275 It's because if they're thin, all these angles involved 109 00:05:14,275 --> 00:05:17,922 for these normal lines are going to be small. 110 00:05:17,922 --> 00:05:20,503 And if the angles are small, that's a good thing 111 00:05:20,503 --> 00:05:23,212 because in physics, physicists love this one. 112 00:05:23,212 --> 00:05:24,790 Here's a trick we like playing. 113 00:05:24,790 --> 00:05:29,493 Sine theta for small angles is approxoimately just theta 114 00:05:29,493 --> 00:05:31,640 so there's all kinds of approximations here 115 00:05:31,640 --> 00:05:34,237 that you can use if the lenses are thin, 116 00:05:34,237 --> 00:05:36,733 and you get that they all go basically 117 00:05:36,733 --> 00:05:38,951 through the focal point, but there's a difference 118 00:05:38,951 --> 00:05:41,336 between basically going through the focal point 119 00:05:41,336 --> 00:05:43,422 and exactly going through the focal point. 120 00:05:43,422 --> 00:05:45,177 The farther you get up here, 121 00:05:45,177 --> 00:05:46,933 the larger this angle is going to be, 122 00:05:46,933 --> 00:05:48,813 the more deviation you're going to get. 123 00:05:48,813 --> 00:05:53,542 It's just a problem inherit to this spherical lens. 124 00:05:53,542 --> 00:05:55,684 The problem is, it's easy to mix spherical lenses. 125 00:05:55,684 --> 00:05:57,853 I mean, it's easy to make a perfectly spherical shape. 126 00:05:57,853 --> 00:05:59,779 If you wanted to make one that did send them 127 00:05:59,779 --> 00:06:02,523 exactly through the center, it would be harder to do. 128 00:06:02,523 --> 00:06:03,938 You'd have to pick a different shape 129 00:06:03,938 --> 00:06:07,753 because spheres just don't cut it in that case. 130 00:06:08,535 --> 00:06:11,493 Spherical aberration's not even the only type of aberration. 131 00:06:11,493 --> 00:06:12,968 There's other kinds of aberration. 132 00:06:12,968 --> 00:06:16,741 One of them is chromatic aberration, 133 00:06:16,741 --> 00:06:21,446 and as the name suggests, this has to do with color 134 00:06:21,446 --> 00:06:25,854 and remember, dispersion with lenses or any material, 135 00:06:25,854 --> 00:06:30,472 dispersion says that some colors bend more than others. 136 00:06:30,472 --> 00:06:33,592 So some colors experience a higher index of refraction 137 00:06:33,592 --> 00:06:37,127 red turns out experiences a smaller index of refraction, 138 00:06:37,127 --> 00:06:41,348 so these red rays would get sent that get bent 139 00:06:41,348 --> 00:06:44,038 a little bit less than yellow. 140 00:06:44,038 --> 00:06:45,226 So they might meet up there. 141 00:06:45,226 --> 00:06:50,047 And blue rays, blue gets bent more higher frequency, 142 00:06:50,047 --> 00:06:51,778 light gets bent more. 143 00:06:51,778 --> 00:06:54,891 So you'd get these colors separating. 144 00:06:54,891 --> 00:06:57,992 So this is another problem with spherical lenses 145 00:06:57,992 --> 00:06:58,999 or any type of lens, 146 00:06:58,999 --> 00:07:01,741 is you might get some sort of chromatic aberration. 147 00:07:01,741 --> 00:07:03,120 So these are things to look out for 148 00:07:03,120 --> 00:07:06,228 if you're trying to create a precise optical instrument. 149 00:07:07,504 --> 00:07:10,072 One of the most precise optical instruments 150 00:07:10,072 --> 00:07:11,825 is the human eye, and in the human eye, 151 00:07:11,825 --> 00:07:13,086 you have a lot of parts. 152 00:07:13,086 --> 00:07:15,129 Up front you've got the cornea. 153 00:07:15,129 --> 00:07:17,333 This acts like the main lens. 154 00:07:17,333 --> 00:07:19,151 This is the front lens here. 155 00:07:19,151 --> 00:07:21,195 This does most of the bending of the light, 156 00:07:21,195 --> 00:07:23,110 but you've also got this inner lens 157 00:07:23,110 --> 00:07:24,999 that's just called the lens. 158 00:07:24,999 --> 00:07:27,653 And this inner lens is more adjustable. 159 00:07:27,653 --> 00:07:29,978 This can sort of make fine adjustments 160 00:07:29,978 --> 00:07:32,765 to what you're looking at depending on how close 161 00:07:32,765 --> 00:07:35,035 something is to your eye, this can adjust, 162 00:07:35,035 --> 00:07:38,830 and these ciliary muscles are muscles that can 163 00:07:38,830 --> 00:07:43,496 exert a force on this lens and can change the shape of it. 164 00:07:43,496 --> 00:07:44,581 This is bendable. 165 00:07:44,581 --> 00:07:46,118 This inner lens is bendable, 166 00:07:46,118 --> 00:07:49,131 and depending on what distance away the object is, 167 00:07:49,131 --> 00:07:52,498 these ciliary muscles can change the shape of this lens 168 00:07:52,498 --> 00:07:56,385 to make sure that the image is formed right on your retina. 169 00:07:56,385 --> 00:08:00,885 This back wall acts as the screen of your eyes, 170 00:08:00,885 --> 00:08:02,398 and this is where you want the image to form. 171 00:08:02,398 --> 00:08:05,842 If you form a nice clean precise image on your retina, 172 00:08:05,842 --> 00:08:09,074 the optical nerve can take that information to your brain 173 00:08:09,074 --> 00:08:10,990 and you get a nice clean image 174 00:08:10,990 --> 00:08:12,719 of whatever it is you're looking for. 175 00:08:12,719 --> 00:08:14,183 Maybe it's a tree. 176 00:08:14,183 --> 00:08:17,820 Now the weird thing is, so here's your tree. 177 00:08:17,820 --> 00:08:20,824 Maybe you see this, but here's the weird thing. 178 00:08:20,824 --> 00:08:25,621 You've got this cornea and this inner lens are both convex 179 00:08:25,621 --> 00:08:27,708 and if you're going to see a real image 180 00:08:27,708 --> 00:08:30,472 that's actually projected on a screen here, 181 00:08:30,472 --> 00:08:33,385 this is actually going to be an upside down image. 182 00:08:33,385 --> 00:08:37,723 Your tree image that forms actually on your retina 183 00:08:37,724 --> 00:08:40,451 is an upside down real image. 184 00:08:40,451 --> 00:08:43,020 So your optical nerve sends that information to your brain. 185 00:08:43,020 --> 00:08:47,613 Somewhere in your brain it flips it over and then you get 186 00:08:47,613 --> 00:08:51,574 a clean image of a tree that's right side up. 187 00:08:51,574 --> 00:08:55,045 So, if you were looking at a far away tree - 188 00:08:55,045 --> 00:08:58,186 let's say the tree was really far away 189 00:08:58,186 --> 00:09:01,152 and these light rays were coming in basically parallel 190 00:09:01,152 --> 00:09:06,097 you'd want to make sure your cornea and inner lens 191 00:09:06,097 --> 00:09:08,038 were able to focus these light rays 192 00:09:08,038 --> 00:09:13,038 from some point on the tree, straight into the retina, 193 00:09:14,217 --> 00:09:17,824 and you form a nice clean image at the retina. 194 00:09:17,824 --> 00:09:18,951 So that's good. 195 00:09:18,951 --> 00:09:20,360 Let's say you were able to do that just fine 196 00:09:20,360 --> 00:09:22,658 and you get a clean image of this tree, 197 00:09:22,658 --> 00:09:24,770 what if you got a little bit closer? 198 00:09:24,770 --> 00:09:28,307 Maybe you get a little bit closer, and now the image 199 00:09:28,307 --> 00:09:30,664 isn't so clean, so you got this tree here. 200 00:09:30,664 --> 00:09:33,204 You're looking at a particular part of it. 201 00:09:33,204 --> 00:09:35,255 Maybe you're looking at this part right here. 202 00:09:35,255 --> 00:09:36,586 You're a little closer. 203 00:09:36,586 --> 00:09:38,962 This part comes in here. 204 00:09:38,962 --> 00:09:40,862 We're looking at light rays out of here. 205 00:09:40,862 --> 00:09:43,040 It's not going to get bent as much. 206 00:09:43,040 --> 00:09:45,088 Your ciliary muscles are going to have to adjust, 207 00:09:45,088 --> 00:09:48,807 but maybe they can't cut it and this forms an image 208 00:09:48,807 --> 00:09:50,971 back here, but that's bad. 209 00:09:50,971 --> 00:09:54,206 That's bad because if you form an image behind your retina, 210 00:09:54,206 --> 00:09:56,733 that's going to be blurry. 211 00:09:56,733 --> 00:09:59,008 You're not going to see the nice clean image here. 212 00:09:59,008 --> 00:10:00,889 You're going to get this weird blurred out image, 213 00:10:00,889 --> 00:10:03,563 so your ciliary muscles are going to try to compensate, 214 00:10:03,563 --> 00:10:06,532 but maybe they can't, so this person might need glasses. 215 00:10:06,532 --> 00:10:08,540 This person, if they were able to see 216 00:10:08,540 --> 00:10:10,610 the far away tree just fine, 217 00:10:10,610 --> 00:10:13,776 but things up close were hard for them to focus on, 218 00:10:13,776 --> 00:10:16,314 we'd call this person farsighted. 219 00:10:16,314 --> 00:10:20,903 So farsighted people can see far away stuff just fine. 220 00:10:20,903 --> 00:10:24,143 But when it's too close, they can't focus on it, 221 00:10:24,143 --> 00:10:26,555 so what do we do? We add another lens in here. 222 00:10:26,555 --> 00:10:29,488 We're going to add a lens that tricks our eye. 223 00:10:29,488 --> 00:10:31,575 See, our eye, this farsighted person 224 00:10:31,575 --> 00:10:33,555 was good at seeing stuff far away. 225 00:10:33,555 --> 00:10:37,386 So I'm going to try and take this tree, this object. 226 00:10:37,386 --> 00:10:39,411 I'm going to try and make an image of it farther away. 227 00:10:39,411 --> 00:10:40,688 So how do I do that? 228 00:10:40,688 --> 00:10:44,462 I'm going to prescribe this person a convex lens 229 00:10:44,462 --> 00:10:47,682 because the convex lens will create a virtual image 230 00:10:47,682 --> 00:10:50,830 of the tree at some farther away point. 231 00:10:50,830 --> 00:10:52,073 We trick our eye. 232 00:10:52,073 --> 00:10:53,691 Now it can focus a little better. 233 00:10:53,691 --> 00:10:58,102 We can take this image and bring it up to our retina, 234 00:10:58,102 --> 00:11:00,441 get a nice clean image of the tree. 235 00:11:00,441 --> 00:11:01,873 So that's for a farsighted person. 236 00:11:01,873 --> 00:11:05,012 For a nearsighted person, let me get another image in here. 237 00:11:05,012 --> 00:11:08,676 Nearsighted people can see stuff near just fine 238 00:11:08,676 --> 00:11:12,013 and it's the far stuff that they have trouble with. 239 00:11:12,013 --> 00:11:16,621 So for a nearsighted person, focusing on this tree up here 240 00:11:16,621 --> 00:11:20,994 that's no problem, they can focus on this just fine. 241 00:11:22,055 --> 00:11:25,828 They get a nice clean image of the tree right at the spot 242 00:11:25,828 --> 00:11:28,472 where it's supposed to be at, at the retina. 243 00:11:28,472 --> 00:11:30,124 You get a nice clean image, 244 00:11:30,124 --> 00:11:32,450 but if you move the tree further away, 245 00:11:32,450 --> 00:11:34,295 they'd have trouble. 246 00:11:34,295 --> 00:11:36,076 So we need to take this tree. 247 00:11:36,076 --> 00:11:37,435 I'm going to take it right here. 248 00:11:37,435 --> 00:11:39,076 So I'm going to take this tree 249 00:11:39,076 --> 00:11:41,889 and I'm going to move it farther away. 250 00:11:41,889 --> 00:11:44,365 Now the eye has trouble seeing it. 251 00:11:44,365 --> 00:11:47,423 And so, now the eye is going to form an image. 252 00:11:47,423 --> 00:11:50,205 Maybe the eye forms the image up here. 253 00:11:50,205 --> 00:11:51,607 That's not good. 254 00:11:51,607 --> 00:11:53,892 We need to bring this back over to this way, 255 00:11:53,892 --> 00:11:55,971 so we'll have to prescribe a lens. 256 00:11:55,971 --> 00:11:59,130 This person was able to see near stuff just fine, so again, 257 00:11:59,130 --> 00:12:00,571 we're going to have to trick our eye. 258 00:12:00,571 --> 00:12:01,812 We take this object. 259 00:12:01,812 --> 00:12:04,485 We need a lens that makes our eye think that this object's 260 00:12:04,485 --> 00:12:07,551 closer than it is, and we'll prescribe this person 261 00:12:07,551 --> 00:12:11,788 a diverging lens, or concave lens. 262 00:12:11,788 --> 00:12:16,788 This lens is going to make a virtual image of this tree 263 00:12:17,411 --> 00:12:21,315 that's a little bit closer than the actual object was 264 00:12:21,315 --> 00:12:26,216 so now our light that comes into our eye, 265 00:12:26,216 --> 00:12:27,679 once it gets to our eye, 266 00:12:27,679 --> 00:12:30,646 I'm neglecting a lot of bending going on here. 267 00:12:30,646 --> 00:12:35,121 We can actually get this light to focus right on our retina, 268 00:12:35,121 --> 00:12:37,594 which is what we wanted it to do 269 00:12:37,594 --> 00:12:39,634 and we get a nice clean image. 270 00:12:39,634 --> 00:12:42,514 So, depending on whether your nearsighted or farsighted, 271 00:12:42,514 --> 00:12:44,614 you'd prescribe someone either. 272 00:12:44,614 --> 00:12:46,636 So nearsighted get diverging lenses. 273 00:12:47,390 --> 00:12:51,041 Farsighted people get converging lenses, 274 00:12:51,041 --> 00:12:53,723 and that's one way you can trick the eye 275 00:12:53,723 --> 00:00:00,000 and make it so you can see a nice clear image.