1 00:00:00,876 --> 00:00:03,695 - [Voiceover] Let's talk about thin film interference. 2 00:00:03,695 --> 00:00:04,483 What does this mean? 3 00:00:04,483 --> 00:00:05,757 Well, it's kind of redundant, 4 00:00:05,757 --> 00:00:08,287 film already means something really thin, 5 00:00:08,287 --> 00:00:09,954 a thin amount of substance. 6 00:00:09,954 --> 00:00:13,672 And thin film means really, really thin. 7 00:00:13,672 --> 00:00:14,920 So, how does this happen? 8 00:00:14,920 --> 00:00:16,553 It can happen naturally. 9 00:00:16,553 --> 00:00:20,053 When it rains outside, there will be puddles of water. 10 00:00:20,053 --> 00:00:22,743 And because there's oil left over on the road, 11 00:00:22,743 --> 00:00:26,156 sometimes some oil will float on top of the water, 12 00:00:26,156 --> 00:00:30,499 and it's often a very thin, small amount of oil. 13 00:00:30,499 --> 00:00:33,837 In other words, the thickness of the oil 14 00:00:33,837 --> 00:00:36,969 floating on the water is extremely thin. 15 00:00:36,969 --> 00:00:39,219 So, we'll call this thickness t. 16 00:00:39,219 --> 00:00:40,433 How do we know it's thin 17 00:00:40,433 --> 00:00:42,710 and how do we know it's there, if we can't see it? 18 00:00:42,710 --> 00:00:46,103 We know it's there, because if you look down at it, 19 00:00:46,103 --> 00:00:49,303 if you look down at the water, you'll sometimes see 20 00:00:49,303 --> 00:00:52,561 a colorful pattern in here, and that colorful pattern 21 00:00:52,561 --> 00:00:54,486 on the top of the water, 22 00:00:54,486 --> 00:00:57,912 streaks of red and blue and orange and green, 23 00:00:57,912 --> 00:01:00,135 happen because of thin film interference. 24 00:01:00,135 --> 00:01:01,687 It also happens in bubbles. 25 00:01:01,687 --> 00:01:04,129 If you blow a bubble and you hold it on a bubble wand, 26 00:01:04,129 --> 00:01:07,130 you will see that there's these colors in there. 27 00:01:07,130 --> 00:01:09,185 And those are coming from thin film interference. 28 00:01:09,185 --> 00:01:10,362 How does it happen? 29 00:01:10,362 --> 00:01:13,913 Well, light comes in, so, this might be from the sun 30 00:01:13,913 --> 00:01:16,870 or whatever, some source of light. 31 00:01:16,870 --> 00:01:19,928 Comes in here; that's only one light ray. 32 00:01:19,928 --> 00:01:22,336 We need multiple light rays to get interference. 33 00:01:22,336 --> 00:01:24,345 So, what happens when it hits the oil? 34 00:01:24,345 --> 00:01:28,451 Part of it is gonna reflect off the top of the oil. 35 00:01:28,451 --> 00:01:30,421 So, it's gonna reflect right back on top of itself, 36 00:01:30,421 --> 00:01:33,245 but if I already draw it right back on top of itself, 37 00:01:33,245 --> 00:01:34,771 this would get messy really fast. 38 00:01:34,771 --> 00:01:36,080 So I'm gonna draw it over here, 39 00:01:36,080 --> 00:01:38,562 but know, this light really reflects 40 00:01:38,562 --> 00:01:42,156 right back on top of itself, if it was coming straight in. 41 00:01:42,156 --> 00:01:44,728 We'll call that light ray one. 42 00:01:44,728 --> 00:01:46,296 But that's not all the light does. 43 00:01:46,296 --> 00:01:48,213 Part of it reflects, but part of it 44 00:01:48,213 --> 00:01:49,552 continues through the oil. 45 00:01:49,552 --> 00:01:51,213 So, in order to get thin film interference 46 00:01:51,213 --> 00:01:56,162 the thin film has to be translucent, 47 00:01:56,162 --> 00:01:57,962 it has to let light through. 48 00:01:57,962 --> 00:02:00,129 Not just reflect it, but let light through. 49 00:02:00,129 --> 00:02:03,594 So, some of this light ray is gonna continue on through. 50 00:02:03,594 --> 00:02:05,079 Like that. 51 00:02:05,079 --> 00:02:06,048 But what does it do? 52 00:02:06,048 --> 00:02:07,746 It meets another interface. 53 00:02:07,746 --> 00:02:11,539 And every time light meets an interface between two medium 54 00:02:11,539 --> 00:02:13,120 it's gonna reflect and some of it 55 00:02:13,120 --> 00:02:15,157 is gonna pass through, refract. 56 00:02:15,157 --> 00:02:18,144 In this case, some of it reflects off of this interface. 57 00:02:18,144 --> 00:02:20,614 So, we have a reflection here 58 00:02:20,614 --> 00:02:23,964 and we have a reflection up here. 59 00:02:23,964 --> 00:02:26,296 Both of these were reflections. 60 00:02:26,296 --> 00:02:28,649 Some of this light comes back up again. 61 00:02:28,649 --> 00:02:31,414 I'm not gonna try to draw it right back on top of itself. 62 00:02:31,414 --> 00:02:34,540 I'll draw it over here, so that we can see them. 63 00:02:34,540 --> 00:02:35,996 So, it comes up. 64 00:02:35,996 --> 00:02:38,177 Now these overlap. 65 00:02:38,177 --> 00:02:41,905 Look, now that these are overlapping, wave one and wave two, 66 00:02:41,905 --> 00:02:44,612 now my eye can experience interference, 67 00:02:44,612 --> 00:02:46,895 'cause these two waves are gonna hit my eye. 68 00:02:46,895 --> 00:02:49,762 They might be constructive, they might be destructive. 69 00:02:49,762 --> 00:02:51,547 And I might see different colors in here 70 00:02:51,547 --> 00:02:53,145 depending on the wavelength. 71 00:02:53,145 --> 00:02:54,996 That's what we want to try to figure out. 72 00:02:54,996 --> 00:02:57,261 How does the thickness of this oil 73 00:02:57,261 --> 00:02:59,712 and the wavelength of the light determine, 74 00:02:59,712 --> 00:03:01,308 whether this is gonna be constructive, 75 00:03:01,308 --> 00:03:03,162 destructive, or neither. 76 00:03:03,162 --> 00:03:04,245 Here's what we're gonna do. 77 00:03:04,245 --> 00:03:07,179 We are not gonna stray from what we know. 78 00:03:07,179 --> 00:03:10,512 What we know, is that to get constructive interference 79 00:03:10,512 --> 00:03:11,779 we have two light rays. 80 00:03:11,779 --> 00:03:14,290 What matters is the path length difference. 81 00:03:14,290 --> 00:03:18,679 If the path length difference is zero, lambda... 82 00:03:18,679 --> 00:03:21,745 Right, any integer lambda. 83 00:03:21,745 --> 00:03:24,412 You can just call this m lambda, if you want. 84 00:03:24,412 --> 00:03:27,463 That's gonna be constructive. 85 00:03:27,463 --> 00:03:30,679 And any time the path length difference 86 00:03:30,679 --> 00:03:33,454 is gonna be half integer of what lambda is. 87 00:03:33,454 --> 00:03:37,718 So, half lambda, three halves lambda, and so on. 88 00:03:37,718 --> 00:03:42,718 If you wanted to, you can call this m plus a half lambda. 89 00:03:44,076 --> 00:03:47,451 These are gonna be destructive. 90 00:03:47,451 --> 00:03:49,421 I guess, it doesn't equal constructive, 91 00:03:49,421 --> 00:03:53,404 it implies constructive and destructive. 92 00:03:53,404 --> 00:03:58,091 But, remember, gotta be careful, it can be weird here. 93 00:03:58,091 --> 00:04:03,091 These are flip-flopped, if there's a pi shift between them. 94 00:04:05,596 --> 00:04:10,596 If one of these gets pi shifted and the other does not. 95 00:04:10,625 --> 00:04:13,995 If one of the waves is pi shifted and the other is not, 96 00:04:13,995 --> 00:04:16,089 remember, if this was this thing 97 00:04:16,089 --> 00:04:17,995 with the back of the speakers, if you flipped the wires 98 00:04:17,995 --> 00:04:21,727 on the back of the speakers, now instead of the speaker wave 99 00:04:21,728 --> 00:04:26,679 coming out like that, speaker wave comes out like this. 100 00:04:26,679 --> 00:04:30,027 Now, if you overlap these, this condition gets flip-flopped. 101 00:04:30,027 --> 00:04:31,629 If you forgot why, go back and watch 102 00:04:31,629 --> 00:04:33,728 that video on wave interference. 103 00:04:33,728 --> 00:04:35,663 So, this is the condition. 104 00:04:35,663 --> 00:04:37,496 Integer wavelengths give us constructive, 105 00:04:37,496 --> 00:04:39,695 half integer wavelengths give us destructive, 106 00:04:39,695 --> 00:04:40,967 unless one is pi shifted. 107 00:04:40,967 --> 00:04:44,028 If they're both pi shifted, then this condition still holds. 108 00:04:44,028 --> 00:04:46,681 But if only one is pi shifted, 109 00:04:46,681 --> 00:04:48,428 you flip-flop these relations, 110 00:04:48,428 --> 00:04:51,078 and the half integer wavelengths give you constructive. 111 00:04:51,078 --> 00:04:54,213 And the whole integer wavelengths give you destructive. 112 00:04:54,213 --> 00:04:56,194 So, does that happen here? 113 00:04:56,194 --> 00:04:57,880 Do we have to worry about pi shifts? 114 00:04:57,880 --> 00:05:00,344 We didn't with double slit. 115 00:05:00,344 --> 00:05:01,438 Remember, with double slit, 116 00:05:01,438 --> 00:05:03,862 shoot, we didn't worry about any pi shifts. 117 00:05:03,862 --> 00:05:06,294 That was because one wave came in. 118 00:05:06,294 --> 00:05:09,444 And now these were both from the exact same wave, 119 00:05:09,444 --> 00:05:12,035 so now we know they started off in phase. 120 00:05:12,035 --> 00:05:14,745 How about these waves for thin film? 121 00:05:14,745 --> 00:05:17,638 Could there be any shift in pi? 122 00:05:17,638 --> 00:05:18,425 Well, there can. 123 00:05:18,425 --> 00:05:23,355 Every time there's a reflection, there can be a pi shift. 124 00:05:23,355 --> 00:05:27,011 I repeat, every time light reflects, 125 00:05:27,011 --> 00:05:29,817 there may be a pi shift. 126 00:05:29,817 --> 00:05:30,809 How do you know? 127 00:05:30,809 --> 00:05:34,507 It depends on the speed of the wave in those materials. 128 00:05:34,507 --> 00:05:37,021 Let's say we had air out here. 129 00:05:37,021 --> 00:05:39,312 Light has some speed in the air. 130 00:05:39,312 --> 00:05:41,112 Turns out the speed in air is about the same 131 00:05:41,112 --> 00:05:42,938 as the speed in vacuum. 132 00:05:42,938 --> 00:05:46,295 Three times 10 to the eighth meters per second. 133 00:05:46,295 --> 00:05:49,633 But I'm just gonna write it as V air out here. 134 00:05:49,633 --> 00:05:51,537 And then you have a certain speed of the light. 135 00:05:51,537 --> 00:05:54,061 Light will travel at certain speed in the oil. 136 00:05:54,061 --> 00:05:57,880 So, V oil in here is gonna be less. 137 00:05:57,880 --> 00:06:00,466 Let's just say, for the sake of argument, 138 00:06:00,466 --> 00:06:04,312 V oil, the speed of the light wave in the oil, 139 00:06:04,312 --> 00:06:06,163 is less, it's gotta be less, let's just say 140 00:06:06,163 --> 00:06:11,163 it's 2.7 times 10 to the eighth meters per second. 141 00:06:13,142 --> 00:06:15,046 And in water, again, it's gonna have 142 00:06:15,046 --> 00:06:17,380 a speed of light in the water. 143 00:06:17,380 --> 00:06:19,371 Let's say, the speed of light in the water, 144 00:06:19,371 --> 00:06:20,996 well, we don't have to say, we know 145 00:06:20,996 --> 00:06:25,996 that's about 2.25 times 10 to the eighth meters per second. 146 00:06:29,465 --> 00:06:31,871 So, how do we determine, knowing these speeds, 147 00:06:31,871 --> 00:06:34,124 whether there's going to be a pi shift or not? 148 00:06:34,124 --> 00:06:35,101 Here's how we tell. 149 00:06:35,101 --> 00:06:39,627 Every time light reflects off of a slow substance, 150 00:06:39,627 --> 00:06:41,344 there's a pi shift. 151 00:06:41,344 --> 00:06:42,473 So, what do I mean by that? 152 00:06:42,473 --> 00:06:46,260 The light here has started off in this material. 153 00:06:46,260 --> 00:06:48,870 And did it reflect off of a slow substance? 154 00:06:48,870 --> 00:06:51,093 It was in air, that's pretty fast, 155 00:06:51,093 --> 00:06:52,263 three times 10 to the eighth. 156 00:06:52,263 --> 00:06:55,988 It reflected off of oil, it reflected off of a medium, 157 00:06:55,988 --> 00:06:58,037 where it would have traveled slower. 158 00:06:58,037 --> 00:07:02,931 So, this reflection right here does get a pi shift. 159 00:07:02,931 --> 00:07:05,577 There's a pi shift for this reflection. 160 00:07:05,577 --> 00:07:06,992 The light wave that came in. 161 00:07:06,992 --> 00:07:09,285 If it came in at a peak, 162 00:07:09,285 --> 00:07:12,127 then it's getting sent back out as a valley. 163 00:07:12,127 --> 00:07:15,410 And if it came in as this point going up, 164 00:07:15,410 --> 00:07:17,052 it'll leave as this point going down. 165 00:07:17,052 --> 00:07:20,401 It's gonna get shifted by 180 degrees, or pi. 166 00:07:20,401 --> 00:07:22,059 How about this one down here, 167 00:07:22,059 --> 00:07:23,769 did it reflect off of a slow medium? 168 00:07:23,769 --> 00:07:25,994 It did, it was in oil. 169 00:07:25,994 --> 00:07:28,210 It would have traveled into water, 170 00:07:28,210 --> 00:07:30,418 which is slower than the oil. 171 00:07:30,418 --> 00:07:34,326 So, this one also gets a pi shift. 172 00:07:34,326 --> 00:07:36,376 And same thing, if it came in as a peak, 173 00:07:36,376 --> 00:07:37,760 it'll leave as a valley. 174 00:07:37,760 --> 00:07:39,859 What does that mean for this condition up here? 175 00:07:39,859 --> 00:07:42,527 If both are pi shifted, 176 00:07:42,527 --> 00:07:45,215 it's as if neither of them gets shifted. 177 00:07:45,215 --> 00:07:47,059 If we flipped both of them upside down, 178 00:07:47,059 --> 00:07:48,726 well, everything is cool again. 179 00:07:48,726 --> 00:07:51,244 We just made everything back to where it was. 180 00:07:51,244 --> 00:07:55,127 So, we would not swap these conditions in this case. 181 00:07:55,127 --> 00:07:58,798 If, for some reason, we use something besides water, 182 00:07:58,798 --> 00:08:00,649 we use some other liquid here, 183 00:08:00,649 --> 00:08:05,649 and this liquid had a speed of, instead of 2.25, 184 00:08:07,462 --> 00:08:12,462 let's say the speed here was 2.85 times 10 to the eighth. 185 00:08:14,794 --> 00:08:17,567 Now, that doesn't change anything up here. 186 00:08:17,567 --> 00:08:19,464 This is still getting a pi shift. 187 00:08:19,464 --> 00:08:23,143 It was in air, it reflected off of something slower, oil. 188 00:08:23,143 --> 00:08:26,879 And by slower I mean, if the light traveled into it, 189 00:08:26,879 --> 00:08:29,132 it would travel slower, so that gets a pi shift. 190 00:08:29,132 --> 00:08:31,460 But now this one down here, this light ray 191 00:08:31,460 --> 00:08:35,529 that was in the oil, would have gone through water, 192 00:08:35,529 --> 00:08:39,073 sorry, this isn't water anymore, this is some new liquid. 193 00:08:39,073 --> 00:08:42,100 It reflected off of this liquid 194 00:08:42,100 --> 00:08:45,011 that it would have traveled faster through. 195 00:08:45,011 --> 00:08:46,568 So, does it get a pi shift? 196 00:08:46,568 --> 00:08:48,994 Nope, there would be no more pi shift down here, 197 00:08:48,994 --> 00:08:52,980 only one of these reflected light rays get a pi shift. 198 00:08:52,980 --> 00:08:57,980 And if that ever happens, if one of the light rays 199 00:08:57,995 --> 00:09:00,244 gets pi shifted and the other does not, 200 00:09:00,244 --> 00:09:02,260 then we would swap these conditions, 201 00:09:02,260 --> 00:09:04,378 and it'd be the half integer wavelengths 202 00:09:04,378 --> 00:09:06,271 that would give us constructive, 203 00:09:06,271 --> 00:09:07,942 and the whole integer wavelengths 204 00:09:07,942 --> 00:09:09,943 that would give us destructive. 205 00:09:09,943 --> 00:09:11,299 Let me just be clear here, 206 00:09:11,299 --> 00:09:12,976 let me show you what I'm talking about. 207 00:09:12,976 --> 00:09:14,212 Let me clear this off. 208 00:09:14,212 --> 00:09:19,212 If I had material, and right here it's slow 209 00:09:19,534 --> 00:09:22,090 compared to this one. 210 00:09:22,090 --> 00:09:27,090 If it reflects off of a fast material, no pi shift. 211 00:09:27,274 --> 00:09:29,910 No 180 degree shift. 212 00:09:29,910 --> 00:09:32,244 But if it's in a fast material 213 00:09:32,244 --> 00:09:34,793 and it reflects off of a slow material, 214 00:09:34,793 --> 00:09:39,793 then yes, this gets a pi shift. 215 00:09:40,124 --> 00:09:42,382 This gets a 180 degree shift. 216 00:09:42,382 --> 00:09:45,054 That's how you determine it, is whether it reflects off 217 00:09:45,054 --> 00:09:49,816 of a fast material or if it reflects off of a slow material. 218 00:09:49,816 --> 00:09:52,990 For both sides, the top two up here, 219 00:09:52,990 --> 00:09:54,758 you gotta ask the same question: 220 00:09:54,758 --> 00:09:58,758 did it go from slow to fast, reflect off of a fast, 221 00:09:58,758 --> 00:10:01,760 or did it reflect off of a slow. 222 00:10:01,760 --> 00:10:03,057 That's how you determine. 223 00:10:03,057 --> 00:10:06,620 If it reflects off of a fast, no pi shift. 224 00:10:06,620 --> 00:10:10,036 If it reflects off of a slow material, 225 00:10:10,036 --> 00:10:11,744 then it does get a pi shift. 226 00:10:11,744 --> 00:10:14,128 Okay, so that's how you deal with pi shifts. 227 00:10:14,128 --> 00:10:15,836 Let's go back to this one. 228 00:10:15,836 --> 00:10:17,797 There's a few more details here. 229 00:10:17,797 --> 00:10:20,276 People have a lot of trouble with thin film, to be honest. 230 00:10:20,276 --> 00:10:22,494 That's one problem, is they don't like figuring out 231 00:10:22,494 --> 00:10:24,117 whether it was pi shifted or not. 232 00:10:24,117 --> 00:10:26,403 It's actually not that hard once you know the rule. 233 00:10:26,403 --> 00:10:29,652 But there's another problem here, what's delta x? 234 00:10:29,652 --> 00:10:31,272 We never even said what delta x is. 235 00:10:31,272 --> 00:10:33,750 It's gotta be related to the thickness. 236 00:10:33,750 --> 00:10:35,822 Imagine these both waves come in, 237 00:10:35,822 --> 00:10:39,414 imagine both waves are combined in this big wave coming in. 238 00:10:39,414 --> 00:10:42,142 They were both in there to start off with. 239 00:10:42,142 --> 00:10:44,127 They both travel that distance. 240 00:10:44,127 --> 00:10:48,324 Wave one reflects off and just travels this distance. 241 00:10:48,324 --> 00:10:52,011 Wave two also travels that distance, 242 00:10:52,011 --> 00:10:55,295 but only after wave two traveled 243 00:10:55,295 --> 00:10:58,859 this extra distance within the thin film. 244 00:10:58,859 --> 00:11:02,327 So, the extra path length the wave two traveled 245 00:11:02,327 --> 00:11:06,260 compared to wave one was not the thickness t. 246 00:11:06,260 --> 00:11:08,032 Here's where people make the mistake, 247 00:11:08,032 --> 00:11:11,423 people think that delta x for thin film is t. 248 00:11:11,423 --> 00:11:14,874 No, the wave two had to travel down and then back up. 249 00:11:14,874 --> 00:11:16,749 So it's two t. 250 00:11:16,749 --> 00:11:19,966 This is the key for thin film interference. 251 00:11:19,966 --> 00:11:23,498 The path length difference will always be two t. 252 00:11:23,498 --> 00:11:27,233 I'd just have to come up here, I know what delta x is. 253 00:11:27,233 --> 00:11:31,474 For thin film it's always gonna just be equal 254 00:11:31,474 --> 00:11:36,474 to two times the thickness of the thin film. 255 00:11:37,218 --> 00:11:38,741 So I'm gonna put two t here. 256 00:11:38,741 --> 00:11:41,170 This is my condition, this is how I change this 257 00:11:41,170 --> 00:11:44,641 to make it relevant for thin film. 258 00:11:44,641 --> 00:11:48,135 For double slit delta x was d sin theta. 259 00:11:48,135 --> 00:11:50,773 For the thin film delta x, the path length difference, 260 00:11:50,773 --> 00:11:53,500 is just two times t, so it's kind of simpler. 261 00:11:53,500 --> 00:11:55,034 You've got these pi shifts to worry about, 262 00:11:55,034 --> 00:11:57,018 but the delta x is simpler. 263 00:11:57,018 --> 00:11:58,833 All right, so that's not too bad. 264 00:11:58,833 --> 00:12:00,384 Anything left to worry about? 265 00:12:00,384 --> 00:00:00,000 Yes, one more thing to worry about.