1 00:00:01,642 --> 00:00:04,065 This wavelength, this just says wavelength, 2 00:00:04,065 --> 00:00:06,155 but there's going to be a certain wavelength 3 00:00:06,155 --> 00:00:09,728 in the air or this material one. 4 00:00:09,728 --> 00:00:11,401 I'll call it lambda A. 5 00:00:11,401 --> 00:00:12,526 It could be air. 6 00:00:12,526 --> 00:00:16,417 It could be anything out here that light can travel through. 7 00:00:16,417 --> 00:00:17,362 And then it's also going to have 8 00:00:17,362 --> 00:00:19,793 a certain wavelength in the oil. 9 00:00:19,793 --> 00:00:23,287 And the wavelength in this oil is going to be different. 10 00:00:23,287 --> 00:00:25,553 I'll call this wavelength B. 11 00:00:25,553 --> 00:00:26,747 It's going to be different from the wavelength 12 00:00:26,747 --> 00:00:30,438 in this first material if the speed is different. 13 00:00:30,438 --> 00:00:33,683 It could even have a different wavelength than the water, 14 00:00:33,683 --> 00:00:36,301 but we don't worry about the wave traveling down here. 15 00:00:36,301 --> 00:00:38,443 So let's not confuse ourselves. 16 00:00:38,443 --> 00:00:40,553 Some of the light will pass through here, 17 00:00:40,553 --> 00:00:43,163 but it's not necessarily going to get back to my I. 18 00:00:43,163 --> 00:00:46,631 So I'm not going to worry about this part. 19 00:00:46,631 --> 00:00:48,741 Which one do we use in this condition? 20 00:00:48,741 --> 00:00:52,967 Do we use the wavelength in the first medium, A, in the air? 21 00:00:52,967 --> 00:00:54,987 Or do we use the wavelength in the oil? 22 00:00:54,987 --> 00:00:57,502 Well, we use the wavelength in the oil. 23 00:00:57,502 --> 00:01:01,965 Most definitely, we use always this wavelength here. 24 00:01:01,965 --> 00:01:06,965 Both of these are always the wavelength in the thin film. 25 00:01:07,955 --> 00:01:10,999 So, the wavelength the light had in the thin film 26 00:01:10,999 --> 00:01:14,224 because that was the portion of the path where 27 00:01:14,224 --> 00:01:16,533 the light traveled an extra distance. 28 00:01:16,533 --> 00:01:17,946 So that's the part that will matter. 29 00:01:17,946 --> 00:01:22,946 We want to know how much further up, if this first light ray 30 00:01:24,114 --> 00:01:26,020 when it reflected was right here. 31 00:01:26,020 --> 00:01:27,956 We want to know where's this other one 32 00:01:27,956 --> 00:01:30,329 going to be at when it emerges. 33 00:01:30,329 --> 00:01:34,690 Because if it emerges also right at that point, 34 00:01:34,690 --> 00:01:37,753 say this wave cycle, say it also 35 00:01:37,753 --> 00:01:41,119 emerges exactly at that point here. 36 00:01:41,119 --> 00:01:42,489 Well, they'll be constructive. 37 00:01:42,489 --> 00:01:46,064 But if it emerges over here, that's only 180 degrees, 38 00:01:46,064 --> 00:01:47,754 that's 180 degrees out of phase. 39 00:01:47,754 --> 00:01:49,250 Then it would be destructive. 40 00:01:49,250 --> 00:01:52,860 We want to know how much this cycle got progressed 41 00:01:52,860 --> 00:01:55,404 by this wave traveling through here. 42 00:01:55,404 --> 00:01:57,624 So we need to know the wavelength in here. 43 00:01:57,624 --> 00:01:59,336 That's the wavelength that actually matters. 44 00:01:59,336 --> 00:02:01,386 The wavelength in the thin film. 45 00:02:01,386 --> 00:02:03,173 Often times you're not given the 46 00:02:03,173 --> 00:02:04,998 wavelength in the thin film. 47 00:02:04,998 --> 00:02:06,154 You're given the wavelength in 48 00:02:06,154 --> 00:02:09,949 the air, or whatever this material is. 49 00:02:09,949 --> 00:02:11,963 So if you know this wavelength, how do you get 50 00:02:11,963 --> 00:02:15,072 the wavelength in the oil, or the thin film? 51 00:02:15,072 --> 00:02:18,129 How do we find this wavelength? 52 00:02:18,129 --> 00:02:19,632 It's not too hard. 53 00:02:19,632 --> 00:02:21,945 The most straight forward conceptual way to think about it 54 00:02:21,945 --> 00:02:24,762 is that frequency doesn't change. 55 00:02:24,762 --> 00:02:29,707 The frequency in material A is going to equal 56 00:02:29,707 --> 00:02:32,952 the frequency of the light when it enters material B. 57 00:02:32,952 --> 00:02:34,883 Frequency is determined by the source. 58 00:02:34,883 --> 00:02:38,119 If it's the sun up here that emitted that light ray, 59 00:02:38,119 --> 00:02:40,008 or the laser, that's what's determining the 60 00:02:40,008 --> 00:02:42,685 frequency of this particular light ray. 61 00:02:42,685 --> 00:02:44,385 And that stays the same, whether it reflects 62 00:02:44,385 --> 00:02:47,220 whether it refracts, no matter what it does. 63 00:02:47,220 --> 00:02:48,708 The frequency stays the same. 64 00:02:48,708 --> 00:02:50,114 That's a useful thing to know. 65 00:02:50,114 --> 00:02:51,825 And it's useful in this case because... 66 00:02:51,825 --> 00:02:54,183 Well, how do we relate this to wavelengths? 67 00:02:54,183 --> 00:02:58,445 We know the speed of a wave equals 68 00:02:58,445 --> 00:03:00,764 wavelength times the frequency. 69 00:03:00,764 --> 00:03:02,935 And so if I wanted to solve this for frequency, 70 00:03:02,935 --> 00:03:04,837 I'd divide both sides by the wavelength and 71 00:03:04,837 --> 00:03:06,249 I get that this is equal to the speed 72 00:03:06,249 --> 00:03:08,669 of the wave over the wavelength. 73 00:03:08,669 --> 00:03:10,310 I can replace that over here. 74 00:03:10,310 --> 00:03:15,082 VA, so frequency and material A, is just speed 75 00:03:15,082 --> 00:03:17,615 of the light in A, because of this formula. 76 00:03:17,615 --> 00:03:21,715 Over, wavelength of the light in region A. 77 00:03:21,715 --> 00:03:22,970 You can think of A as air. 78 00:03:22,970 --> 00:03:24,769 It doesn't have to be air, but it could be. 79 00:03:24,769 --> 00:03:25,998 It was in this case. 80 00:03:25,998 --> 00:03:28,838 Frequency of the light in B, which is our oil, 81 00:03:28,838 --> 00:03:32,071 would be the speed of light in region B, 82 00:03:32,071 --> 00:03:34,933 divided by the wavelength in region B. 83 00:03:34,933 --> 00:03:37,149 Okay, so now we can just solve for wavelength 84 00:03:37,149 --> 00:03:40,778 in region B, and we get that wavelength 85 00:03:40,778 --> 00:03:43,808 in our thin film will equal... 86 00:03:43,808 --> 00:03:47,094 I multiply it both sides by wavelength in B, 87 00:03:47,094 --> 00:03:48,712 and then I multiply these out, and what you'll 88 00:03:48,712 --> 00:03:53,712 end up getting is velocity of the light, speed of the light 89 00:03:53,905 --> 00:03:58,802 in region B, divided by speed of the light in region A. 90 00:03:58,802 --> 00:04:03,777 That factor, times the wavelength of the light in A. 91 00:04:03,777 --> 00:04:06,256 So this is one way to determine. 92 00:04:06,256 --> 00:04:09,073 If you're given the speeds like I did here... 93 00:04:09,073 --> 00:04:10,824 Remember I gave you the speed of the light in the air. 94 00:04:10,824 --> 00:04:11,700 That you can look up because 95 00:04:11,700 --> 00:04:13,561 everyone knows you can look it up. 96 00:04:13,561 --> 00:04:14,716 It's online. 97 00:04:14,716 --> 00:04:16,587 And speed of the light in the oil, 98 00:04:16,587 --> 00:04:18,319 I just told you what that was. 99 00:04:18,319 --> 00:04:20,379 If you're given these speeds, take the ratio, 100 00:04:20,379 --> 00:04:22,528 speed of the light in oil divided by 101 00:04:22,528 --> 00:04:24,064 the speed of light in the air. 102 00:04:24,064 --> 00:04:27,397 Multiply by the wavelength in the air, this first medium 103 00:04:27,397 --> 00:04:28,756 and you'll get the wavelength in the 104 00:04:28,756 --> 00:04:31,230 second medium, which is the oil. 105 00:04:31,230 --> 00:04:35,886 This would be what you'd plug into these formulas up here. 106 00:04:35,886 --> 00:04:36,772 What if you're not... 107 00:04:36,772 --> 00:04:39,250 Sometimes you're not even given the speed. 108 00:04:39,250 --> 00:04:42,246 What if you're given the index of refraction? 109 00:04:42,246 --> 00:04:47,154 And you're like, "Ugh, index of refraction, shoot". 110 00:04:47,154 --> 00:04:52,150 Well if they gave you the N in region A, and instead 111 00:04:52,150 --> 00:04:54,688 gave you the N in region B, instead of 112 00:04:54,688 --> 00:04:57,301 giving you the speeds, remember index 113 00:04:57,301 --> 00:05:00,254 of refraction is defined to B. 114 00:05:00,254 --> 00:05:02,771 Speed of light in a vacuum divided by 115 00:05:02,771 --> 00:05:05,174 the speed of light in that material. 116 00:05:05,174 --> 00:05:09,831 So, NA, index of refraction of region A is just 117 00:05:09,831 --> 00:05:12,545 three times ten to the eighth, divided by the speed in A. 118 00:05:12,545 --> 00:05:15,312 And NB would be three times ten to 119 00:05:15,312 --> 00:05:18,829 the eight over the speed in B. 120 00:05:18,829 --> 00:05:21,161 How would this change? 121 00:05:21,161 --> 00:05:25,353 I could just solve this for VA if I wanted to. 122 00:05:25,353 --> 00:05:28,021 I'd get VA... 123 00:05:28,021 --> 00:05:29,653 I'm running out of room here, excuse me. 124 00:05:29,653 --> 00:05:34,653 Equals C over NA and VB would equal the speed of light 125 00:05:40,255 --> 00:05:43,916 in a vacuum divided by index of refraction in B. 126 00:05:43,916 --> 00:05:46,581 Now I'm actually just plug it into here. 127 00:05:46,581 --> 00:05:51,581 I'm going to plug in VB, which is this, for VB. 128 00:05:52,226 --> 00:05:56,859 I'm going to plug in VA, which is this, for VA. 129 00:05:56,859 --> 00:05:58,040 I'd get a new condition. 130 00:05:58,040 --> 00:05:59,573 What would that new condition be? 131 00:05:59,573 --> 00:06:02,794 That new condition would say that wavelength in B 132 00:06:02,794 --> 00:06:07,794 equals C over NB, is what I get. 133 00:06:09,015 --> 00:06:14,015 C over NB divided by C over NA 134 00:06:17,316 --> 00:06:21,201 from this condition, times lambda A. 135 00:06:21,201 --> 00:06:22,127 I can simplify that. 136 00:06:22,127 --> 00:06:27,127 The Cs cancel and then one over NB divided by one over NA, 137 00:06:28,477 --> 00:06:33,477 just gives me NA over NB times lambda in the air. 138 00:06:36,662 --> 00:06:38,423 So here's another one. 139 00:06:38,423 --> 00:06:39,474 Here's another condition. 140 00:06:39,474 --> 00:06:40,735 Another way to find it. 141 00:06:40,735 --> 00:06:44,104 This would also equal the wavelength 142 00:06:44,104 --> 00:06:46,442 in the oil, or the thin film. 143 00:06:46,442 --> 00:06:48,063 So if you're given the speeds, 144 00:06:48,063 --> 00:06:49,942 you can take the ratio of the speeds. 145 00:06:49,942 --> 00:06:54,282 You'd do the oil speed divided by the outside speed. 146 00:06:54,282 --> 00:06:56,100 Multiply by the wavelength in the air. 147 00:06:56,100 --> 00:06:58,345 But you're given the indexes of refraction, 148 00:06:58,345 --> 00:07:00,799 you'd take the outside index of refraction 149 00:07:00,799 --> 00:07:04,337 divided by the inside index of refraction times lambda A. 150 00:07:04,337 --> 00:07:05,391 You're thinking, "Oh my god, how am 151 00:07:05,391 --> 00:07:06,792 "I going to remember all this?" 152 00:07:06,792 --> 00:07:07,807 Here's how I remember it. 153 00:07:07,807 --> 00:07:11,383 I know if I go from air to oil, light's going to slow down. 154 00:07:11,383 --> 00:07:15,302 And if light slows down, frequency stays the same. 155 00:07:15,302 --> 00:07:17,835 So if light slows down, wavelength's got to go down. 156 00:07:17,835 --> 00:07:20,750 So I just look over here and I just make my ratio. 157 00:07:20,750 --> 00:07:23,665 If they give me Ns, I just make sure 158 00:07:23,665 --> 00:07:27,140 my ratio of Ns gives me a smaller number. 159 00:07:27,140 --> 00:07:29,355 A number less than one that I multiply by 160 00:07:29,355 --> 00:07:32,112 to get my lambda in the thin film. 161 00:07:32,112 --> 00:07:35,894 And if they gave me speeds, I just take my speeds. 162 00:07:35,894 --> 00:07:37,625 I take my ratio of my speeds so that 163 00:07:37,625 --> 00:07:41,160 I get a smaller lambda in the thin film. 164 00:07:41,160 --> 00:07:42,334 Just got to be careful. 165 00:07:42,334 --> 00:07:44,672 Make sure you're really slowing down. 166 00:07:44,672 --> 00:07:48,079 They might give you a problem where for some reason 167 00:07:48,079 --> 00:07:50,214 this wasn't air, some other material. 168 00:07:50,214 --> 00:07:52,523 It was going faster through the oil 169 00:07:52,523 --> 00:07:54,295 than it would be through here. 170 00:07:54,295 --> 00:07:56,494 Then you'd want to make this ratio 171 00:07:56,494 --> 00:07:58,524 more than one when you multiply. 172 00:07:58,524 --> 00:08:00,813 But, if in doubt you can always fall back on, 173 00:08:00,813 --> 00:08:04,039 the two frequencies are equal, and use that. 174 00:08:04,039 --> 00:08:05,592 And that's the three things you 175 00:08:05,592 --> 00:08:07,220 got to worry about for thin film. 176 00:08:07,220 --> 00:08:08,644 These are the conditions. 177 00:08:08,644 --> 00:08:10,844 Make sure you pay attention to whether there's a pi shift 178 00:08:10,844 --> 00:08:15,710 and make sure you always use wavelength in the thin film. 179 00:08:15,710 --> 00:08:17,095 So if we wanted to... 180 00:08:17,095 --> 00:08:18,278 This looks messy. 181 00:08:18,278 --> 00:08:19,305 I'm sorry about this. 182 00:08:19,305 --> 00:08:20,626 This looks horrible. 183 00:08:20,626 --> 00:08:24,507 We could turn this all into one super duper equation. 184 00:08:24,507 --> 00:08:25,323 Let's do that. 185 00:08:25,323 --> 00:08:26,060 Let's get... 186 00:08:26,060 --> 00:08:27,767 I can't even look at that anymore. 187 00:08:27,767 --> 00:08:29,272 Alright, let's do this. 188 00:08:29,272 --> 00:08:34,272 So we know for constructive we should have 2T 189 00:08:34,823 --> 00:08:39,823 equals integer, so M is zero, one, two, three, 190 00:08:39,940 --> 00:08:43,801 times the wavelength in the oil or the thin film. 191 00:08:43,801 --> 00:08:46,043 But, I don't want to solve for that every time. 192 00:08:46,043 --> 00:08:47,176 We already did it. 193 00:08:47,176 --> 00:08:48,589 Let's just write this. 194 00:08:48,589 --> 00:08:52,142 We know velocity in this region is A. 195 00:08:52,142 --> 00:08:55,088 The thin film region, we'll call B. 196 00:08:55,088 --> 00:09:00,088 Then we know that V in B divided by V in A times wavelength 197 00:09:02,952 --> 00:09:06,126 in region A, which is often times the air, 198 00:09:06,126 --> 00:09:08,137 this would give you constructive. 199 00:09:08,137 --> 00:09:12,682 Or, if you're unlucky and you got index of refraction 200 00:09:12,682 --> 00:09:15,887 then you could use index of refraction in A 201 00:09:15,887 --> 00:09:20,070 divided by index of refraction in B, times the wavelength 202 00:09:20,070 --> 00:09:23,122 in the A region, and that would be what 203 00:09:23,122 --> 00:09:26,278 you would need for constructive. 204 00:09:26,278 --> 00:09:27,830 We could do the same thing for destructive. 205 00:09:27,830 --> 00:09:32,252 2 times T should be, 1/2 integers, so we could do 206 00:09:32,252 --> 00:09:36,272 M plus a 1/2 times this same thing, wavelength 207 00:09:36,272 --> 00:09:41,272 in the thin film, which again is VB over VA times lambda A. 208 00:09:44,681 --> 00:09:49,681 Or, same thing, 1/2 integers times wavelength. 209 00:09:49,922 --> 00:09:51,668 But if you had index of refraction 210 00:09:51,668 --> 00:09:56,668 you'd want to use NA over NB, lambda A. 211 00:09:57,610 --> 00:09:59,985 This would give you destructive. 212 00:09:59,985 --> 00:10:02,288 Only other thing to worry about is 213 00:10:02,288 --> 00:10:05,772 if there's a relative pi shift. 214 00:10:05,772 --> 00:10:08,015 You would flip flop these conditions. 215 00:10:08,015 --> 00:10:10,541 These 1/2 integers would give you constructive 216 00:10:10,541 --> 00:10:12,780 and the integers would give you destructive. 217 00:10:12,780 --> 00:10:17,780 If one wave, and only one wave, gets a pi shift. 218 00:10:19,256 --> 00:10:24,256 If one wave gets a pi shift then you swap these conditions. 219 00:10:24,434 --> 00:10:26,806 This still looks a little bit intimidating. 220 00:10:26,806 --> 00:10:27,410 I'm sorry. 221 00:10:27,410 --> 00:10:28,555 That looks intimidating. 222 00:10:28,555 --> 00:10:30,554 So sometimes it gets even better. 223 00:10:30,554 --> 00:10:35,554 If this region A is air... 224 00:10:35,671 --> 00:10:39,381 The index of refraction in air is just one. 225 00:10:39,381 --> 00:10:41,291 So that cleans things up a little bit. 226 00:10:41,291 --> 00:10:46,150 This just becomes one and this up here just becomes one. 227 00:10:46,150 --> 00:10:50,777 So you end up with M times one over NB times lambda A. 228 00:10:50,777 --> 00:10:54,898 Or in other words, M times lambda A 229 00:10:54,898 --> 00:10:57,614 over NB would give you constructive. 230 00:10:57,614 --> 00:11:00,183 And M plus a 1/2 times lambda A 231 00:11:00,183 --> 00:11:03,858 over NB would give you destructive for every 232 00:11:03,858 --> 00:11:08,858 M equals zero, one, two, three, and so on. 233 00:11:10,795 --> 00:11:12,583 Zero, can you really have zero? 234 00:11:12,583 --> 00:11:14,906 Yeah you could, kind of. 235 00:11:14,906 --> 00:11:18,358 If M equals zero, that would say the thickness is zero. 236 00:11:18,358 --> 00:11:20,074 Doesn't that mean you have no thin film? 237 00:11:20,074 --> 00:11:25,074 Well, sort of, but if this thickness is very small 238 00:11:26,145 --> 00:11:28,945 compared to the wavelength of the light, it's as if 239 00:11:28,945 --> 00:11:32,410 the thickness is zero and that will give you either 240 00:11:32,410 --> 00:11:35,654 constructive or destructive depending on the pi shift. 241 00:11:35,654 --> 00:11:36,719 And sometimes you can do that. 242 00:11:36,719 --> 00:11:39,726 Anti-reflective coating is often just a coating 243 00:11:39,726 --> 00:11:43,440 that's so thin, completely thin, compared 244 00:11:43,440 --> 00:11:46,414 to the wavelength of light, which just makes all 245 00:11:46,414 --> 00:11:48,645 the light reflect destructively. 246 00:11:48,645 --> 00:11:50,763 Because in that case you do get a pi shift 247 00:11:50,763 --> 00:11:54,198 and these integers give you destructive points. 248 00:11:54,198 --> 00:11:56,127 So that's thin film interference. 249 00:11:56,127 --> 00:11:58,654 Sometimes it confuses people. 250 00:11:58,654 --> 00:12:00,365 Hopefully, you do well with it. 251 00:12:00,365 --> 00:00:00,000 These are the ways you deal with it.