1 00:00:00 --> 00:00:02,044 2 00:00:02,044 --> 00:00:07,005 So last time we discussed the interference patterns due to two 3 00:00:07,005 --> 00:00:11,317 coherent light sources. Today I will expand on this by 4 00:00:11,317 --> 00:00:14,001 exploring many many light sources. 5 00:00:14,001 --> 00:00:18,881 Suppose instead of having two slits through which I allow the 6 00:00:18,881 --> 00:00:22,46 light to go I have many. I have N, capital N. 7 00:00:22,46 --> 00:00:26,772 And let the separation between two adjacent ones be D, 8 00:00:26,772 --> 00:00:31,327 and so plain parallel waves come in and each one of these 9 00:00:31,327 --> 00:00:34,999 light sources is going to be a 10 00:00:34,999 --> 00:00:38,75 Huygens source, is going to produce spherical 11 00:00:38,75 --> 00:00:41,904 waves. And so now we can ask ourselves 12 00:00:41,904 --> 00:00:46,847 the same question that we did before, and that is look at a 13 00:00:46,847 --> 00:00:50,683 long distance far away at certain angle theta. 14 00:00:50,683 --> 00:00:55,201 Where will we see maxima and where will we see minima? 15 00:00:55,201 --> 00:01:00,145 And then we can put up here a screen at a distance L and we 16 00:01:00,145 --> 00:01:05,752 will call this X equals zero, and then we can even ask 17 00:01:05,752 --> 00:01:10,495 the question where exactly on that screen will we see these 18 00:01:10,495 --> 00:01:13,194 maxima? You will have constructive 19 00:01:13,194 --> 00:01:18,018 interference exactly the same situation that we had with the 20 00:01:18,018 --> 00:01:22,516 double-slit interference pattern, when the sine of theta 21 00:01:22,516 --> 00:01:25,215 of N equals N lambda divided by D. 22 00:01:25,215 --> 00:01:29,222 And if you're dealing with very small angle theta, 23 00:01:29,222 --> 00:01:34,129 you should all remember that the sine of an angle is the same 24 00:01:34,129 --> 00:01:39,072 as the angle itself, provided that you work in 25 00:01:39,072 --> 00:01:41,311 radians. So for small angles, 26 00:01:41,311 --> 00:01:44,271 you can always use this approximation, 27 00:01:44,271 --> 00:01:47,23 if you remember that it is in radians. 28 00:01:47,23 --> 00:01:51,069 And that's only in the small angle approximation. 29 00:01:51,069 --> 00:01:55,708 And so the conclusion then is if we work in radians for now 30 00:01:55,708 --> 00:02:00,506 that theta of N for the maxima is then at N lambda divided by 31 00:02:00,506 --> 00:02:04,505 D, N being zero right here, N being one right here, 32 00:02:04,505 --> 00:02:09,905 N being two right there. And if you want to express that 33 00:02:09,905 --> 00:02:13,596 in terms of a linear displacement from zero then X of 34 00:02:13,596 --> 00:02:16,932 N again for small angles is L times that number. 35 00:02:16,932 --> 00:02:21,333 And so now you get displacement here in terms of centimeters or 36 00:02:21,333 --> 00:02:25,166 in terms of millimeters. So you will say well big deal, 37 00:02:25,166 --> 00:02:28,999 it's the same result that we had for uh the double-slit 38 00:02:28,999 --> 00:02:31,696 interferometer. We had exactly the same 39 00:02:31,696 --> 00:02:34,039 equation. There was no difference. 40 00:02:34,039 --> 00:02:38,937 And D now is the separation between two sources here. 41 00:02:38,937 --> 00:02:42,476 It is obvious that it is the same because if these two are 42 00:02:42,476 --> 00:02:46,388 constructively interfering then these two will too and these two 43 00:02:46,388 --> 00:02:49,555 will too and these two will too so all of them will, 44 00:02:49,555 --> 00:02:53,467 so it's not too surprising that you get exactly the same result. 45 00:02:53,467 --> 00:02:57,13 But now comes the big surprise. We haven't discussed yet the 46 00:02:57,13 --> 00:03:00,67 issue where the locations are where light plus light gives 47 00:03:00,67 --> 00:03:02,719 darkness. We haven't discussed the 48 00:03:02,719 --> 00:03:06,134 destructive interference. And to derive that properly is 49 00:03:06,134 --> 00:03:08,618 very tricky. In fact if you take eight oh 50 00:03:08,618 --> 00:03:12,433 three you will see a perfect derivation. 51 00:03:12,433 --> 00:03:14,96 But I will give you the results. 52 00:03:14,96 --> 00:03:19,198 What is not so intuitive, that if you have N sources, 53 00:03:19,198 --> 00:03:24,17 that between two major maxima, that means between this maximum 54 00:03:24,17 --> 00:03:27,92 at N equals zero and a maximum at N equals one, 55 00:03:27,92 --> 00:03:31,506 there are now N, capital N, minus one minima. 56 00:03:31,506 --> 00:03:35,582 And minima means complete destructive interference. 57 00:03:35,582 --> 00:03:39,331 So if capital N is two, which we did last time, 58 00:03:39,331 --> 00:03:44,548 two minus one is one, exactly, that was correct. 59 00:03:44,548 --> 00:03:48,404 We had only one zero in between the two maxima. 60 00:03:48,404 --> 00:03:53,434 But that's not the case anymore when capital N is much larger 61 00:03:53,434 --> 00:03:56,787 than two. And so let me now make you a -- 62 00:03:56,787 --> 00:04:01,314 a sketch whereby I plot the intensity of the light as a 63 00:04:01,314 --> 00:04:05,421 function of angle theta and this is the intensity, 64 00:04:05,421 --> 00:04:10,032 so that's in watts per square meter, remember that's the 65 00:04:10,032 --> 00:04:14,307 pointing vector, and let this be zero, 66 00:04:14,307 --> 00:04:20,149 and let the angle theta one be here, and for small angles then 67 00:04:20,149 --> 00:04:25,415 that's lambda divided by D, and here you have theta two, 68 00:04:25,415 --> 00:04:29,533 which is two lambda divided by D, and so on. 69 00:04:29,533 --> 00:04:32,98 I take the small angle approximation. 70 00:04:32,98 --> 00:04:35,949 So this angle is now in radians. 71 00:04:35,949 --> 00:04:41,215 What you're going to see now is the following intensity, 72 00:04:41,215 --> 00:04:46,673 as a function of theta. You see here a peak, 73 00:04:46,673 --> 00:04:51,153 and you're going to see here a peak, and you're going to see 74 00:04:51,153 --> 00:04:54,949 here one, and so on, and the same of course is true 75 00:04:54,949 --> 00:04:58,289 on the other side. And here in between you're 76 00:04:58,289 --> 00:05:02,844 going to see now N minus one locations whereby you have total 77 00:05:02,844 --> 00:05:07,019 destructive interference. And the same is the case here. 78 00:05:07,019 --> 00:05:10,36 And this can be huge. N can be a few hundred. 79 00:05:10,36 --> 00:05:16,129 So we have many many locations where you have a hundred percent 80 00:05:16,129 --> 00:05:20,543 destructive interference. Now this point, 81 00:05:20,543 --> 00:05:25,177 this first location, where we hit the zero, 82 00:05:25,177 --> 00:05:31,466 that now is at the position lambda divided by D divided by 83 00:05:31,466 --> 00:05:35,99 capital N. And I will call that angle from 84 00:05:35,99 --> 00:05:42,059 the maximum to that zero from this maximum to this zero, 85 00:05:42,059 --> 00:05:47,245 I will call that angle for now delta 86 00:05:47,245 --> 00:05:50,846 theta. Because that delta theta is a 87 00:05:50,846 --> 00:05:56,3 measure for the width of the line, here is at maximum, 88 00:05:56,3 --> 00:06:00,931 here it is zero, and so that angle delta theta 89 00:06:00,931 --> 00:06:06,076 in terms of radians is lambda divided by D times N, 90 00:06:06,076 --> 00:06:11,222 which then is approximately theta one divided by N, 91 00:06:11,222 --> 00:06:16,058 because theta one itself is lambda divided by D. 92 00:06:16,058 --> 00:06:20,12 And so you see that it is N times 93 00:06:20,12 --> 00:06:24,009 smaller than this distance. And so if N is large, 94 00:06:24,009 --> 00:06:28,384 these lines become extremely narrow, and that's the big 95 00:06:28,384 --> 00:06:33,002 difference between two-slit interference and multiple-slit 96 00:06:33,002 --> 00:06:35,676 interference. And the larger N is, 97 00:06:35,676 --> 00:06:40,294 the higher these peaks will be. The height of these peaks, 98 00:06:40,294 --> 00:06:44,183 the intensity here, is proportional to N squared. 99 00:06:44,183 --> 00:06:50,422 And you may see gee why -- why not -- is why is it not linearly 100 00:06:50,422 --> 00:06:53,004 proportional to N? Well that's easy to see. 101 00:06:53,004 --> 00:06:56,139 Suppose I increase capital N, the number of sources, 102 00:06:56,139 --> 00:06:59,275 by a factor of three. Then the electric field vector 103 00:06:59,275 --> 00:07:01,98 where there are maxima is three times larger. 104 00:07:01,98 --> 00:07:05,484 But if the electric field vector is three times larger the 105 00:07:05,484 --> 00:07:07,697 pointing vector is nine times larger. 106 00:07:07,697 --> 00:07:09,665 So you get nine times more light. 107 00:07:09,665 --> 00:07:12,431 Now you may say, gee that's a violation of the 108 00:07:12,431 --> 00:07:15,383 conservation of energy. Three times more sources, 109 00:07:15,383 --> 00:07:17,719 nine times more light, how can that be, 110 00:07:17,719 --> 00:07:21,469 well you overlook then that if you make N go up by a factor of 111 00:07:21,469 --> 00:07:25,121 three that the lines get narrower by 112 00:07:25,121 --> 00:07:27,76 a factor of three, because of this N here, 113 00:07:27,76 --> 00:07:30,462 and so they get higher by a factor of nine, 114 00:07:30,462 --> 00:07:33,165 and they get narrower by a factor of three, 115 00:07:33,165 --> 00:07:35,868 and so you gain a factor of three in light. 116 00:07:35,868 --> 00:07:38,185 Of course you gain a factor of three. 117 00:07:38,185 --> 00:07:40,309 You have three times more sources. 118 00:07:40,309 --> 00:07:44,299 You get three times more light. So you see there's no violation 119 00:07:44,299 --> 00:07:46,487 of the conservation of energy here. 120 00:07:46,487 --> 00:07:50,283 And I want to demonstrate this to you using a -- a red laser 121 00:07:50,283 --> 00:07:53,823 which we have used before. And I will use what we call a 122 00:07:53,823 --> 00:07:57,985 grading, a grading is a plate which is 123 00:07:57,985 --> 00:08:00,985 specially prepared, a transparent plate, 124 00:08:00,985 --> 00:08:05,216 which has grooves in it, and the one that I will use has 125 00:08:05,216 --> 00:08:09,14 tw- twenty-five hundred grooves, we call them lines, 126 00:08:09,14 --> 00:08:11,909 per inch. That means the separation D 127 00:08:11,909 --> 00:08:16,602 between two adjacent grooves in my case is about two point one 128 00:08:16,602 --> 00:08:19,679 six microns. A micron is ten to the minus 129 00:08:19,679 --> 00:08:22,603 six meters. And the wavelength that I'm 130 00:08:22,603 --> 00:08:28,49 going to use is our red laser, which is about six point three 131 00:08:28,49 --> 00:08:31,231 times ten to the minus seven meters. 132 00:08:31,231 --> 00:08:34,519 And I'm going to put the whole thing there. 133 00:08:34,519 --> 00:08:38,434 I'm going to make you see it there at a distance L. 134 00:08:38,434 --> 00:08:42,662 Which is about ten meters. And so this allows me now to 135 00:08:42,662 --> 00:08:47,516 calculate where the zero order will fall, where the first order 136 00:08:47,516 --> 00:08:50,335 and where the second order will fall. 137 00:08:50,335 --> 00:08:54,014 We call when N is zero, we call that zero order, 138 00:08:54,014 --> 00:08:57,773 so this is zero order, when N is one we call that 139 00:08:57,773 --> 00:09:01,97 first order, and when N is two we call that 140 00:09:01,97 --> 00:09:04,372 second order. And you have of course the 141 00:09:04,372 --> 00:09:07,884 first order also on this side and the second order also on 142 00:09:07,884 --> 00:09:10,286 this side. Everything that you have here 143 00:09:10,286 --> 00:09:13,675 you have to also think of it as being on the other side. 144 00:09:13,675 --> 00:09:17,248 So I can predict now where the zero order will be when N is 145 00:09:17,248 --> 00:09:18,849 zero. That is zero degrees. 146 00:09:18,849 --> 00:09:21,745 That's immediately obvious. I use that equation. 147 00:09:21,745 --> 00:09:25,256 If N is zero the zero order is always right at the center, 148 00:09:25,256 --> 00:09:27,967 provided that all these sources are in phase. 149 00:09:27,967 --> 00:09:32,403 And they will be in phase because I use plain waves. 150 00:09:32,403 --> 00:09:36,395 So Huygens will tell you that they're going to oscillate 151 00:09:36,395 --> 00:09:40,459 exactly at the same time they produce the same frequency, 152 00:09:40,459 --> 00:09:44,161 they produce the same wavelength, and they're all in 153 00:09:44,161 --> 00:09:47,863 phase with each other. So there will be a maximum at 154 00:09:47,863 --> 00:09:51,202 theta one equals zero. And then there will be a 155 00:09:51,202 --> 00:09:55,266 maximum which I calculated to be at three point five five 156 00:09:55,266 --> 00:09:57,807 degrees. I calculated that from this 157 00:09:57,807 --> 00:10:02,234 equation and then theta two will be at roughly seven point one 158 00:10:02,234 --> 00:10:04,847 degrees. If you want to know how wide 159 00:10:04,847 --> 00:10:08,985 the width of this peak is going to be, 160 00:10:08,985 --> 00:10:14,307 then you have to know how many lines of my grading I will be 161 00:10:14,307 --> 00:10:17,375 using. Well, my grading is like so. 162 00:10:17,375 --> 00:10:22,698 Here I have these lines not unlike the grading that you have 163 00:10:22,698 --> 00:10:27,028 in your optics kit. There are twenty-five hundred 164 00:10:27,028 --> 00:10:31,72 of those lines per inch. And my laser beam is roughly 165 00:10:31,72 --> 00:10:35,689 two millimeters in size. So this is about two 166 00:10:35,689 --> 00:10:40,652 millimeters. And that tells me then that I 167 00:10:40,652 --> 00:10:46,026 cover about two hundred lines. And if I have two hundred lines 168 00:10:46,026 --> 00:10:50,696 I can now calculate how wide that line is going to be. 169 00:10:50,696 --> 00:10:54,573 Because this factor of N enters into it here. 170 00:10:54,573 --> 00:10:59,508 And if I express that in terms of that angle delta theta, 171 00:10:59,508 --> 00:11:04,442 then the angle delta theta going back here so delta theta 172 00:11:04,442 --> 00:11:09,288 is then the three point five five degrees divided by two 173 00:11:09,288 --> 00:11:13,288 hundred, and that's an extremely small 174 00:11:13,288 --> 00:11:16,921 angle, that angle is approximately one arc minute, 175 00:11:16,921 --> 00:11:20,183 which is sixty times smaller than one degree. 176 00:11:20,183 --> 00:11:24,483 And if you want to translate that in terms of how wide that 177 00:11:24,483 --> 00:11:27,597 spot will be, if I see it on the screen ten 178 00:11:27,597 --> 00:11:31,155 meters away from me, and if you want to call that 179 00:11:31,155 --> 00:11:35,159 delta X, then you would naively predict that delta X is 180 00:11:35,159 --> 00:11:38,94 something like three millimeters, and the reason why 181 00:11:38,94 --> 00:11:43,759 I say naively because you will not see that it is 182 00:11:43,759 --> 00:11:46,931 three millimeters, it will be extremely narrow, 183 00:11:46,931 --> 00:11:50,655 but it will be more than three millimeters, because the 184 00:11:50,655 --> 00:11:54,586 limiting factor is always the divergence of my laser beam. 185 00:11:54,586 --> 00:11:58,586 And so the divergence of my laser beam is more than one arc 186 00:11:58,586 --> 00:12:02,654 minute, and so I don't get down to the one arc minute narrow 187 00:12:02,654 --> 00:12:04,93 beam. I'm not too far away from it 188 00:12:04,93 --> 00:12:07,482 though. So this is what I want to show 189 00:12:07,482 --> 00:12:10,24 you first. I will turn on the laser first 190 00:12:10,24 --> 00:12:14,102 and then make it very dark because we do need darkness or 191 00:12:14,102 --> 00:12:17,61 this has to come off because that 192 00:12:17,61 --> 00:12:21,11 would obviously -- oh, I turned off the wrong laser, 193 00:12:21,11 --> 00:12:24,815 but that -- I turned on the wrong laser, but that's OK. 194 00:12:24,815 --> 00:12:28,658 That's a second demonstration which I do with uh with the 195 00:12:28,658 --> 00:12:32,501 green laser, this is the one that I need, this is the red 196 00:12:32,501 --> 00:12:34,697 laser, will come on very quickly. 197 00:12:34,697 --> 00:12:37,579 There it is. Tom, if you can turn that off, 198 00:12:37,579 --> 00:12:40,941 maybe that will help, although everyone can see it 199 00:12:40,941 --> 00:12:44,098 but it would help. So you see here very clearly 200 00:12:44,098 --> 00:12:47,76 the um the zero order is at the m- at 201 00:12:47,76 --> 00:12:51,387 the -- right in the middle. This one, so theta is zero, 202 00:12:51,387 --> 00:12:54,679 and this theta one is my three-and-a-half degrees, 203 00:12:54,679 --> 00:12:57,164 this is also three-and-a-half degrees. 204 00:12:57,164 --> 00:13:00,187 This is the seven point one degrees and so on. 205 00:13:00,187 --> 00:13:03,344 And so you see this whole pattern of -- uh of uh 206 00:13:03,344 --> 00:13:06,166 interference as a result of multiple slits. 207 00:13:06,166 --> 00:13:10,196 And so this is a -- these are grooves in a piece of plastics. 208 00:13:10,196 --> 00:13:15,235 And notice how small they are, how narrow they are compared 209 00:13:15,235 --> 00:13:18,148 with the double-slit interference. 210 00:13:18,148 --> 00:13:22,738 So they don't have that theoretical minimum with this 211 00:13:22,738 --> 00:13:27,859 one over N, but they approach that, and the reason why they 212 00:13:27,859 --> 00:13:33,332 are not that narrow is because the divergence of the laser beam 213 00:13:33,332 --> 00:13:38,541 itself is larger than that one arc minute that I calculated. 214 00:13:38,541 --> 00:13:42,072 And so you can never beat that of course. 215 00:13:42,072 --> 00:13:46,221 We did this experiment with white, 216 00:13:46,221 --> 00:13:49,345 with uh red light, but keep in mind that if I take 217 00:13:49,345 --> 00:13:52,085 red light, here is a maximum, at zero order, 218 00:13:52,085 --> 00:13:55,017 here is a maximum, provided that this lambda is 219 00:13:55,017 --> 00:13:57,12 lambda for red, here is a maximum, 220 00:13:57,12 --> 00:13:59,67 provided that this is the lambda for red. 221 00:13:59,67 --> 00:14:02,984 But if I have white light, then of course I deal with 222 00:14:02,984 --> 00:14:05,725 other colors. And if I have blue light in my 223 00:14:05,725 --> 00:14:08,593 white light, it will also have a maximum here, 224 00:14:08,593 --> 00:14:11,588 that's nonnegotiable, but it has its first order 225 00:14:11,588 --> 00:14:14,01 maximum here, because the wavelength is 226 00:14:14,01 --> 00:14:16,241 shorter. And it will have its second 227 00:14:16,241 --> 00:14:18,846 order maximum here. 228 00:14:18,846 --> 00:14:22,571 This will be the same distance. And so when you do this with 229 00:14:22,571 --> 00:14:26,169 white light you're going to see always at zero order white 230 00:14:26,169 --> 00:14:29,642 light, because all the colors have their maximum at zero 231 00:14:29,642 --> 00:14:32,672 order, but at first and second and higher orders, 232 00:14:32,672 --> 00:14:36,334 the cor- the -- the -- the colors uh walk at their own pace 233 00:14:36,334 --> 00:14:38,606 so to speak. And then the smaller the 234 00:14:38,606 --> 00:14:42,457 wavelength is the closer it will be to the zero order and then 235 00:14:42,457 --> 00:14:46,372 the spacings between first and second will also be smaller than 236 00:14:46,372 --> 00:14:49,717 in the case of the long wavelength, 237 00:14:49,717 --> 00:14:52,666 in this case red. And this is something that I 238 00:14:52,666 --> 00:14:56,794 also want to demonstrate to you. It is not so easy to get a very 239 00:14:56,794 --> 00:14:59,218 strong powerful source of white light. 240 00:14:59,218 --> 00:15:02,101 I'm using for this a -- a reflection grading. 241 00:15:02,101 --> 00:15:04,657 You can also use gradings in reflection. 242 00:15:04,657 --> 00:15:08,391 You take metal and then the -- the grooves are made on the 243 00:15:08,391 --> 00:15:10,423 metal. And you get a reflection, 244 00:15:10,423 --> 00:15:12,782 which we will have there on the wall. 245 00:15:12,782 --> 00:15:16,451 This reflection grading has a spacing which is four times 246 00:15:16,451 --> 00:15:19,923 smaller than the one we have here. 247 00:15:19,923 --> 00:15:23,238 It's only two-and-a-half microns and so the angle of 248 00:15:23,238 --> 00:15:26,617 theta one will not be three-and-a-half degrees but it 249 00:15:26,617 --> 00:15:30,322 will be four times larger. The main purpose wh- why I want 250 00:15:30,322 --> 00:15:34,156 to show you this is I use white light that the zero order is 251 00:15:34,156 --> 00:15:36,366 white. And then we will see also of 252 00:15:36,366 --> 00:15:40,07 course the first and the second order if we have good eyes 253 00:15:40,07 --> 00:15:43,774 because the f- the -- the whole thing is not so -- so very 254 00:15:43,774 --> 00:15:46,244 bright. Make sure that I have the -- my 255 00:15:46,244 --> 00:15:49,364 light, flashlight, so your eyes 256 00:15:49,364 --> 00:15:53,311 may have to adjust a little bit to the darkness. 257 00:15:53,311 --> 00:15:58,434 The effect is not overpowering because our light source is not 258 00:15:58,434 --> 00:16:01,71 very bright. But you see the where is my 259 00:16:01,71 --> 00:16:05,489 laser pointer, this is the zero order maximum, 260 00:16:05,489 --> 00:16:10,277 and the zero order maximum is very wide, the reason is the 261 00:16:10,277 --> 00:16:15,316 divergence of the white light beam, it's not this factor of N 262 00:16:15,316 --> 00:16:20,355 that I gain, I gain much less, uh I can turn on 263 00:16:20,355 --> 00:16:24,94 also a laser which I use at the same time, and you will see that 264 00:16:24,94 --> 00:16:28,652 the red laser will give its own th- there they come, 265 00:16:28,652 --> 00:16:32,8 so the zero order of the red laser is of course also here, 266 00:16:32,8 --> 00:16:36,511 all colors are here, and then you see here the first 267 00:16:36,511 --> 00:16:39,277 order of the red, that's a large angle, 268 00:16:39,277 --> 00:16:43,279 but the D is very small, you see here the first order of 269 00:16:43,279 --> 00:16:47,282 the red, second order of the red, you see here the first 270 00:16:47,282 --> 00:16:51,503 order of the blue, first order of the blue, 271 00:16:51,503 --> 00:16:55,464 you see a big difference, between the separation of the 272 00:16:55,464 --> 00:16:59,499 red and the separation from the zero order and the blue, 273 00:16:59,499 --> 00:17:03,388 it's a big difference. There is actually a much better 274 00:17:03,388 --> 00:17:07,79 way that I can make you see all this and that is if I ask you 275 00:17:07,79 --> 00:17:11,678 which I think I'm going to do now to use your grading, 276 00:17:11,678 --> 00:17:14,026 but hold -- hold it for a second. 277 00:17:14,026 --> 00:17:17,254 Before you get your -- your own gradings out. 278 00:17:17,254 --> 00:17:21,363 Our equations that we have derived so far 279 00:17:21,363 --> 00:17:24,458 only hold if we look very far away. 280 00:17:24,458 --> 00:17:29,831 These angles of theta are only true if you go very far away. 281 00:17:29,831 --> 00:17:34,93 For reasons that we discussed last time we can however do 282 00:17:34,93 --> 00:17:39,391 something very clever. We can use a lens and if we 283 00:17:39,391 --> 00:17:44,126 have a lens we can bring the image very close without 284 00:17:44,126 --> 00:17:48,041 disturbing the angles. If this is a grading, 285 00:17:48,041 --> 00:17:53,049 this is the number of sources that I have, 286 00:17:53,049 --> 00:17:58,48 and so the light comes in in this direction and if I put here 287 00:17:58,48 --> 00:18:03,729 a lens and this is the screen, the focal point of the lens, 288 00:18:03,729 --> 00:18:08,798 then if the angle theta -- if the angle theta for which I 289 00:18:08,798 --> 00:18:13,414 would have expected in this direction my first order 290 00:18:13,414 --> 00:18:17,848 maximum, and here of course my zero order maximum, 291 00:18:17,848 --> 00:18:21,469 then the lens will not change that angle. 292 00:18:21,469 --> 00:18:27,01 We never discussed lenses so it may not be so obvious to 293 00:18:27,01 --> 00:18:28,909 you. But the lens will always 294 00:18:28,909 --> 00:18:31,079 maintain the integrity of angles. 295 00:18:31,079 --> 00:18:34,672 So the angle theta that we derived here is the correct 296 00:18:34,672 --> 00:18:38,944 angle, but of course in terms of X that is enormously reduced if 297 00:18:38,944 --> 00:18:42,945 this distance is very small. So then we have the option that 298 00:18:42,945 --> 00:18:46,945 we don't have to allow for very large distances like now ten 299 00:18:46,945 --> 00:18:49,319 meters. And so your eye is a perfect 300 00:18:49,319 --> 00:18:53,523 tool to use for that because you have a lens in your -- in your 301 00:18:53,523 --> 00:18:57,252 eye, that's the whole idea. And so now I want you to get 302 00:18:57,252 --> 00:18:59,873 your gradings out. 303 00:18:59,873 --> 00:19:04,15 And I want you to hold the gradings in front of your eyes 304 00:19:04,15 --> 00:19:08,658 and manipulate the gradings a little bit so that you get the 305 00:19:08,658 --> 00:19:12,095 lines vertical. And you will easily be able to 306 00:19:12,095 --> 00:19:14,692 do that, this is your light source. 307 00:19:14,692 --> 00:19:18,588 Your lines, your gradings, have a thousand lines per 308 00:19:18,588 --> 00:19:21,72 millimeter. That means the spacing of your 309 00:19:21,72 --> 00:19:25,769 grading is one micron. One micron is ten times smaller 310 00:19:25,769 --> 00:19:29,36 than this number. So the angles are huge in your 311 00:19:29,36 --> 00:19:33,583 case. They're way larger than what we 312 00:19:33,583 --> 00:19:36,846 have there. I will make it completely dark 313 00:19:36,846 --> 00:19:41,621 and then I want you to rotate your gradings such that you get 314 00:19:41,621 --> 00:19:46,077 the spectra on either side, on the left and on the right. 315 00:19:46,077 --> 00:19:50,374 That means your grooves are then in vertical direction. 316 00:19:50,374 --> 00:19:55,387 And what you see now way better than what I could show you in my 317 00:19:55,387 --> 00:19:59,525 previous demonstration, you see the zero order is the 318 00:19:59,525 --> 00:20:03,522 lamp itself. All the colors are right at the 319 00:20:03,522 --> 00:20:04,952 center. That's the lamp. 320 00:20:04,952 --> 00:20:08,682 That's your zero order maximum. And then you see if you go to 321 00:20:08,682 --> 00:20:11,977 the right you see the blue coming in beautifully first 322 00:20:11,977 --> 00:20:15,645 because that's the smallest wavelength, you're going further 323 00:20:15,645 --> 00:20:18,195 to the right, you see the first order red, 324 00:20:18,195 --> 00:20:21,801 you're going further to the right, you see the second order 325 00:20:21,801 --> 00:20:25,407 blue, you go further to the right, and you see second order 326 00:20:25,407 --> 00:20:28,577 red, but since D is so amazingly small in your case, 327 00:20:28,577 --> 00:20:31,251 there may not be too many maxima in the red. 328 00:20:31,251 --> 00:20:36,43 In fact I will ask you on one of the homework assignments 329 00:20:36,43 --> 00:20:41,039 which is the optional one how many maxima in the red you will 330 00:20:41,039 --> 00:20:43,574 see. So essential here is that you 331 00:20:43,574 --> 00:20:47,876 see that the f- zero order maximum at the center is white 332 00:20:47,876 --> 00:20:50,564 light. And so it's not until you get 333 00:20:50,564 --> 00:20:54,943 to first and second order that you begin to see the colors 334 00:20:54,943 --> 00:20:57,939 separate. Now these gradings can be used 335 00:20:57,939 --> 00:21:01,779 to do atomic physics. There are atoms and molecules 336 00:21:01,779 --> 00:21:05,851 uh which emit very discrete frequencies, very discrete 337 00:21:05,851 --> 00:21:10,331 wavelength. And when you look at them with 338 00:21:10,331 --> 00:21:14,387 a grading you can see very distinctly where these lines 339 00:21:14,387 --> 00:21:16,94 fall. Where these wavelengths fall. 340 00:21:16,94 --> 00:21:20,169 And that's the next thing that I want to do. 341 00:21:20,169 --> 00:21:24 I will show you now, I will turn off the white light 342 00:21:24 --> 00:21:26,853 source and I will turn on for you neon. 343 00:21:26,853 --> 00:21:31,059 And so I want you to look now at the neon and if you give 344 00:21:31,059 --> 00:21:35,039 yourself some time you will see that the neon is not a 345 00:21:35,039 --> 00:21:40,596 continuous spectrum like you saw with the white light bulb 346 00:21:40,596 --> 00:21:43,982 but you see very distinct locations where you see maxima. 347 00:21:43,982 --> 00:21:47,248 You see many in the red, and I think you see several in 348 00:21:47,248 --> 00:21:50,936 the orange, and I noticed this morning that I see two lines in 349 00:21:50,936 --> 00:21:53,415 the green. You have to look very carefully 350 00:21:53,415 --> 00:21:56,257 because these lines in the green are very faint. 351 00:21:56,257 --> 00:21:59,884 And so the whole purpose then is that with these gradings you 352 00:21:59,884 --> 00:22:03,452 can not only find out which wavelengths are emitted by these 353 00:22:03,452 --> 00:22:07,019 atoms and these molecules but you can also find the relative 354 00:22:07,019 --> 00:22:10,708 strength, and that is of course entering the 355 00:22:10,708 --> 00:22:13,782 domain of atomic physics. And these gradings are 356 00:22:13,782 --> 00:22:17,772 extremely powerful to do that. And I would advise you to carry 357 00:22:17,772 --> 00:22:21,893 these gradings with you at least for the next few weeks and when 358 00:22:21,893 --> 00:22:25,817 you're outside and you get a chance to see some bright lights 359 00:22:25,817 --> 00:22:29,219 out on highways or on the street, to look through the 360 00:22:29,219 --> 00:22:32,882 grading and see whether you can see these emission lines, 361 00:22:32,882 --> 00:22:36,806 uh mercury if you get mercury lamps, they are very beautiful. 362 00:22:36,806 --> 00:22:39,881 You see many many different colors very discrete 363 00:22:39,881 --> 00:22:43,544 frequencies, very discrete wavelengths, 364 00:22:43,544 --> 00:22:48,58 are emitted by mercury in the same way, the same kind of 365 00:22:48,58 --> 00:22:52,976 physics that you see that here with um with neon. 366 00:22:52,976 --> 00:22:58,197 So now comes something that may come as a surprise to you. 367 00:22:58,197 --> 00:23:02,776 Because now I would like to discuss with you um the 368 00:23:02,776 --> 00:23:06,897 interference pattern if we have only one slit. 369 00:23:06,897 --> 00:23:10,926 We discussed two, we discussed capital N is a 370 00:23:10,926 --> 00:23:15,178 large number, but what now if we have only 371 00:23:15,178 --> 00:23:17,782 one slit? Even if you have only one slit 372 00:23:17,782 --> 00:23:21,589 there will be directions in space whereby light plus light 373 00:23:21,589 --> 00:23:24,461 gives darkness, and there will be directions 374 00:23:24,461 --> 00:23:28,401 whereby the light constructively interferes with each other. 375 00:23:28,401 --> 00:23:31,808 And strangely enough this is given a different name. 376 00:23:31,808 --> 00:23:35,481 We call this diffraction. It's exactly the same physics. 377 00:23:35,481 --> 00:23:38,753 There is no difference. It should have been called 378 00:23:38,753 --> 00:23:41,625 interference, but it's in the literature you 379 00:23:41,625 --> 00:23:44,163 will see it under the name diffraction. 380 00:23:44,163 --> 00:23:47,836 It all comes down again to Huygens' 381 00:23:47,836 --> 00:23:50,757 principle. So let me here now have a 382 00:23:50,757 --> 00:23:55,848 single opening and this opening is a slit perpendicular to the 383 00:23:55,848 --> 00:23:59,102 blackboard and the opening is A in size. 384 00:23:59,102 --> 00:24:02,774 A single one. And the plain waves come in and 385 00:24:02,774 --> 00:24:05,278 Mr. Huygens says that all these 386 00:24:05,278 --> 00:24:10,452 sources here are all going to be emitting the light at the same 387 00:24:10,452 --> 00:24:15,459 frequency, the same wavelength, and they will all be in phase 388 00:24:15,459 --> 00:24:20,215 with each other. Because these plain waves 389 00:24:20,215 --> 00:24:22,685 arrive here all at the same time. 390 00:24:22,685 --> 00:24:27,161 And so I could now ask myself the question at what angle of 391 00:24:27,161 --> 00:24:31,406 theta will I see maximum, what angle of theta will I see 392 00:24:31,406 --> 00:24:36,268 minimum, and you can also put a screen then at large distance L, 393 00:24:36,268 --> 00:24:40,975 you can call X equals zero here and you can ask yourself where 394 00:24:40,975 --> 00:24:45,374 will I see these maxima and where will I see these minima? 395 00:24:45,374 --> 00:24:48,384 To derive this in this case is not easy. 396 00:24:48,384 --> 00:24:50,776 Again I refer to eight oh three. 397 00:24:50,776 --> 00:24:55,561 It's as difficult as deriving in this case this 398 00:24:55,561 --> 00:24:58,307 whole structure in between the maxima. 399 00:24:58,307 --> 00:25:02,834 One thing is obvious and that is that you got to get a maximum 400 00:25:02,834 --> 00:25:06,099 that is nonnegotiable when theta equals zero. 401 00:25:06,099 --> 00:25:09,736 That's simply a matter of symmetry of the problem. 402 00:25:09,736 --> 00:25:13,966 If all these sources are in phase, clearly you're going to 403 00:25:13,966 --> 00:25:17,306 get a maximum here. No one will question that. 404 00:25:17,306 --> 00:25:21,536 The minima is very tricky. And the minima will fall at the 405 00:25:21,536 --> 00:25:26,583 following locations. The sine of theta of N equals N 406 00:25:26,583 --> 00:25:29,837 times lambda divided by A. And for small angle 407 00:25:29,837 --> 00:25:33,02 approximation, this is the same as theta N in 408 00:25:33,02 --> 00:25:35,769 radians. And when you see that equation 409 00:25:35,769 --> 00:25:40,109 your first reaction should be that maybe I goofed by a factor 410 00:25:40,109 --> 00:25:42,568 of two. Because your first reaction 411 00:25:42,568 --> 00:25:47,053 will be that's the same equation that we have there and then we 412 00:25:47,053 --> 00:25:50,163 have D there, and so how can we have minimum 413 00:25:50,163 --> 00:25:54,069 here where we have maxima there? Well, the situation is 414 00:25:54,069 --> 00:25:56,89 different. The best way that you can see 415 00:25:56,89 --> 00:26:00,818 that that equation is not wrong is 416 00:26:00,818 --> 00:26:04,567 perhaps the following. Suppose you take the angle 417 00:26:04,567 --> 00:26:07,457 theta one. So that's for N equals one. 418 00:26:07,457 --> 00:26:12,065 Then the relation that you see there will tell you that this 419 00:26:12,065 --> 00:26:16,439 source here, this Huygens source, and this Huygens source 420 00:26:16,439 --> 00:26:19,719 have a difference in path length of lambda. 421 00:26:19,719 --> 00:26:23,389 And so you will then say aha that's constructive 422 00:26:23,389 --> 00:26:25,342 interference, that's true, 423 00:26:25,342 --> 00:26:29,97 but that means this Huygens source and this Huygens 424 00:26:29,97 --> 00:26:32,965 source will then have a difference in path of half 425 00:26:32,965 --> 00:26:35,165 lambda. So they will kill each other. 426 00:26:35,165 --> 00:26:38,648 And that means this Huygens source and this Huygens source 427 00:26:38,648 --> 00:26:42,071 will have a difference in path length of one-half lambda. 428 00:26:42,071 --> 00:26:44,087 So they will also kill each other. 429 00:26:44,087 --> 00:26:47,693 And so in this upper half there is always one Huygens source 430 00:26:47,693 --> 00:26:49,954 which will kill the one at the bottom. 431 00:26:49,954 --> 00:26:53,193 And you can do a similar reasoning for the angle theta 432 00:26:53,193 --> 00:26:54,966 two. And so that is indeed the 433 00:26:54,966 --> 00:26:58,633 correct equation. You will find complete 434 00:26:58,633 --> 00:27:03,326 minima when theta one in terms of radians is lambda divided by 435 00:27:03,326 --> 00:27:07,327 A and theta two is two lambda divided by A and so on. 436 00:27:07,327 --> 00:27:09,866 That's where you find your minima. 437 00:27:09,866 --> 00:27:14,405 And if you convert that into X where they actually fall on a 438 00:27:14,405 --> 00:27:19,252 screen, well then X one will be for small angle approximations L 439 00:27:19,252 --> 00:27:22,792 times lambda divided by A. That's no different. 440 00:27:22,792 --> 00:27:25,715 And so now what I owe you is a pattern. 441 00:27:25,715 --> 00:27:28,1 What will the pattern look like? 442 00:27:28,1 --> 00:27:31,871 When I look on the screen there, 443 00:27:31,871 --> 00:27:35,226 what will I really see? Well, it's looking, 444 00:27:35,226 --> 00:27:39,22 it's going to look very different from what you may 445 00:27:39,22 --> 00:27:42,096 think. I will plot it now in terms of 446 00:27:42,096 --> 00:27:44,333 X. I could have plotted it in 447 00:27:44,333 --> 00:27:47,688 terms of theta. But I decided to plot it in 448 00:27:47,688 --> 00:27:50,963 terms of X. So here at X equals zero there 449 00:27:50,963 --> 00:27:53,28 is unmistakable, unnegotiable, 450 00:27:53,28 --> 00:27:57,194 there is a maximum, that is -- that coincides with 451 00:27:57,194 --> 00:28:01,108 theta equals zero. And then here at lambda divided 452 00:28:01,108 --> 00:28:05,981 by A, completely destructive interference, 453 00:28:05,981 --> 00:28:09,005 that's that angle theta one uh times L. 454 00:28:09,005 --> 00:28:12,745 And then here L two lambda divided by A complete 455 00:28:12,745 --> 00:28:17,599 destructive interference and the same is true of course on the 456 00:28:17,599 --> 00:28:20,702 other side. And what you're going to see 457 00:28:20,702 --> 00:28:24,919 now in terms of the intensity that I showed you there, 458 00:28:24,919 --> 00:28:28,898 watts per square meters, is a curve that looks like 459 00:28:28,898 --> 00:28:31,444 this. You get an enormously broad 460 00:28:31,444 --> 00:28:36,329 maximum, absolutely zero here, very small maximum, 461 00:28:36,329 --> 00:28:39,694 absolutely zero there, very small maximum and zero 462 00:28:39,694 --> 00:28:42,51 there, and this continues for a long time. 463 00:28:42,51 --> 00:28:46,286 And this is very different from anything we've seen with 464 00:28:46,286 --> 00:28:49,239 multiple sources. If the intensity here is I 465 00:28:49,239 --> 00:28:53,085 zero, then the maximum here which I didn't even calculate 466 00:28:53,085 --> 00:28:56,93 where it is, it is somewhere in between these two minima, 467 00:28:56,93 --> 00:28:59,952 but I didn't calculate precisely where it is, 468 00:28:59,952 --> 00:29:03,385 that maximum is very low, it's only four point five 469 00:29:03,385 --> 00:29:08,329 percent in strength of I zero. And this is even lower. 470 00:29:08,329 --> 00:29:12,006 This is only one point six percent of I zero. 471 00:29:12,006 --> 00:29:15,431 So when you look at a diffraction pattern, 472 00:29:15,431 --> 00:29:19,107 we call this a diffraction pattern like this, 473 00:29:19,107 --> 00:29:23,786 you will see a very broad center maximum and then you see 474 00:29:23,786 --> 00:29:28,715 these dark spots on either side, and you see light coming up 475 00:29:28,715 --> 00:29:32,057 again in between them, sort of submaxima. 476 00:29:32,057 --> 00:29:36,318 And so the width of this center maximum, this width, 477 00:29:36,318 --> 00:29:41,279 which is really X one, that width is then L lambda 478 00:29:41,279 --> 00:29:45,435 divided by A and if you want to be picky and you say well the 479 00:29:45,435 --> 00:29:48,621 center maximum is really twice that much, fine, 480 00:29:48,621 --> 00:29:51,46 be my guest, but this is clearly a measure 481 00:29:51,46 --> 00:29:55,408 for how wide that center spot will be when you see it on a 482 00:29:55,408 --> 00:29:57,901 screen. And now there comes something 483 00:29:57,901 --> 00:30:01,918 that is completely not intuitive for you as well as for me. 484 00:30:01,918 --> 00:30:05,935 And that is if you make A very small that means you let the 485 00:30:05,935 --> 00:30:09,951 light go through an extremely narrow slit, 486 00:30:09,951 --> 00:30:13,907 then this what you will see on the wall is extremely wide. 487 00:30:13,907 --> 00:30:16,474 The smaller A is the wider it will be. 488 00:30:16,474 --> 00:30:19,666 It's exactly opposed to what you would predict. 489 00:30:19,666 --> 00:30:23,83 You would think if you make the opening through which you put 490 00:30:23,83 --> 00:30:27,022 light very small, you would think that what you 491 00:30:27,022 --> 00:30:29,52 see on the screen is also very small. 492 00:30:29,52 --> 00:30:33,267 It's exactly the opposite. And that's is what I want to 493 00:30:33,267 --> 00:30:36,459 demonstrate to you. I have here a demonstration 494 00:30:36,459 --> 00:30:38,818 with a variable slit. I can vary A. 495 00:30:38,818 --> 00:30:42,936 And we will use the brightest laser that we 496 00:30:42,936 --> 00:30:46,714 have, a beam of green laser light, about five thousand four 497 00:30:46,714 --> 00:30:49,711 hundred Angstroms. And what I will do is I will 498 00:30:49,711 --> 00:30:53,098 make this opening narrower and narrower and narrower. 499 00:30:53,098 --> 00:30:55,964 And as I make the opening I start very large. 500 00:30:55,964 --> 00:30:59,482 I start with a large opening of maybe five millimeters. 501 00:30:59,482 --> 00:31:03,064 At a large opening A is so large that this is negligibly 502 00:31:03,064 --> 00:31:06,842 small because A is very large, then this is not very large, 503 00:31:06,842 --> 00:31:09,839 this is very small. But as I make A smaller and 504 00:31:09,839 --> 00:31:14,847 smaller and smaller and smaller there comes a time that 505 00:31:14,847 --> 00:31:19,523 the diffraction width is going to be dominating the whole scene 506 00:31:19,523 --> 00:31:24,123 and what you will see then on the screen there that the bright 507 00:31:24,123 --> 00:31:26,612 spot will get wider, wider, wider, 508 00:31:26,612 --> 00:31:29,176 wider. And that for me is always so 509 00:31:29,176 --> 00:31:33,776 enormously fascinating because it goes so strongly against our 510 00:31:33,776 --> 00:31:36,868 intuition. And so this is what I have next 511 00:31:36,868 --> 00:31:40,111 on the menu. I have here this variable slit. 512 00:31:40,111 --> 00:31:46,144 I must make sure that I have my flashlight and I'll turn on this 513 00:31:46,144 --> 00:31:49,95 laser that I earlier accidentally turned on. 514 00:31:49,95 --> 00:31:52,782 I hope it's coming on. Yes it is. 515 00:31:52,782 --> 00:31:56,853 And so you see there the slit is now very wide. 516 00:31:56,853 --> 00:32:01,986 And so the size of that slit that you see there -- the size 517 00:32:01,986 --> 00:32:07,207 of the -- of the bright spot is now entirely dictated by the 518 00:32:07,207 --> 00:32:11,809 divergence of my laser beam. The diffraction width is 519 00:32:11,809 --> 00:32:15,349 negligibly small because A is very large. 520 00:32:15,349 --> 00:32:19,42 But now watch. Now I'm going to 521 00:32:19,42 --> 00:32:22,947 tighten, make A smaller. And I'm doing that now. 522 00:32:22,947 --> 00:32:25,424 I'm making it smaller and smaller. 523 00:32:25,424 --> 00:32:28,502 The diffraction width is still negligible. 524 00:32:28,502 --> 00:32:30,078 Making it smaller. Ah. 525 00:32:30,078 --> 00:32:32,705 I'm beginning to see the dark lines. 526 00:32:32,705 --> 00:32:35,257 Ah. The diffraction width is taking 527 00:32:35,257 --> 00:32:37,659 over. Look at the center maximum. 528 00:32:37,659 --> 00:32:39,986 Right there. It's getting wider. 529 00:32:39,986 --> 00:32:43,589 It's getting wider. And I make the slit narrower. 530 00:32:43,589 --> 00:32:46,442 It's getting wider. It's getting wider. 531 00:32:46,442 --> 00:32:51,043 Look how beautiful you see these destructive 532 00:32:51,043 --> 00:32:53,694 interferences. Where light plus light gives 533 00:32:53,694 --> 00:32:54,641 darkness. Wider. 534 00:32:54,641 --> 00:32:56,787 Wider. Right now it is at least ten 535 00:32:56,787 --> 00:33:00,386 times wider than it was before. And now it is twenty times 536 00:33:00,386 --> 00:33:02,217 wider. And it gets very faint. 537 00:33:02,217 --> 00:33:05,941 Of course it gets very faint because if I make the slit very 538 00:33:05,941 --> 00:33:09,476 narrow not much light goes through, there's nothing I can 539 00:33:09,476 --> 00:33:11,812 do about it. But notice how incredibly 540 00:33:11,812 --> 00:33:14,779 impressive this is. How wide that center maximum 541 00:33:14,779 --> 00:33:17,241 becomes. And that is very characteristic 542 00:33:17,241 --> 00:33:20,208 for diffraction. The narrower the slit the wider 543 00:33:20,208 --> 00:33:25,272 the diffraction pattern at the center maximum. 544 00:33:25,272 --> 00:33:30,735 Now I did this in monochromatic light, monochromatic light means 545 00:33:30,735 --> 00:33:34,637 that you have practically only one wavelength. 546 00:33:34,637 --> 00:33:39,84 And there is a way that I can make you see this from your own 547 00:33:39,84 --> 00:33:43,049 seats. And that is what we're going to 548 00:33:43,049 --> 00:33:46,778 do with the um with the cards that you have. 549 00:33:46,778 --> 00:33:53,194 So if you can get the cards out now, we did this in one color, 550 00:33:53,194 --> 00:33:55,752 right, in green light, almost one color, 551 00:33:55,752 --> 00:33:59,096 almost monochromatic, so you see a beautiful pattern 552 00:33:59,096 --> 00:34:01,325 here, very well-defined dark lines. 553 00:34:01,325 --> 00:34:04,341 You now can use this little slit that you have, 554 00:34:04,341 --> 00:34:08,078 put it in front of your eye, and I'm going to make you see 555 00:34:08,078 --> 00:34:12,143 this white light and you would see all the features that you're 556 00:34:12,143 --> 00:34:16,077 supposed to see but it's even more interesting in white light 557 00:34:16,077 --> 00:34:19,093 because with white light you have a little red, 558 00:34:19,093 --> 00:34:22,241 you have a little blue, you have a little yellow, 559 00:34:22,241 --> 00:34:25,585 and so these minima will fall at 560 00:34:25,585 --> 00:34:29,282 different locations of course. And so you don't see it as 561 00:34:29,282 --> 00:34:32,979 beautiful as I showed you, as distinct as I showed you in 562 00:34:32,979 --> 00:34:36,412 green, but you see very distinctly the center maximum 563 00:34:36,412 --> 00:34:39,119 and you see the dark lines on either side. 564 00:34:39,119 --> 00:34:43,081 But the main reason why I want you to see this is that if you 565 00:34:43,081 --> 00:34:46,778 manage to manipulate the size of the slit, the size of A, 566 00:34:46,778 --> 00:34:50,673 if you manage to manipulate that, when you make it narrower, 567 00:34:50,673 --> 00:34:54,569 notice that the diffraction pattern gets broader and not the 568 00:34:54,569 --> 00:34:58,761 other way around. So first make sure that you get 569 00:34:58,761 --> 00:35:02,594 it, that you begin to see the dark areas, and then try to make 570 00:35:02,594 --> 00:35:05,987 it a little narrower and then you see that it opens up. 571 00:35:05,987 --> 00:35:09,506 This is precisely what I did with the variable slit here. 572 00:35:09,506 --> 00:35:13,401 So give it a d- b- bit of time. What helps me that actually you 573 00:35:13,401 --> 00:35:17,108 don't have to pull it open but yet you can move one piece of 574 00:35:17,108 --> 00:35:20,878 the card behind the other card. So your one thumb goes to the 575 00:35:20,878 --> 00:35:23,58 back and the other your thumb comes forward. 576 00:35:23,58 --> 00:35:27,853 That works very well for me. Who can see clearly the 577 00:35:27,853 --> 00:35:30,891 diffraction pattern? Unmistakably. 578 00:35:30,891 --> 00:35:33,93 Very good. Take the card with you, 579 00:35:33,93 --> 00:35:38,718 impress your parents. And look at home at very bright 580 00:35:38,718 --> 00:35:43,874 street lights and you will still see the same diffraction 581 00:35:43,874 --> 00:35:47,189 pattern. Although not as ideal as you 582 00:35:47,189 --> 00:35:52,806 see it here because our source is a line source and that helps 583 00:35:52,806 --> 00:35:57,226 of course if your slit if vertical. 584 00:35:57,226 --> 00:35:59,454 OK. If I don't have a slit as an 585 00:35:59,454 --> 00:36:03,838 opening but if I have a circular opening then the pattern that 586 00:36:03,838 --> 00:36:08,006 you would expect is the same that you see here but you have 587 00:36:08,006 --> 00:36:11,887 to rotate it about this line because you now have axial 588 00:36:11,887 --> 00:36:14,618 symmetry. So you don't have a -- a long 589 00:36:14,618 --> 00:36:17,277 slit, but you have a circular opening. 590 00:36:17,277 --> 00:36:20,152 And indeed that is approximately correct. 591 00:36:20,152 --> 00:36:24,393 If you had a circular opening you would see a center maximum 592 00:36:24,393 --> 00:36:28,418 which would be very bright and then you 593 00:36:28,418 --> 00:36:31,165 would see rings around it of zeroes. 594 00:36:31,165 --> 00:36:35,719 And so if I try to make you see it this would be the center 595 00:36:35,719 --> 00:36:38,545 maximum. It would be a ring around it 596 00:36:38,545 --> 00:36:40,979 here. Complete darkness and then 597 00:36:40,979 --> 00:36:44,277 again a little bit of light, not very much, 598 00:36:44,277 --> 00:36:48,752 because remember that this maximum is only four-and-a-half 599 00:36:48,752 --> 00:36:52,677 percent of that one. And then you would see again a 600 00:36:52,677 --> 00:36:55,582 ring with complete darkness and so on. 601 00:36:55,582 --> 00:37:00,842 So you have a little pinhole and this is the image 602 00:37:00,842 --> 00:37:05,197 that you would get on a screen. From that pinhole. 603 00:37:05,197 --> 00:37:10,441 And you would think now that this angle from here to here is 604 00:37:10,441 --> 00:37:14,795 this theta equals zero and we call that theta one. 605 00:37:14,795 --> 00:37:19,328 This is the theta one where you see your first zero, 606 00:37:19,328 --> 00:37:24,571 you would think that that is lambda divided by A if A is the 607 00:37:24,571 --> 00:37:28,837 diameter of your pinhole. Well, it's almost that. 608 00:37:28,837 --> 00:37:32,836 It is a little larger. Because a 609 00:37:32,836 --> 00:37:36,395 pinhole, a circular geometry is different from a line. 610 00:37:36,395 --> 00:37:40,49 And so take my word for it that it comes not at lambda divided 611 00:37:40,49 --> 00:37:44,652 by A but it comes at roughly one point two lambda divided by A. 612 00:37:44,652 --> 00:37:48,546 If you want to be picky it's really one point two two times 613 00:37:48,546 --> 00:37:52,44 lambda divided by A and this of course is in radians again. 614 00:37:52,44 --> 00:37:56,065 I work now exclusively in terms of radians, small angle 615 00:37:56,065 --> 00:37:59,086 approximation. And so this raises the issue of 616 00:37:59,086 --> 00:38:01,906 what we call in physics angular resolution. 617 00:38:01,906 --> 00:38:05,396 Suppose I have a pinhole and I look 618 00:38:05,396 --> 00:38:07,382 at the images of two light sources. 619 00:38:07,382 --> 00:38:10,652 One light comes in from there and the other comes in from 620 00:38:10,652 --> 00:38:14,215 there, could be the headlights of a car, could be two stars in 621 00:38:14,215 --> 00:38:16,668 the sky, well, each one of them will give a 622 00:38:16,668 --> 00:38:19,062 diffraction pattern, that's nonnegotiable, 623 00:38:19,062 --> 00:38:20,931 you can never bypass diffraction. 624 00:38:20,931 --> 00:38:23,734 So one star will give a diffraction pattern here, 625 00:38:23,734 --> 00:38:26,187 or one headlight, and the other will give a 626 00:38:26,187 --> 00:38:29,282 diffraction pattern here. You would have no problem to 627 00:38:29,282 --> 00:38:30,742 say oh, yeah, they're all, 628 00:38:30,742 --> 00:38:34,012 there are two light sources, there's one star and there's 629 00:38:34,012 --> 00:38:36,089 another star. 630 00:38:36,089 --> 00:38:38,233 OK. Now make the angle between the 631 00:38:38,233 --> 00:38:42,261 two sources smaller and smaller and smaller and smaller so that 632 00:38:42,261 --> 00:38:46,289 these two diffraction patterns come close and closer and closer 633 00:38:46,289 --> 00:38:48,758 and closer. How close can you now bring 634 00:38:48,758 --> 00:38:51,486 them so that we, you and I, will still say, 635 00:38:51,486 --> 00:38:53,63 yeah, there are still two sources? 636 00:38:53,63 --> 00:38:55,644 We call that angular resolution. 637 00:38:55,644 --> 00:38:59,347 And so how we define angular resolution is that both light 638 00:38:59,347 --> 00:39:03,115 sources have exactly the same strength and let's assume for 639 00:39:03,115 --> 00:39:07,487 now for simplicity that they're monochromatic, 640 00:39:07,487 --> 00:39:11,268 so that there's only one wavelength that they emit. 641 00:39:11,268 --> 00:39:15,426 Then the criterion that is generally accepted so that we 642 00:39:15,426 --> 00:39:19,131 can still decide that there are two light sources, 643 00:39:19,131 --> 00:39:21,929 that this one, the center of this one, 644 00:39:21,929 --> 00:39:26,239 is no closer than the location where this one has complete 645 00:39:26,239 --> 00:39:28,053 darkness. In other words, 646 00:39:28,053 --> 00:39:32,136 the spot of the second star should fall right where the 647 00:39:32,136 --> 00:39:37,353 other one has darkness. If you bring them closer your 648 00:39:37,353 --> 00:39:41,271 brains will say no. No, no, that's not two sources. 649 00:39:41,271 --> 00:39:45,895 That's really only one source. And we call this the Rayleigh 650 00:39:45,895 --> 00:39:50,126 criterion of resolution. And that Rayleigh criterion of 651 00:39:50,126 --> 00:39:55,141 resolution therefore is that the separation between the two light 652 00:39:55,141 --> 00:39:59,843 beams, stars or the headlights from a car, the separation has 653 00:39:59,843 --> 00:40:04,152 to be larger than this angle. And it is a function of A. 654 00:40:04,152 --> 00:40:07,914 If A is larger, then that angle can 655 00:40:07,914 --> 00:40:12,058 be substantially smaller. And this is what we call the 656 00:40:12,058 --> 00:40:15,498 diffraction limitation on angular resolution. 657 00:40:15,498 --> 00:40:20,034 It doesn't matter whether you have a pinhole or whether you 658 00:40:20,034 --> 00:40:24,569 have a lens a c- circular lens that we use with telescopes. 659 00:40:24,569 --> 00:40:28,713 Or whether you have concave mirrors, which we use with 660 00:40:28,713 --> 00:40:31,685 telescopes. In all cases are you always 661 00:40:31,685 --> 00:40:36,064 stuck with the idea at best, that's the best you can ever 662 00:40:36,064 --> 00:40:40,755 do, that is the angular separation that theta 663 00:40:40,755 --> 00:40:46,045 I call it here the theta one, is that one point two lambda 664 00:40:46,045 --> 00:40:49,851 divided by A, and that is then in radians. 665 00:40:49,851 --> 00:40:55,233 If you take a lens which has the diameter A of about twenty 666 00:40:55,233 --> 00:41:00,987 centimeters then that translates into a theta one of about half 667 00:41:00,987 --> 00:41:04,885 an arc second, for five thousand Angstroms. 668 00:41:04,885 --> 00:41:10,547 So I take lambda five thousand Angstroms, remember an Angstrom 669 00:41:10,547 --> 00:41:14,442 is ten to the minus ten meters. 670 00:41:14,442 --> 00:41:18,278 So theta one then becomes half an arc second. 671 00:41:18,278 --> 00:41:23,074 Oh point five arc seconds. An arc minute is one-sixtieth 672 00:41:23,074 --> 00:41:26,997 of a d- arc degree, and an arc second is sixty 673 00:41:26,997 --> 00:41:31,619 times lower than that. And so if A were two point four 674 00:41:31,619 --> 00:41:35,891 meters, telescope, two point four meter telescope, 675 00:41:35,891 --> 00:41:39,727 that's a real biggie, then theta one would be 676 00:41:39,727 --> 00:41:43,779 approximately one-twenty-fifth of an arc 677 00:41:43,779 --> 00:41:45,999 second. So the larger you make your 678 00:41:45,999 --> 00:41:49,524 telescope the better angular resolution you would have. 679 00:41:49,524 --> 00:41:53,115 This angular resolution is twelve times better than this 680 00:41:53,115 --> 00:41:55,008 one. Because A is twelve times 681 00:41:55,008 --> 00:41:57,293 larger. So now you may think that if 682 00:41:57,293 --> 00:42:01,341 you take a two point four meter telescope on the ground and you 683 00:42:01,341 --> 00:42:05,258 look at stars that two stars equally bright you would be able 684 00:42:05,258 --> 00:42:09,044 to tell them apart if they are farther away from each other 685 00:42:09,044 --> 00:42:11,525 than one-twenty-fifth of an arc second. 686 00:42:11,525 --> 00:42:14,855 That is not true. The contrary. 687 00:42:14,855 --> 00:42:17,919 It is very bad. You can't even tell them apart 688 00:42:17,919 --> 00:42:20,575 often when they are half a second apart. 689 00:42:20,575 --> 00:42:24,729 And the reason for that is not that the diffraction limitation 690 00:42:24,729 --> 00:42:28,202 is going to kill you, but the reason is that the air 691 00:42:28,202 --> 00:42:31,675 is always turbulent. And it is the turbulence on the 692 00:42:31,675 --> 00:42:35,421 air that makes the image, the diffraction-limited image, 693 00:42:35,421 --> 00:42:38,553 which itself is very small, move around on your 694 00:42:38,553 --> 00:42:41,958 photographic plates, it moves it around in a matter 695 00:42:41,958 --> 00:42:45,364 of ten seconds over an area which 696 00:42:45,364 --> 00:42:47,512 itself could be as large as one second. 697 00:42:47,512 --> 00:42:50,736 Astronomers call that seeing. And so when you look at your 698 00:42:50,736 --> 00:42:53,903 picture, the whole star is smeared out over an area which 699 00:42:53,903 --> 00:42:56,9 is in angular size one arc second or maybe half an arc 700 00:42:56,9 --> 00:42:59,388 second at best. So you can never achieve this 701 00:42:59,388 --> 00:43:01,763 from the ground. So all telescopes from the 702 00:43:01,763 --> 00:43:05,043 ground without exception can do at best half an arc second. 703 00:43:05,043 --> 00:43:08,21 They cannot do much better because of the air turbulence. 704 00:43:08,21 --> 00:43:11,208 And this is now the great thing about the Hubble space 705 00:43:11,208 --> 00:43:12,848 telescope. Hubble is up there, 706 00:43:12,848 --> 00:43:16,128 or maybe down there, whichever it is, 707 00:43:16,128 --> 00:43:19,525 I don't know where it is, maybe Jeffrey knows where it 708 00:43:19,525 --> 00:43:22,473 is, but it is somewhere. And Hubble has no air. 709 00:43:22,473 --> 00:43:25,678 And so Hubble doesn't suffer of the air turbulence. 710 00:43:25,678 --> 00:43:29,14 And so Hubble's mirrors are indeed diffraction-limited. 711 00:43:29,14 --> 00:43:32,537 And Hubble has a mirror which is two point four meters 712 00:43:32,537 --> 00:43:34,844 diameter. And indeed at five thousand 713 00:43:34,844 --> 00:43:38,37 Angstrom, I checked that yesterday with people at Hubble 714 00:43:38,37 --> 00:43:40,421 space telescope, indeed Hubble is 715 00:43:40,421 --> 00:43:43,305 diffraction-limited, and Hubble has an angular 716 00:43:43,305 --> 00:43:46,639 resolution at five thousand Angstroms, which is about 717 00:43:46,639 --> 00:43:50,249 one-twenty-fifth of an arc second. 718 00:43:50,249 --> 00:43:53,537 And at shorter wavelengths, it's even better, 719 00:43:53,537 --> 00:43:57,049 and at longer wavelengths, it is a little worse. 720 00:43:57,049 --> 00:44:01,607 And so I would like to show you at least one picture of Hubble 721 00:44:01,607 --> 00:44:06,016 without going into the details of what you are seeing of the 722 00:44:06,016 --> 00:44:09,753 astro- of the astronomy. And that's the one that is 723 00:44:09,753 --> 00:44:12,817 coming up. It's a very famous picture that 724 00:44:12,817 --> 00:44:17,3 Hubble made several years ago. It is a picture of a supernova 725 00:44:17,3 --> 00:44:20,29 explosion. John if we can have the slide, 726 00:44:20,29 --> 00:44:24,084 there it is. You're looking here at an 727 00:44:24,084 --> 00:44:27,561 explosion, it's called Supernova nineteen eighty-seven A, 728 00:44:27,561 --> 00:44:30,728 which occurred in February of nineteen eighty-seven. 729 00:44:30,728 --> 00:44:34,453 This object is a hundred fifty thousand light-years away from 730 00:44:34,453 --> 00:44:36,564 us. That means the explosion really 731 00:44:36,564 --> 00:44:39,917 took place -- took place a hundred fifty thousand years 732 00:44:39,917 --> 00:44:41,842 ago. But we saw it for the first 733 00:44:41,842 --> 00:44:45,319 time in February eighty-seven. And without going into the 734 00:44:45,319 --> 00:44:48,858 details of what you're looking at, which is of course very 735 00:44:48,858 --> 00:44:51,777 fascinating, but that's not the objective today, 736 00:44:51,777 --> 00:44:55,13 I want you to appreciate that this 737 00:44:55,13 --> 00:44:57,1 distance here is one arc second. 738 00:44:57,1 --> 00:45:00,785 And look at the incredible detail that Hubble can show you. 739 00:45:00,785 --> 00:45:04,789 If you took a picture like this with a ground-based observatory, 740 00:45:04,789 --> 00:45:07,331 this whole part would just be one smudge. 741 00:45:07,331 --> 00:45:09,682 You would not be able to resolve that. 742 00:45:09,682 --> 00:45:13,368 And that is the power that you see in front of you now of a 743 00:45:13,368 --> 00:45:17,244 diffraction-limited telescope which -- which has a diameter of 744 00:45:17,244 --> 00:45:20,485 two point four meters. You get an angular resolution 745 00:45:20,485 --> 00:45:23,599 which is very close to four-hundredths of a an arc 746 00:45:23,599 --> 00:45:27,518 second. The amount of detail that you 747 00:45:27,518 --> 00:45:30,566 see is incredible. That's the big power, 748 00:45:30,566 --> 00:45:34,473 the big reason why this telescope was put in orbit, 749 00:45:34,473 --> 00:45:39,006 to do away with the um air turbulence, what the astronomers 750 00:45:39,006 --> 00:45:42,601 call as seeing. Which is always a limitation of 751 00:45:42,601 --> 00:45:46,352 your angular resolution. So in the remaining five 752 00:45:46,352 --> 00:45:51,041 minutes I want to address the issue of the angular resolution 753 00:45:51,041 --> 00:45:54,636 of your own eye. You can now calculate what the 754 00:45:54,636 --> 00:45:59,559 ultimate angular resolution is of your own eye. 755 00:45:59,559 --> 00:46:03,269 Because you can estimate what the diameter is of the pupil. 756 00:46:03,269 --> 00:46:05,955 The opening of your eye. Three millimeters, 757 00:46:05,955 --> 00:46:09,217 maybe five millimeters, a little bit larger at night 758 00:46:09,217 --> 00:46:11,199 when it is dark. Pupil opens up. 759 00:46:11,199 --> 00:46:13,31 But we can calculate what this is. 760 00:46:13,31 --> 00:46:16,635 Uh if I take four millimeters, so I put in for A four 761 00:46:16,635 --> 00:46:20,281 millimeters, and if I take lambda five thousand Angstroms, 762 00:46:20,281 --> 00:46:23,862 it's not an unreasonable value, then I find that the best 763 00:46:23,862 --> 00:46:27,38 angular resolution of a human eye is half an arc minute. 764 00:46:27,38 --> 00:46:31,92 Cannot be any better. There's just no way around it. 765 00:46:31,92 --> 00:46:35,151 You're always stuck with the diffraction limitation. 766 00:46:35,151 --> 00:46:39,078 I think though that most of you will not be able to see with an 767 00:46:39,078 --> 00:46:41,676 angular resolution of one-half arc minute. 768 00:46:41,676 --> 00:46:45,223 Most of you are probably in the domain of one arc minute. 769 00:46:45,223 --> 00:46:48,073 It's a little larger than diffraction-limited. 770 00:46:48,073 --> 00:46:51,621 But it's very close to that. And that is something that I 771 00:46:51,621 --> 00:46:54,661 would like to test. Not to see how good your eyes 772 00:46:54,661 --> 00:46:58,525 are, but for yourself to get a feeling for angular resolution. 773 00:46:58,525 --> 00:47:02,579 And the way I'm going to do that is as follows. 774 00:47:02,579 --> 00:47:07,198 We have prepared a box which Marcos is going to wheel in very 775 00:47:07,198 --> 00:47:10,354 shortly which has two pinholes at the top. 776 00:47:10,354 --> 00:47:14,357 And these two pinholes are two-and-a-half millimeters 777 00:47:14,357 --> 00:47:17,205 apart. And then there are two pinholes 778 00:47:17,205 --> 00:47:19,668 which are five millimeters apart. 779 00:47:19,668 --> 00:47:24,518 And then there are two pinholes which are ten millimeters apart. 780 00:47:24,518 --> 00:47:29,137 And then there are two pinholes which are fifteen millimeters 781 00:47:29,137 --> 00:47:31,908 apart. So maybe we can take a look at 782 00:47:31,908 --> 00:47:33,447 that. There it comes. 783 00:47:33,447 --> 00:47:38,274 Thank you Marcos. Here are two pinholes which are 784 00:47:38,274 --> 00:47:40,396 two-and-a-half millimeters apart. 785 00:47:40,396 --> 00:47:42,85 We repeat the whole thing three times. 786 00:47:42,85 --> 00:47:46,829 And the reason why we do that is so that the different angles 787 00:47:46,829 --> 00:47:50,874 in the audience you can probably always see two pinholes well. 788 00:47:50,874 --> 00:47:54,72 What am I going to do now to test the angular resolution of 789 00:47:54,72 --> 00:47:57,306 your eyes? If I make the assumption that 790 00:47:57,306 --> 00:48:00,688 your angular resolution is one arc minute, no worse, 791 00:48:00,688 --> 00:48:04,535 no better, remember it can never be better than half an arc 792 00:48:04,535 --> 00:48:07,498 minute, that's nonnegotiable. 793 00:48:07,498 --> 00:48:10,046 But it could be worse than one arc minute. 794 00:48:10,046 --> 00:48:13,278 That would mean that all students who are closer than 795 00:48:13,278 --> 00:48:16,945 nine meters from me should be able to see this as two indep- 796 00:48:16,945 --> 00:48:20,488 independent light sources. Those who are farther than nine 797 00:48:20,488 --> 00:48:23,782 meters away from me will not see these as two sources. 798 00:48:23,782 --> 00:48:27,262 If they did their angular resolution would be better than 799 00:48:27,262 --> 00:48:29,811 one arc minute. And all students which are 800 00:48:29,811 --> 00:48:33,105 closer than seventeen meters will be able to say yeah, 801 00:48:33,105 --> 00:48:36,399 I see these as two sources, and all students which are 802 00:48:36,399 --> 00:48:41,683 closer than thirty-four meters should be able to say yeah, 803 00:48:41,683 --> 00:48:46,278 I see these as two sources. And so we're now going to make 804 00:48:46,278 --> 00:48:49,664 it a little darker. And you don't need your 805 00:48:49,664 --> 00:48:54,502 gradings, you don't need these cards, I just want you to look 806 00:48:54,502 --> 00:48:57,243 at the lights, these light sources, 807 00:48:57,243 --> 00:49:01,838 and then tell me which you're going to see as two separate 808 00:49:01,838 --> 00:49:05,466 light sources. And that then allows me to tell 809 00:49:05,466 --> 00:49:09,335 you very roughly what your angular resolution is. 810 00:49:09,335 --> 00:49:15,126 So try to look at them. And so now my first question is 811 00:49:15,126 --> 00:49:19,565 who can see the upper, either here or there or there, 812 00:49:19,565 --> 00:49:23,406 they're the same, who can clearly see those as 813 00:49:23,406 --> 00:49:25,625 two light sources? Come on. 814 00:49:25,625 --> 00:49:28,527 Come on. You don't see them as two? 815 00:49:28,527 --> 00:49:31,686 Something wrong, is the lights not on? 816 00:49:31,686 --> 00:49:35,271 You must be kidding. Are all of you sick or 817 00:49:35,271 --> 00:49:38,6 something? Oh man I have no difficulties 818 00:49:38,6 --> 00:49:41,417 at all. The upper one is two light 819 00:49:41,417 --> 00:49:45,734 sources. You've all got to see an eye 820 00:49:45,734 --> 00:49:48,581 doctor. OK, who sees the second line as 821 00:49:48,581 --> 00:49:51,128 two? Who sees the third line as two 822 00:49:51,128 --> 00:49:54,349 but not the second? You see how interesting, 823 00:49:54,349 --> 00:49:58,02 just look around you, you see we're moving back in 824 00:49:58,02 --> 00:50:01,016 the audience. Who sees the -- who can see 825 00:50:01,016 --> 00:50:04,013 none of them at two -- two light sources? 826 00:50:04,013 --> 00:50:07,759 OK, so maybe not -- no eye doctors are needed then. 827 00:50:07,759 --> 00:50:11,205 Who can only see the third line as two sources, 828 00:50:11,205 --> 00:50:15,816 only the third line? OK, well, I expect that, 829 00:50:15,816 --> 00:50:19,417 you see, no -- yeah, maybe your angular resolution 830 00:50:19,417 --> 00:50:21,916 is not very -- do you wear glasses? 831 00:50:21,916 --> 00:50:24,121 So you -- yeah, I'm asking you, 832 00:50:24,121 --> 00:50:26,694 so you see the third line as double? 833 00:50:26,694 --> 00:50:30,663 And not the second line? Yeah, there's nothing to worry 834 00:50:30,663 --> 00:50:33,456 about, maybe two arc minute resolution. 835 00:50:33,456 --> 00:50:36,837 So now you have tested your angular resolution. 836 00:50:36,837 --> 00:50:40,806 When you think of diffraction it's really an incredibly 837 00:50:40,806 --> 00:50:45,289 fascinating thing because what this diffraction actually means 838 00:50:45,289 --> 00:50:49,926 that it is a limitation that is put upon us, 839 00:50:49,926 --> 00:50:52,799 on everyone, also God, no one can bypass 840 00:50:52,799 --> 00:50:55,746 diffraction. No matter how hard we try we 841 00:50:55,746 --> 00:51:00,167 can never undo our chains and handcuffs that are imposed upon 842 00:51:00,167 --> 00:51:03,704 us by diffraction. And remember it's all Huygens' 843 00:51:03,704 --> 00:51:05,988 fault. But let's forgive Huygens 844 00:51:05,988 --> 51:11 because after all he was Dutch.