1
00:00:02,490 --> 00:00:04,830
The following content is
provided under a Creative

2
00:00:04,830 --> 00:00:06,250
Commons license.

3
00:00:06,250 --> 00:00:08,460
Your support will help
MIT OpenCourseWare

4
00:00:08,460 --> 00:00:12,550
continue to offer high-quality
educational resources for free.

5
00:00:12,550 --> 00:00:15,090
To make a donation or to
view additional materials

6
00:00:15,090 --> 00:00:19,020
from hundreds of MIT courses,
visit MIT OpenCourseWare

7
00:00:19,020 --> 00:00:20,280
at ocw.mit.edu.

8
00:00:23,784 --> 00:00:24,450
YEN-JIE LEE: OK.

9
00:00:24,450 --> 00:00:29,010
So welcome back,
everybody, to 8.03.

10
00:00:29,010 --> 00:00:31,200
So before we start
the lecture today,

11
00:00:31,200 --> 00:00:34,710
we will give you, as usual,
a short review on what we

12
00:00:34,710 --> 00:00:39,600
have learned, and also, an
introduction about what we

13
00:00:39,600 --> 00:00:42,490
are going to learn today.

14
00:00:42,490 --> 00:00:45,410
So last lecture,
we were discussing

15
00:00:45,410 --> 00:00:50,760
an interesting phenomenon, which
is seeing film interference

16
00:00:50,760 --> 00:00:51,660
pattern.

17
00:00:51,660 --> 00:00:54,120
As you can see
from this slide, we

18
00:00:54,120 --> 00:00:59,690
were wondering why the
soap bubbles are colorful.

19
00:00:59,690 --> 00:01:02,160
And in the end of the
class, we actually

20
00:01:02,160 --> 00:01:07,080
recognized that the reason why
the soap bubbles are colorful

21
00:01:07,080 --> 00:01:10,130
is because of the
interference phenomenon

22
00:01:10,130 --> 00:01:16,470
between the refracted
light on the bubble.

23
00:01:16,470 --> 00:01:20,210
One puzzle path is that
the light goes into the--

24
00:01:20,210 --> 00:01:25,330
goes refracted directly from
the surface of the soap film.

25
00:01:25,330 --> 00:01:29,250
The other possible
optical path is

26
00:01:29,250 --> 00:01:34,290
to get refracted by the
inner surface of the film.

27
00:01:34,290 --> 00:01:37,410
Therefore, the interference
between these two paths

28
00:01:37,410 --> 00:01:44,390
actually created a colorful
pattern on the bubble.

29
00:01:44,390 --> 00:01:51,790
So we also learned about
how thick is the soap film.

30
00:01:51,790 --> 00:01:54,670
And I think just a quick
reminder, actually,

31
00:01:54,670 --> 00:02:01,300
we concluded that in order
to see a colorful pattern,

32
00:02:01,300 --> 00:02:05,020
the thickness of the
wall or, say, the film,

33
00:02:05,020 --> 00:02:09,269
should be something like in
the order of 100 nanometer.

34
00:02:09,269 --> 00:02:10,810
So that's actually
pretty remarkable,

35
00:02:10,810 --> 00:02:14,970
because that's already in the
order of the size of a virus.

36
00:02:14,970 --> 00:02:15,540
OK.

37
00:02:15,540 --> 00:02:19,120
OK that's actually pretty cool.

38
00:02:19,120 --> 00:02:22,210
So what are we
going to do today?

39
00:02:22,210 --> 00:02:24,940
What we are going to do today
is to continue the discussion

40
00:02:24,940 --> 00:02:28,300
that all kinds of
different phenomenons,

41
00:02:28,300 --> 00:02:31,810
which can be explained
by interference.

42
00:02:31,810 --> 00:02:36,580
We will learn interference
phenomenon with a double slit

43
00:02:36,580 --> 00:02:42,820
experiment and using, for
example, laser or water,

44
00:02:42,820 --> 00:02:46,040
and which I have
a water tank here,

45
00:02:46,040 --> 00:02:48,740
which I will show you
the interference pattern.

46
00:02:48,740 --> 00:02:51,820
And also, the second thing
we are going to learn today

47
00:02:51,820 --> 00:02:58,650
is how does a phased
radar actually works.

48
00:02:58,650 --> 00:02:59,520
OK?

49
00:02:59,520 --> 00:03:03,470
So by the end of the
lecture today, you

50
00:03:03,470 --> 00:03:07,200
should be able to learn
why we should construct

51
00:03:07,200 --> 00:03:13,420
the radar in the way
and how to actually

52
00:03:13,420 --> 00:03:17,140
focus on the
electromagnetic wave

53
00:03:17,140 --> 00:03:19,390
to work one specific direction.

54
00:03:19,390 --> 00:03:21,760
So that's essentially what
we are going to learn today.

55
00:03:21,760 --> 00:03:24,130
The third goal is
that we are going

56
00:03:24,130 --> 00:03:29,590
to make a connection to quantum
mechanics from the lecture

57
00:03:29,590 --> 00:03:31,250
today.

58
00:03:31,250 --> 00:03:31,750
All right.

59
00:03:31,750 --> 00:03:34,570
So let's immediately
get started.

60
00:03:34,570 --> 00:03:39,520
So before we start the
discussion of a double slit

61
00:03:39,520 --> 00:03:42,580
experiment, I would
like to remind everybody

62
00:03:42,580 --> 00:03:46,510
about Huygens' Principle, which
you may already learned it

63
00:03:46,510 --> 00:03:49,970
from 8.02 or in the
high school days.

64
00:03:49,970 --> 00:03:52,490
So what essentially
is this principle?

65
00:03:52,490 --> 00:03:55,630
So this principle
is saying that if I

66
00:03:55,630 --> 00:04:02,980
take a look at all the points
in the wavefront, basically,

67
00:04:02,980 --> 00:04:08,080
you can treat all those points
on the wavefront a point

68
00:04:08,080 --> 00:04:09,040
source.

69
00:04:09,040 --> 00:04:11,770
And this point source,
essentially, a point source

70
00:04:11,770 --> 00:04:14,830
of a spherical wave.

71
00:04:14,830 --> 00:04:19,390
And it's immediate from all
the points on the wavefront.

72
00:04:19,390 --> 00:04:23,130
So you can see from
this slide, basically,

73
00:04:23,130 --> 00:04:28,240
if we choose to focus on the
yellow point on the wavefront,

74
00:04:28,240 --> 00:04:30,670
you can see that from
each yellow point,

75
00:04:30,670 --> 00:04:37,900
you can actually treat that as
a spherical wave point source.

76
00:04:37,900 --> 00:04:41,500
And then what you actually
need to do in order

77
00:04:41,500 --> 00:04:45,610
to calculate what would be
the total electric field,

78
00:04:45,610 --> 00:04:49,240
for example, is to add
up all those contribution

79
00:04:49,240 --> 00:04:50,590
from each point.

80
00:04:50,590 --> 00:04:53,610
And then you will be
able to actually explain

81
00:04:53,610 --> 00:04:59,530
the interference pattern,
which we see in the experiment.

82
00:04:59,530 --> 00:05:05,200
You may wonder where is this
Huygens' Principle coming from?

83
00:05:05,200 --> 00:05:08,130
And although we are not
going to derive that directly

84
00:05:08,130 --> 00:05:11,380
in the lecture today,
but I can actually safely

85
00:05:11,380 --> 00:05:14,530
tell you that essentially,
it can be derived

86
00:05:14,530 --> 00:05:16,290
from Maxwell's equation.

87
00:05:16,290 --> 00:05:16,870
OK?

88
00:05:16,870 --> 00:05:19,300
I will link some
document, which actually

89
00:05:19,300 --> 00:05:23,060
shows the proof of the
principle on the website

90
00:05:23,060 --> 00:05:25,870
and for your reference.

91
00:05:25,870 --> 00:05:29,450
The other thing which you
may or you may not know

92
00:05:29,450 --> 00:05:38,050
is that we are really lucky so
that we can use this Huygens'

93
00:05:38,050 --> 00:05:40,890
Principle in our universe.

94
00:05:40,890 --> 00:05:42,220
Why is that?

95
00:05:42,220 --> 00:05:45,280
Because if you look at
the mathematical proof

96
00:05:45,280 --> 00:05:51,310
of this principle, it is because
the number of dimension, number

97
00:05:51,310 --> 00:05:54,880
of spatial dimension
is odd, which

98
00:05:54,880 --> 00:05:56,830
is three in our universe--

99
00:05:56,830 --> 00:05:59,610
Or in my universe
also is yours, OK,

100
00:05:59,610 --> 00:06:02,300
[LAUGHS] happened to
be yours, as well--

101
00:06:02,300 --> 00:06:06,280
such that the Huygens'
principle actually works.

102
00:06:06,280 --> 00:06:11,680
On the other hand, if the
number of dimension is even,

103
00:06:11,680 --> 00:06:13,720
there's no Huygens'
principle, actually.

104
00:06:13,720 --> 00:06:15,700
So that's pretty
interesting in that we

105
00:06:15,700 --> 00:06:19,780
are really lucky that it
actually works in our universe.

106
00:06:19,780 --> 00:06:24,580
But I will not go
into detail in 8.03.

107
00:06:24,580 --> 00:06:28,180
So let's get started with
a concrete example, which

108
00:06:28,180 --> 00:06:31,630
we would like to further
investigate to understand

109
00:06:31,630 --> 00:06:34,120
the interference phenomena.

110
00:06:34,120 --> 00:06:36,370
And those will prepare
ourselves to the understanding

111
00:06:36,370 --> 00:06:40,000
of the design of the
radar, for example.

112
00:06:40,000 --> 00:06:40,630
All right.

113
00:06:40,630 --> 00:06:44,440
So suppose I have
experimental set

114
00:06:44,440 --> 00:06:50,350
up here which contain a
wall where on the wall,

115
00:06:50,350 --> 00:06:55,450
there are two slit, A and a B.
The upper one is A. The lower

116
00:06:55,450 --> 00:06:58,120
one is B, as designed here.

117
00:06:58,120 --> 00:07:04,570
And from the left inside
there's an insert plane wave

118
00:07:04,570 --> 00:07:08,460
with a wavelength lambda,
which is showing here.

119
00:07:08,460 --> 00:07:11,780
And this plane wave, plane
electromagnetic wave,

120
00:07:11,780 --> 00:07:15,760
or can be water wave,
et cetera, essentially

121
00:07:15,760 --> 00:07:20,020
approaching the wall with
these two slits there.

122
00:07:20,020 --> 00:07:24,040
And we were wondering what
would be the resulting

123
00:07:24,040 --> 00:07:26,750
pattern on the screen.

124
00:07:26,750 --> 00:07:30,250
This screen is actually
pretty far away

125
00:07:30,250 --> 00:07:34,720
from the experimental setup,
the wall on the left-hand side.

126
00:07:34,720 --> 00:07:37,030
How far is that?

127
00:07:37,030 --> 00:07:41,700
The distance between the screen,
which shows the resulting

128
00:07:41,700 --> 00:07:46,710
interference pattern, and that
the wall is actually defined.

129
00:07:46,710 --> 00:07:48,260
It's actually given here.

130
00:07:48,260 --> 00:07:51,720
It's actually
called L, capital L.

131
00:07:51,720 --> 00:07:56,660
And in this experimental setup
L essentially pretty, pretty

132
00:07:56,660 --> 00:08:01,960
large and is much, much larger
than the d, where d, small d,

133
00:08:01,960 --> 00:08:05,180
is the distance
between the two slits.

134
00:08:05,180 --> 00:08:06,700
OK?

135
00:08:06,700 --> 00:08:10,810
So our job now is to
understand what will be--

136
00:08:10,810 --> 00:08:13,660
and to predict what is
going to be the interference

137
00:08:13,660 --> 00:08:19,390
pattern coming from the
electromagnetic wave which

138
00:08:19,390 --> 00:08:23,170
pass through point
A and point B,

139
00:08:23,170 --> 00:08:26,030
and what is going
to happen over, say,

140
00:08:26,030 --> 00:08:29,790
what would be the result which
we will observe on the screen.

141
00:08:29,790 --> 00:08:30,600
OK?

142
00:08:30,600 --> 00:08:32,100
So the first thing
which we can do

143
00:08:32,100 --> 00:08:36,190
is that we can now
assign observer,

144
00:08:36,190 --> 00:08:39,809
which is called P, one
of the point of interest

145
00:08:39,809 --> 00:08:42,840
on the screen, which
is located here.

146
00:08:42,840 --> 00:08:45,160
And then we can
link or, say, the

147
00:08:45,160 --> 00:08:49,530
connect the point A, which is
the location of the first slit

148
00:08:49,530 --> 00:08:53,310
and the location of
the second slit, which

149
00:08:53,310 --> 00:08:58,260
is called B. We can link those
points together by a line.

150
00:08:58,260 --> 00:09:03,550
And that is actually denoted by
AP and the BP, these two lines.

151
00:09:03,550 --> 00:09:08,080
Since we are talking about L,
which is essentially very, very

152
00:09:08,080 --> 00:09:12,270
large, assuming that
the distance, the length

153
00:09:12,270 --> 00:09:15,250
scale of the distance between
the wall and the screen

154
00:09:15,250 --> 00:09:17,650
is much, much larger
than the length

155
00:09:17,650 --> 00:09:21,490
scale of the distance between
the two slit, which is d.

156
00:09:21,490 --> 00:09:28,495
Therefore, I can safely
assume that AP and the BP

157
00:09:28,495 --> 00:09:31,260
are almost parallel
to each other.

158
00:09:31,260 --> 00:09:32,960
Right?

159
00:09:32,960 --> 00:09:38,620
And I can also try to express
the location of the P point

160
00:09:38,620 --> 00:09:44,140
by using the angle between BP
and the horizontal direction.

161
00:09:44,140 --> 00:09:45,160
OK?

162
00:09:45,160 --> 00:09:47,070
And the horizontal
direction is actually

163
00:09:47,070 --> 00:09:49,330
showing there's
a dash line here.

164
00:09:49,330 --> 00:09:52,300
And the angle between BP
and the horizontal direction

165
00:09:52,300 --> 00:09:54,990
it's called theta here.

166
00:09:54,990 --> 00:09:55,660
OK.

167
00:09:55,660 --> 00:10:01,380
So since AP and the BP are
almost parallel to each other,

168
00:10:01,380 --> 00:10:05,850
I can now calculate what would
be the optical path length

169
00:10:05,850 --> 00:10:09,600
difference between
AP and the BP.

170
00:10:09,600 --> 00:10:10,440
Right?

171
00:10:10,440 --> 00:10:13,590
So in order to
actually calculate

172
00:10:13,590 --> 00:10:19,170
the phase difference between
the electromagnetic wave coming

173
00:10:19,170 --> 00:10:25,320
from slit A compared to slit
B, I need to calculate--

174
00:10:25,320 --> 00:10:33,865
again, like what we did last
time-- optical path length

175
00:10:33,865 --> 00:10:34,811
difference.

176
00:10:37,500 --> 00:10:38,000
OK?

177
00:10:38,000 --> 00:10:44,150
In this case, I can call the
distance between A and P, rA.

178
00:10:44,150 --> 00:10:47,930
And then I can also call
the distance between B

179
00:10:47,930 --> 00:10:50,570
and the P, rB.

180
00:10:50,570 --> 00:10:53,270
Then the optical path
length difference

181
00:10:53,270 --> 00:10:57,405
is called rB minus rA.

182
00:10:57,405 --> 00:10:58,970
And then we can
actually calculate

183
00:10:58,970 --> 00:11:04,400
that because we have already
given you the angle between BP

184
00:11:04,400 --> 00:11:06,380
and the horizontal direction.

185
00:11:06,380 --> 00:11:08,900
And basically, we
can safely conclude

186
00:11:08,900 --> 00:11:14,780
that the path length difference
is actually this line here.

187
00:11:14,780 --> 00:11:17,900
Therefore, I can actually
calculate and get

188
00:11:17,900 --> 00:11:19,780
the optical path
length difference,

189
00:11:19,780 --> 00:11:25,850
the difference between rB and
the rA to be d sine theta.

190
00:11:25,850 --> 00:11:27,310
OK?

191
00:11:27,310 --> 00:11:30,650
Once we have that, it's
actually pretty straightforward

192
00:11:30,650 --> 00:11:33,666
to calculate what would
be the phase difference.

193
00:11:37,560 --> 00:11:44,940
The phase difference between the
field coming from slit A, which

194
00:11:44,940 --> 00:11:48,640
I will call it EA
here, and the field

195
00:11:48,640 --> 00:11:55,790
coming from the slit B,
which I will call it EB here.

196
00:11:55,790 --> 00:12:00,750
The phase difference, as
you define a lot of time

197
00:12:00,750 --> 00:12:06,390
to be delta, delta can be
calculated by the optical path

198
00:12:06,390 --> 00:12:10,460
length difference,
d sin theta, divided

199
00:12:10,460 --> 00:12:16,170
by lambda, which essentially
telling you how many period

200
00:12:16,170 --> 00:12:23,130
have passed when the light have
to actually overcome this--

201
00:12:23,130 --> 00:12:27,396
or say have to pass through this
optical path length difference.

202
00:12:27,396 --> 00:12:28,770
And, of course,
these things need

203
00:12:28,770 --> 00:12:32,930
to be modified by 2 pi
in order to translate

204
00:12:32,930 --> 00:12:35,970
from a number of period
to a phase difference.

205
00:12:35,970 --> 00:12:41,220
Therefore, you get the phase
difference between AP and BP

206
00:12:41,220 --> 00:12:44,280
to be delta equal
to d sine theta

207
00:12:44,280 --> 00:12:48,520
divided by lambda times 2 pi.

208
00:12:48,520 --> 00:12:49,020
OK.

209
00:12:49,020 --> 00:12:52,020
So you can see that
all those calculations

210
00:12:52,020 --> 00:12:53,290
are pretty straightforward.

211
00:12:53,290 --> 00:12:57,885
Maybe you have already seen
that before in an earlier class.

212
00:12:57,885 --> 00:13:01,110
But what I want to say
is that it is actually

213
00:13:01,110 --> 00:13:04,560
because of Huygens'
Principle, such

214
00:13:04,560 --> 00:13:09,000
that you can't expect something
which will show up at point P,

215
00:13:09,000 --> 00:13:11,790
right?

216
00:13:11,790 --> 00:13:13,920
If you don't have
Huygens' Principle

217
00:13:13,920 --> 00:13:15,690
what is going to happen?

218
00:13:15,690 --> 00:13:19,380
What is going to happen
is that the light

219
00:13:19,380 --> 00:13:23,100
passing through this slit
will just go straight.

220
00:13:23,100 --> 00:13:25,510
And they will never
overlap each other.

221
00:13:25,510 --> 00:13:26,010
OK?

222
00:13:26,010 --> 00:13:33,920
So that's actually why, because
of the Huygens' principle,

223
00:13:33,920 --> 00:13:38,820
all the points on the wavefront
are treated as a point

224
00:13:38,820 --> 00:13:41,570
source of a spherical wave.

225
00:13:41,570 --> 00:13:42,090
OK?

226
00:13:42,090 --> 00:13:46,140
So that is essentially why you
can expect that something will

227
00:13:46,140 --> 00:13:51,720
hit the P point, which
is because, in this case,

228
00:13:51,720 --> 00:13:54,810
we have two points,
two point source.

229
00:13:54,810 --> 00:14:00,420
And they are emitting
spherical waves

230
00:14:00,420 --> 00:14:02,390
coming from these two points.

231
00:14:02,390 --> 00:14:02,970
OK?

232
00:14:02,970 --> 00:14:06,600
So it is really because of
Huygens' Principle, which

233
00:14:06,600 --> 00:14:13,380
applies here, such that we can
actually observe the phenomenon

234
00:14:13,380 --> 00:14:15,510
at the P. And now,
we have managed

235
00:14:15,510 --> 00:14:17,550
to calculate the
phase difference,

236
00:14:17,550 --> 00:14:20,670
which is delta, presented here.

237
00:14:20,670 --> 00:14:26,620
So what the next question is,
what would be the intensity?

238
00:14:26,620 --> 00:14:32,200
Since we have already calculated
the phase difference delta,

239
00:14:32,200 --> 00:14:35,720
what would be the
intensity observed at P?

240
00:14:35,720 --> 00:14:40,370
So for that, we have
already prepared ourselves

241
00:14:40,370 --> 00:14:42,580
from the last few lectures.

242
00:14:42,580 --> 00:14:44,320
So now, we can
actually calculate

243
00:14:44,320 --> 00:14:47,610
what would be the total
E. The total E will

244
00:14:47,610 --> 00:14:54,130
be equal to EA plus EB.

245
00:14:54,130 --> 00:14:57,350
And here, I'm going to
use complex notation just

246
00:14:57,350 --> 00:14:59,010
for simplicity.

247
00:14:59,010 --> 00:15:01,940
And basically,
you can rewrite EA

248
00:15:01,940 --> 00:15:14,650
and the EB as E0 exponential
i omega t minus k times rA

249
00:15:14,650 --> 00:15:25,160
plus E0 exponential
i omega t minus k rB.

250
00:15:25,160 --> 00:15:29,120
The first term is actually
telling you the contribution

251
00:15:29,120 --> 00:15:34,610
from the first slit, slit A.
And the second term is actually

252
00:15:34,610 --> 00:15:39,832
telling you the contribution
coming from slit B.

253
00:15:39,832 --> 00:15:43,910
In this set up, I'm telling
you that I have the plane

254
00:15:43,910 --> 00:15:48,080
wave coming from the left
hand side of the experiment

255
00:15:48,080 --> 00:15:50,330
and actually hitting the wall.

256
00:15:50,330 --> 00:15:52,420
And you can see that
from the drawing.

257
00:15:52,420 --> 00:15:57,525
Actually, the
wavefront, essentially,

258
00:15:57,525 --> 00:16:02,450
actually telling you that the
direction of the electric field

259
00:16:02,450 --> 00:16:08,960
is actually in the Z direction
in my coordinate system shown

260
00:16:08,960 --> 00:16:09,980
on the board.

261
00:16:09,980 --> 00:16:14,180
So basically, the Z direction is
actually pointing to you guys.

262
00:16:14,180 --> 00:16:18,020
And that means the
electric field is actually

263
00:16:18,020 --> 00:16:20,120
oscillating in this direction.

264
00:16:20,120 --> 00:16:20,720
OK?

265
00:16:20,720 --> 00:16:24,140
So therefore, I have to be
careful of those vectors.

266
00:16:24,140 --> 00:16:26,990
So therefore, I need to
give it other direction.

267
00:16:26,990 --> 00:16:31,360
And in this case, it's
actually the Z direction.

268
00:16:31,360 --> 00:16:34,280
And also, you can see that
the amplitude is actually

269
00:16:34,280 --> 00:16:41,620
denoted by E0 because I always
assuming that both slit have

270
00:16:41,620 --> 00:16:44,120
the same finite width.

271
00:16:44,120 --> 00:16:47,060
For the moment, ignore
the width of the slit.

272
00:16:47,060 --> 00:16:49,740
And also, they are coming
from the same plane wave.

273
00:16:49,740 --> 00:16:54,980
Therefore, the amplitude
is all denoted by E0.

274
00:16:54,980 --> 00:16:55,820
OK?

275
00:16:55,820 --> 00:16:58,060
So now, I have the
expression here.

276
00:16:58,060 --> 00:17:01,610
And I can now go ahead and
simplify this expression

277
00:17:01,610 --> 00:17:04,020
and rewrite that in this form.

278
00:17:04,020 --> 00:17:06,190
So I can now extract the E0.

279
00:17:06,190 --> 00:17:09,349
And also, I extract the
common factors here,

280
00:17:09,349 --> 00:17:15,950
which essentially the
exponential i omega t

281
00:17:15,950 --> 00:17:19,235
and also, minus k rA.

282
00:17:19,235 --> 00:17:22,310
I can actually
factorize some part

283
00:17:22,310 --> 00:17:25,220
of the exponential function out.

284
00:17:25,220 --> 00:17:27,869
So the choice I made
is that I actually

285
00:17:27,869 --> 00:17:33,320
could factorize out exponential
i omega t minus k times r.

286
00:17:33,320 --> 00:17:34,670
Basically, I take these out.

287
00:17:34,670 --> 00:17:41,900
And I get this term showing
here, omega t minus k rA.

288
00:17:41,900 --> 00:17:43,860
I take this out.

289
00:17:43,860 --> 00:17:46,760
Then basically, what you
are doing to get inside

290
00:17:46,760 --> 00:17:52,770
will be 1 plus exponential
minus i delta, actually.

291
00:17:55,656 --> 00:17:57,100
times z.

292
00:17:57,100 --> 00:17:57,920
OK?

293
00:17:57,920 --> 00:17:59,240
Why is that delta?

294
00:17:59,240 --> 00:18:04,010
Because once you factorize out
or take out exponential i omega

295
00:18:04,010 --> 00:18:07,310
t minus k rA,
basically, you are left

296
00:18:07,310 --> 00:18:13,200
with something proportional
to exponential i minus k

297
00:18:13,200 --> 00:18:15,600
rB minus rA, right?

298
00:18:15,600 --> 00:18:20,310
And that is actually the optical
path length difference here.

299
00:18:20,310 --> 00:18:25,650
And also, of course, you
can always rewrite lambda

300
00:18:25,650 --> 00:18:27,560
over 2 pi, right?

301
00:18:27,560 --> 00:18:34,800
Basically, you write this
to be k times d times theta.

302
00:18:34,800 --> 00:18:35,300
Right?

303
00:18:35,300 --> 00:18:39,740
So therefore, you can
actually immediately identify

304
00:18:39,740 --> 00:18:43,830
the second term is to
essentially exponential

305
00:18:43,830 --> 00:18:45,670
minus i delta.

306
00:18:45,670 --> 00:18:47,270
OK?

307
00:18:47,270 --> 00:18:49,330
Any questions here?

308
00:18:49,330 --> 00:18:50,280
OK.

309
00:18:50,280 --> 00:18:54,810
Because d sine theta
essentially is just rB minus rA,

310
00:18:54,810 --> 00:18:58,530
therefore, I safely
replace that by delta here.

311
00:18:58,530 --> 00:18:59,361
OK?

312
00:18:59,361 --> 00:18:59,860
All right.

313
00:18:59,860 --> 00:19:02,430
So since everybody's
on the same page,

314
00:19:02,430 --> 00:19:07,440
I can now, again, factorize
out not only the omega t

315
00:19:07,440 --> 00:19:11,320
minus kA term,
but I can actually

316
00:19:11,320 --> 00:19:14,960
do a trick to factorize
out, also, exponential

317
00:19:14,960 --> 00:19:18,200
minus i delta divided by 2 out.

318
00:19:18,200 --> 00:19:19,830
And basically, what
I'm going to get

319
00:19:19,830 --> 00:19:26,480
is exponential i delta over 2
plus exponential minus i delta

320
00:19:26,480 --> 00:19:29,910
over 2.

321
00:19:29,910 --> 00:19:33,360
This reason why I'm doing
this is because, huh, now,

322
00:19:33,360 --> 00:19:36,180
I have this term identified.

323
00:19:36,180 --> 00:19:40,210
And this is actually
just 2 times cosine delta

324
00:19:40,210 --> 00:19:41,210
divided by 2.

325
00:19:41,210 --> 00:19:43,860
All right?

326
00:19:43,860 --> 00:19:45,240
OK?

327
00:19:45,240 --> 00:19:50,320
So now, I'm really pretty
close to the intensity.

328
00:19:50,320 --> 00:19:52,590
So what would be the
intensity coming out

329
00:19:52,590 --> 00:19:55,200
of this electric field?

330
00:19:55,200 --> 00:20:00,090
That is actually going
to be average intensity,

331
00:20:00,090 --> 00:20:03,450
as we discussed last
time in the lecture.

332
00:20:03,450 --> 00:20:08,220
The average intensity is
proportional to square

333
00:20:08,220 --> 00:20:09,740
of E vector.

334
00:20:09,740 --> 00:20:10,650
Right?

335
00:20:10,650 --> 00:20:12,810
In the complex
notation, how do we

336
00:20:12,810 --> 00:20:17,940
evaluate the absolute
value of E vector square?

337
00:20:17,940 --> 00:20:20,260
In the complex
notation, basically, you

338
00:20:20,260 --> 00:20:28,530
get basically, E times E
star, where E is actually

339
00:20:28,530 --> 00:20:33,790
the amplitude, which is the size
of the E vector, the magnitude

340
00:20:33,790 --> 00:20:35,560
of the E vector.

341
00:20:35,560 --> 00:20:37,800
Then, basically, you
will see that this

342
00:20:37,800 --> 00:20:45,035
will be proportional to cosine
square delta divided by 2.

343
00:20:45,035 --> 00:20:46,510
Right?

344
00:20:46,510 --> 00:20:51,010
Because you can see that
if I calculate EE star,

345
00:20:51,010 --> 00:20:56,380
then all the terms with related
to exponential i something

346
00:20:56,380 --> 00:20:57,730
actually got cancelled.

347
00:20:57,730 --> 00:20:58,480
Right?

348
00:20:58,480 --> 00:21:01,470
So therefore, you can see
the "aha" very, very quickly.

349
00:21:01,470 --> 00:21:04,180
We can show that
the intensity will

350
00:21:04,180 --> 00:21:08,590
be proportional to cosine
square delta divided by 2,

351
00:21:08,590 --> 00:21:12,280
where delta is the
phase difference

352
00:21:12,280 --> 00:21:15,160
between the first path
and the second path.

353
00:21:15,160 --> 00:21:16,090
OK?

354
00:21:16,090 --> 00:21:17,080
Any questions so far?

355
00:21:20,890 --> 00:21:22,580
OK.

356
00:21:22,580 --> 00:21:30,050
So we can see that the intensity
essentially changing really

357
00:21:30,050 --> 00:21:34,266
rapidly as a function of delta.

358
00:21:34,266 --> 00:21:35,040
Right?

359
00:21:35,040 --> 00:21:41,210
So when I have a situation
where delta is equal to 0--

360
00:21:41,210 --> 00:21:47,420
let's actually stop here a
bit and enjoy what we have

361
00:21:47,420 --> 00:21:48,800
as you learn from here.

362
00:21:48,800 --> 00:21:49,310
All right?

363
00:21:49,310 --> 00:21:53,310
So if you have delta equal
to 0, what does that mean?

364
00:21:53,310 --> 00:21:56,630
That means there's
no phase difference

365
00:21:56,630 --> 00:21:58,810
between the first and
second electric field.

366
00:21:58,810 --> 00:22:02,580
Therefore, when you
add them together--

367
00:22:02,580 --> 00:22:06,050
just a reminder about the
notation we were using before.

368
00:22:06,050 --> 00:22:10,130
So if you draw the vector
in a complex frame, what

369
00:22:10,130 --> 00:22:13,790
you are doing is that you
are actually adding EA

370
00:22:13,790 --> 00:22:20,180
and the EB together in the
most efficient way, right?

371
00:22:20,180 --> 00:22:23,270
Because the delta is equal
to 0, the phase differences

372
00:22:23,270 --> 00:22:24,470
is equal to 0.

373
00:22:24,470 --> 00:22:27,610
Therefore, you are actually
adding them in a straight line.

374
00:22:27,610 --> 00:22:28,430
OK?

375
00:22:28,430 --> 00:22:32,400
So that actually will give
you the maxima intensity.

376
00:22:32,400 --> 00:22:37,111
Because when delta is
equal to 0, cosine 0 is 1.

377
00:22:37,111 --> 00:22:37,610
Right?

378
00:22:37,610 --> 00:22:42,210
Therefore, you are reaching
the maxima in the intensity.

379
00:22:42,210 --> 00:22:45,940
So now, I can always
increase my delta

380
00:22:45,940 --> 00:22:49,940
until a number which
is actually pi.

381
00:22:49,940 --> 00:22:52,610
What is going to happen
is that if I still

382
00:22:52,610 --> 00:22:56,870
use the notation which I was
using for the complex frame,

383
00:22:56,870 --> 00:22:58,650
what it does this is that, huh.

384
00:22:58,650 --> 00:23:04,670
Now, I am actually completely
cancel the electric field,

385
00:23:04,670 --> 00:23:08,670
because the phase
difference now is pi, right?

386
00:23:08,670 --> 00:23:11,480
So therefore, in
the complex frame,

387
00:23:11,480 --> 00:23:15,710
you are adding the two
vectors in way such

388
00:23:15,710 --> 00:23:18,140
that they completely
cancel each other.

389
00:23:18,140 --> 00:23:20,300
The magnitude of
the two vectors are

390
00:23:20,300 --> 00:23:24,020
the same, as shown here,
which is actually E0, right?

391
00:23:24,020 --> 00:23:27,440
Therefore, what you are
going to get, as you expect,

392
00:23:27,440 --> 00:23:32,030
is going to be 0, because
they completely cancel.

393
00:23:32,030 --> 00:23:32,880
OK?

394
00:23:32,880 --> 00:23:36,770
You can also see that from
this formula we did right here.

395
00:23:36,770 --> 00:23:41,000
When delta is equal to pi, then
essentially, cosine pi over 2.

396
00:23:41,000 --> 00:23:44,210
Then you get
intensity equal to 0.

397
00:23:44,210 --> 00:23:44,990
OK?

398
00:23:44,990 --> 00:23:47,330
Everybody accept this?

399
00:23:47,330 --> 00:23:48,790
All right.

400
00:23:48,790 --> 00:23:53,380
Now, I can still continue
and increase the delta,

401
00:23:53,380 --> 00:23:56,750
for example, until
delta is equal to 2 pi.

402
00:23:56,750 --> 00:23:58,370
Then you are getting this again.

403
00:23:58,370 --> 00:24:04,210
Basically, you have EA and the
EB, again, line up each other.

404
00:24:04,210 --> 00:24:08,530
And the difference is
that this EB actually

405
00:24:08,530 --> 00:24:14,890
rotated maybe 360 degree.

406
00:24:14,890 --> 00:24:20,540
And basically, you will see
that, again, the intensity

407
00:24:20,540 --> 00:24:22,200
become the maxima again.

408
00:24:22,200 --> 00:24:23,350
OK?

409
00:24:23,350 --> 00:24:26,110
So that is actually
how we can actually

410
00:24:26,110 --> 00:24:30,190
understand this result.
And, of course, you

411
00:24:30,190 --> 00:24:34,450
can also go ahead
and plot or simulate

412
00:24:34,450 --> 00:24:42,670
this result in the computer
and really draw the amplitude,

413
00:24:42,670 --> 00:24:47,560
really draw the intensity
as a function of angle here,

414
00:24:47,560 --> 00:24:49,630
or, say, the delta here.

415
00:24:49,630 --> 00:24:52,520
As you can see from
here, that the intensity

416
00:24:52,520 --> 00:24:58,450
is actually reaching the
maximum in the center.

417
00:24:58,450 --> 00:24:59,470
Why is that?

418
00:24:59,470 --> 00:25:04,500
In the center, if I
have observer here

419
00:25:04,500 --> 00:25:07,270
in the center, what
is going to happen

420
00:25:07,270 --> 00:25:10,210
is that the path
length, optical path

421
00:25:10,210 --> 00:25:14,860
length between AP
prong and the BP prong

422
00:25:14,860 --> 00:25:18,520
is going to be the
same by symmetry,

423
00:25:18,520 --> 00:25:21,010
because it's actually
in the optical center.

424
00:25:21,010 --> 00:25:26,900
Therefore, you will expect that
delta is actually equal to 0.

425
00:25:26,900 --> 00:25:27,400
OK?

426
00:25:27,400 --> 00:25:31,170
So that's essentially why
you see the maxima there.

427
00:25:31,170 --> 00:25:34,210
And if you start to
move away from there,

428
00:25:34,210 --> 00:25:37,730
you will see that the
delta start to increase.

429
00:25:37,730 --> 00:25:41,170
And at some point, you'll
reach a minima, which

430
00:25:41,170 --> 00:25:44,630
you can see that on the plot.

431
00:25:44,630 --> 00:25:47,670
And that is actually
because now,

432
00:25:47,670 --> 00:25:50,320
due to the increasing
optical path length

433
00:25:50,320 --> 00:25:52,310
difference and the
phase difference,

434
00:25:52,310 --> 00:25:54,550
the two electric
field is starting

435
00:25:54,550 --> 00:25:57,640
to cancel each other,
which actually produce

436
00:25:57,640 --> 00:26:00,220
the black pattern there.

437
00:26:00,220 --> 00:26:06,790
And finally, after it
pass delta equal to pi,

438
00:26:06,790 --> 00:26:10,210
then these two electric fields
start to work together again.

439
00:26:10,210 --> 00:26:10,910
All right?

440
00:26:10,910 --> 00:26:12,610
They're collaborating again.

441
00:26:12,610 --> 00:26:14,050
And you can see that again.

442
00:26:14,050 --> 00:26:18,010
You would get another
maxima afterward.

443
00:26:18,010 --> 00:26:18,850
OK?

444
00:26:18,850 --> 00:26:23,260
And here, you can see that
is actually my calculation.

445
00:26:23,260 --> 00:26:28,000
And, of course, I can do
a demonstration to you

446
00:26:28,000 --> 00:26:29,560
to really show that
this is actually

447
00:26:29,560 --> 00:26:35,760
what we are going to see
based on the demonstration we

448
00:26:35,760 --> 00:26:37,060
are going to show here.

449
00:26:37,060 --> 00:26:39,260
So now, I am going to
turn the light off.

450
00:26:44,630 --> 00:26:49,790
And here, I have a device which
actually contain a water tank.

451
00:26:49,790 --> 00:26:53,210
And I need to actually
turn this thing up.

452
00:26:59,310 --> 00:27:04,310
On the water tank I have two
vibrator, which is actually

453
00:27:04,310 --> 00:27:07,090
acting as a point source.

454
00:27:07,090 --> 00:27:10,540
So basically, those vibrator
vibrating up and down

455
00:27:10,540 --> 00:27:15,640
to create waves in this tank.

456
00:27:15,640 --> 00:27:16,240
OK?

457
00:27:16,240 --> 00:27:18,910
So basically, you can
see that, huh, really,

458
00:27:18,910 --> 00:27:21,350
you have two point-like source.

459
00:27:21,350 --> 00:27:26,350
And you can see spherical waves
is actually really generated

460
00:27:26,350 --> 00:27:30,220
and is really propagating
away from the point source.

461
00:27:30,220 --> 00:27:31,540
OK?

462
00:27:31,540 --> 00:27:34,930
And what I can do
now, you can see

463
00:27:34,930 --> 00:27:38,380
that this picture is
really dynamic, because we

464
00:27:38,380 --> 00:27:40,510
can see that wavefront
essentially moving

465
00:27:40,510 --> 00:27:41,900
as a function of time.

466
00:27:41,900 --> 00:27:45,700
So what I'm going to
do is to really change

467
00:27:45,700 --> 00:27:48,730
the frequency of the
light, which is actually

468
00:27:48,730 --> 00:27:52,280
shining on this water,
so that you can actually

469
00:27:52,280 --> 00:27:55,150
see the fixed pattern here.

470
00:27:55,150 --> 00:28:01,520
And now, I am going to
change the light frequency.

471
00:28:01,520 --> 00:28:05,870
You can see now I only
shine the water tank

472
00:28:05,870 --> 00:28:10,460
at the specific time which match
the speed of the propagation

473
00:28:10,460 --> 00:28:11,840
of the water wave.

474
00:28:11,840 --> 00:28:13,790
And you can see, aha,
I've actually managed

475
00:28:13,790 --> 00:28:16,370
to freeze the wavefront.

476
00:28:16,370 --> 00:28:16,951
We see?

477
00:28:16,951 --> 00:28:17,450
OK.

478
00:28:17,450 --> 00:28:23,610
So you can see, now, really, you
can see coming from the source,

479
00:28:23,610 --> 00:28:28,210
they are circular
wavefront, which

480
00:28:28,210 --> 00:28:32,840
actually mimicking the result
from Huygens' Principle.

481
00:28:32,840 --> 00:28:35,810
And you can see that
they are complicated

482
00:28:35,810 --> 00:28:39,240
interference pattern forming.

483
00:28:39,240 --> 00:28:41,600
You can see that
at some point they

484
00:28:41,600 --> 00:28:43,520
have constructive interference.

485
00:28:43,520 --> 00:28:46,100
If you focus on
the central part,

486
00:28:46,100 --> 00:28:50,840
you can see that the maxima
is actually reach there.

487
00:28:50,840 --> 00:28:53,720
On the other hand, if you
move away, a little bit

488
00:28:53,720 --> 00:28:57,770
away from the center, you can
see that really, the intensity

489
00:28:57,770 --> 00:28:58,550
drop.

490
00:28:58,550 --> 00:29:03,885
And at some point, you will
also see that, OK, again, I

491
00:29:03,885 --> 00:29:06,190
am changing the
procedure in such

492
00:29:06,190 --> 00:29:10,250
that the phase difference
between the contribution

493
00:29:10,250 --> 00:29:14,320
of our source A and the B
essentially equal to 2 pi.

494
00:29:14,320 --> 00:29:21,340
In that case, you will be able
to see that another maxima is

495
00:29:21,340 --> 00:29:22,660
actually created again.

496
00:29:28,600 --> 00:29:30,660
So now, we can
actually also show you

497
00:29:30,660 --> 00:29:37,890
that a lot, in fact, based
on this glorious pattern,

498
00:29:37,890 --> 00:29:40,630
let's actually take a look
at the projector here.

499
00:29:40,630 --> 00:29:47,280
So if I look at on the
individual slide, which

500
00:29:47,280 --> 00:29:51,160
I have here, you can see
that those are actually

501
00:29:51,160 --> 00:29:55,450
a point-light source and is
creating a circular pattern.

502
00:29:55,450 --> 00:29:59,130
And now, I can actually overlap
with two patterns together.

503
00:29:59,130 --> 00:30:09,270
And you can see that when I have
the center of the two circles

504
00:30:09,270 --> 00:30:12,850
pretty close to each other,
you can see that really, you

505
00:30:12,850 --> 00:30:14,610
have very small d.

506
00:30:14,610 --> 00:30:17,520
In this case, you have
very small distance

507
00:30:17,520 --> 00:30:20,610
between source number
one and number two.

508
00:30:20,610 --> 00:30:25,350
Then basically, based
on our expression,

509
00:30:25,350 --> 00:30:30,390
so you can see that delta is
equal to d sine theta divided

510
00:30:30,390 --> 00:30:32,820
by lambda times two pi, right?

511
00:30:32,820 --> 00:30:36,120
And you can actually
calculate sine theta

512
00:30:36,120 --> 00:30:42,051
will be equal to delta
divided by k times t.

513
00:30:42,051 --> 00:30:42,550
OK?

514
00:30:53,060 --> 00:30:56,890
When delta is equal to pi,
that is going to give you

515
00:30:56,890 --> 00:31:01,030
a minima where, essentially,
also showing here,

516
00:31:01,030 --> 00:31:04,510
the minima is shown as
the black pattern here.

517
00:31:04,510 --> 00:31:05,240
OK?

518
00:31:05,240 --> 00:31:07,660
You can see from on here.

519
00:31:07,660 --> 00:31:10,270
So what this says, your
formula is showing you

520
00:31:10,270 --> 00:31:15,280
that when I have d,
which is very small,

521
00:31:15,280 --> 00:31:16,840
what is going to
happen is that I'm

522
00:31:16,840 --> 00:31:22,870
going to get sine theta to be
very large when d is actually

523
00:31:22,870 --> 00:31:23,770
very small.

524
00:31:23,770 --> 00:31:25,370
And that can be shown here.

525
00:31:25,370 --> 00:31:28,930
When I have d, which is the
distance between the center

526
00:31:28,930 --> 00:31:32,510
of these two point
source, very small,

527
00:31:32,510 --> 00:31:38,140
you can see that the
place you get the minima

528
00:31:38,140 --> 00:31:44,710
is really far away from the
center, which is actually here.

529
00:31:44,710 --> 00:31:45,550
OK?

530
00:31:45,550 --> 00:31:48,910
Now, what I'm going to do
is to increase the distance

531
00:31:48,910 --> 00:31:50,200
between these two source.

532
00:31:50,200 --> 00:31:53,410
According to our position,
what is going to happen

533
00:31:53,410 --> 00:32:00,220
is that the central
maxima will decrease.

534
00:32:00,220 --> 00:32:04,810
The position where you get a
minima will be moving closer

535
00:32:04,810 --> 00:32:07,870
to the center, according
to that formula,

536
00:32:07,870 --> 00:32:10,210
because it's
proportional to 1 over d.

537
00:32:10,210 --> 00:32:12,400
And we can do this
really carefully

538
00:32:12,400 --> 00:32:14,900
to see if I can succeed.

539
00:32:14,900 --> 00:32:19,900
And you can see that
really, when I am moving

540
00:32:19,900 --> 00:32:22,960
these two slides
away from each other,

541
00:32:22,960 --> 00:32:25,590
you can see that the
pattern is changing, right?

542
00:32:25,590 --> 00:32:34,390
And the center maxima, or, say,
this Gaussian-like curve there

543
00:32:34,390 --> 00:32:37,020
becoming narrower and narrower.

544
00:32:37,020 --> 00:32:37,600
OK?

545
00:32:37,600 --> 00:32:40,058
So that essentially what we
can actually observe form here.

546
00:32:40,058 --> 00:32:45,822
And our calculation really
works very well here.

547
00:32:48,720 --> 00:32:49,500
Very good.

548
00:32:49,500 --> 00:32:53,480
So do we have any
questions regarding

549
00:32:53,480 --> 00:32:55,030
the demonstration we have here?

550
00:32:59,360 --> 00:33:00,300
OK.

551
00:33:00,300 --> 00:33:04,560
So all those things seems to be
pretty straightforward to you.

552
00:33:04,560 --> 00:33:08,700
And what we are actually
now is seeing a position

553
00:33:08,700 --> 00:33:13,030
where we can actually
discuss how we actually

554
00:33:13,030 --> 00:33:22,570
can understand the radar, which
is how actually radar works.

555
00:33:22,570 --> 00:33:25,090
So here is actually
how radar works.

556
00:33:25,090 --> 00:33:28,860
Suppose you have
some unknown object,

557
00:33:28,860 --> 00:33:31,350
which is like an airplane, OK?

558
00:33:31,350 --> 00:33:35,220
And you would like to
know where is this object.

559
00:33:35,220 --> 00:33:41,550
What you do, actually, is to
shoot whatever radio waves

560
00:33:41,550 --> 00:33:43,840
toward some direction
and see if there

561
00:33:43,840 --> 00:33:45,300
are something coming back.

562
00:33:45,300 --> 00:33:45,960
Right?

563
00:33:45,960 --> 00:33:49,290
Then you know there's
something on the sky

564
00:33:49,290 --> 00:33:51,770
because you can detect
the refracted wave.

565
00:33:51,770 --> 00:33:52,760
Right?

566
00:33:52,760 --> 00:33:56,070
So we shoot this airplane.

567
00:33:56,070 --> 00:33:59,050
And then something is
going to come back.

568
00:33:59,050 --> 00:34:01,630
And now, we can say OK.

569
00:34:01,630 --> 00:34:03,870
In that direction I have
something coming back.

570
00:34:03,870 --> 00:34:06,370
That means there's
something there.

571
00:34:06,370 --> 00:34:09,090
And I can also measure
the time it takes

572
00:34:09,090 --> 00:34:10,590
for the wave to come back.

573
00:34:10,590 --> 00:34:13,211
Then I know where it's
actually that object.

574
00:34:13,211 --> 00:34:13,710
Right?

575
00:34:13,710 --> 00:34:18,750
So that's actually a pretty
straightforward thing to do.

576
00:34:18,750 --> 00:34:23,170
However, there's one difficulty.

577
00:34:23,170 --> 00:34:27,790
So this is actually
the radiation pattern

578
00:34:27,790 --> 00:34:32,920
of oscillating dipole which
we actually learned before.

579
00:34:32,920 --> 00:34:36,280
So the problem is that,
OK, what we really

580
00:34:36,280 --> 00:34:40,600
need is electromagnetic wave,
which is actually very, very

581
00:34:40,600 --> 00:34:44,920
narrow in angle and pointing
to some specific direction.

582
00:34:44,920 --> 00:34:46,449
And then I would
like to see if I

583
00:34:46,449 --> 00:34:49,920
can get some refractive wave
coming from that direction.

584
00:34:49,920 --> 00:34:50,710
OK?

585
00:34:50,710 --> 00:34:53,770
The problem is that, look!

586
00:34:53,770 --> 00:34:57,040
if I oscillate some
charge up and down,

587
00:34:57,040 --> 00:35:00,590
the radiation I'm getting
is really, really broad.

588
00:35:00,590 --> 00:35:01,090
Right?

589
00:35:01,090 --> 00:35:04,090
So it's going toward all
kinds of different direction.

590
00:35:04,090 --> 00:35:07,240
So if you use this
to detect things,

591
00:35:07,240 --> 00:35:10,810
you are always going to
get something coming back,

592
00:35:10,810 --> 00:35:14,080
because it's actually shooting
the electromagnetic wave

593
00:35:14,080 --> 00:35:16,450
into random direction.

594
00:35:16,450 --> 00:35:20,530
And you are not
sure any more where

595
00:35:20,530 --> 00:35:23,570
is actually this object
you are trying to detect.

596
00:35:23,570 --> 00:35:24,070
OK?

597
00:35:24,070 --> 00:35:27,890
So that's actually
apparently a problem.

598
00:35:27,890 --> 00:35:33,520
And what we can actually do is
to make use of the interference

599
00:35:33,520 --> 00:35:35,440
phenomenon, which
we can actually

600
00:35:35,440 --> 00:35:39,400
learn from here to
actually try to make sure

601
00:35:39,400 --> 00:35:41,470
that the electromagnetic
wave is actually

602
00:35:41,470 --> 00:35:46,130
pointing to some specific
direction we want.

603
00:35:46,130 --> 00:35:51,100
So let's actually go ahead
consider a three slit

604
00:35:51,100 --> 00:35:52,099
experiment.

605
00:35:56,230 --> 00:35:59,130
I have this setup changed.

606
00:35:59,130 --> 00:36:00,900
Originally, I have two slits.

607
00:36:00,900 --> 00:36:05,440
And now, I drew it in
three holes on the wall.

608
00:36:05,440 --> 00:36:11,140
And, again, I have the distance
between the slits to be d.

609
00:36:11,140 --> 00:36:16,060
And I call this slit
number 1, 2, and 3.

610
00:36:16,060 --> 00:36:19,150
And we were wondering what
would be the interference

611
00:36:19,150 --> 00:36:23,380
pattern on the screen,
which is actually

612
00:36:23,380 --> 00:36:28,540
far away from the wall,
as a distance of L.

613
00:36:28,540 --> 00:36:32,020
And I'm interested
in their intensity

614
00:36:32,020 --> 00:36:34,130
at the point P on this screen.

615
00:36:34,130 --> 00:36:35,500
OK?

616
00:36:35,500 --> 00:36:39,310
So what I am going to do
is to basically repeat

617
00:36:39,310 --> 00:36:43,080
what we have done in
the previous example.

618
00:36:43,080 --> 00:36:46,540
I'm trying to connect
1 to the P, 2 P,

619
00:36:46,540 --> 00:36:50,150
and the 3 P, basically,
connect the slit

620
00:36:50,150 --> 00:36:54,400
to the point of
interest on the screen.

621
00:36:54,400 --> 00:36:58,390
And I can actually also--

622
00:36:58,390 --> 00:37:03,520
you know this angle, this 1 P
to the horizontal direction,

623
00:37:03,520 --> 00:37:09,280
this angle is called
theta in my notation.

624
00:37:09,280 --> 00:37:11,850
Then clearly, I can
go ahead and calculate

625
00:37:11,850 --> 00:37:15,280
what will be the
optical path length

626
00:37:15,280 --> 00:37:17,710
difference between
of the light coming

627
00:37:17,710 --> 00:37:21,650
from slit number 1, slit
number 2 and the slit number 3.

628
00:37:21,650 --> 00:37:22,205
OK?

629
00:37:22,205 --> 00:37:27,020
And in this case,
what I'm interested

630
00:37:27,020 --> 00:37:33,530
is delta 1, 2 and delta 1, 3.

631
00:37:33,530 --> 00:37:34,850
Right?

632
00:37:34,850 --> 00:37:39,770
Since the screen is really
far away from the wall,

633
00:37:39,770 --> 00:37:42,860
therefore, I can actually
savor the assurance

634
00:37:42,860 --> 00:37:49,640
that these two angle is actually
theta because the three lines,

635
00:37:49,640 --> 00:37:52,210
due to the large
distance, this L

636
00:37:52,210 --> 00:37:54,030
is actually really,
really large.

637
00:37:54,030 --> 00:37:56,870
Therefore, they are actually
almost parallel to each other.

638
00:37:56,870 --> 00:37:57,800
OK?

639
00:37:57,800 --> 00:38:02,270
So what is going to happen
is that delta 1, 2, which

640
00:38:02,270 --> 00:38:05,170
is the phase difference
between light

641
00:38:05,170 --> 00:38:08,590
from the first slit
and second slit,

642
00:38:08,590 --> 00:38:17,330
is actually going to
be equal to delta 2, 3.

643
00:38:17,330 --> 00:38:19,100
It's going to be
equal to the phase

644
00:38:19,100 --> 00:38:22,250
difference between the
second slit, the light

645
00:38:22,250 --> 00:38:24,450
from second slit and third slit.

646
00:38:24,450 --> 00:38:26,330
And what is actually
that number?

647
00:38:26,330 --> 00:38:31,275
This number is going to
be equal to d sine theta

648
00:38:31,275 --> 00:38:34,432
divided by lambda times 2 pi.

649
00:38:34,432 --> 00:38:38,150
It's exactly the same
as what we actually

650
00:38:38,150 --> 00:38:39,840
get from the first example.

651
00:38:39,840 --> 00:38:40,340
OK?

652
00:38:43,310 --> 00:38:45,790
Therefore, what
is going to happen

653
00:38:45,790 --> 00:38:51,190
is that no matter
what theta I choose,

654
00:38:51,190 --> 00:38:54,700
the phase difference
between nearby slit

655
00:38:54,700 --> 00:38:58,000
is actually a constant,
which is actually this one.

656
00:38:58,000 --> 00:39:01,710
And I will call this phase
difference to be delta.

657
00:39:04,650 --> 00:39:08,670
I would like to ask
you a question now.

658
00:39:08,670 --> 00:39:13,530
The question is, how
do we choose the delta

659
00:39:13,530 --> 00:39:22,030
here such that I have completely
destructive interference?

660
00:39:22,030 --> 00:39:29,802
Now, I have three vectors,
vector E1, vector E2,

661
00:39:29,802 --> 00:39:31,295
and the vector E3.

662
00:39:37,600 --> 00:39:41,500
The phase difference
between E1, E2, and E3,

663
00:39:41,500 --> 00:39:47,330
the nearby phase difference
is actually delta.

664
00:39:47,330 --> 00:39:51,190
So the question is, how do
I actually completely cancel

665
00:39:51,190 --> 00:39:54,070
the electric field so
that I have completely

666
00:39:54,070 --> 00:39:55,600
destructive interference?

667
00:39:55,600 --> 00:39:59,520
Can somebody help me here?

668
00:39:59,520 --> 00:40:04,890
The hint is that you can
actually use this vector sum

669
00:40:04,890 --> 00:40:08,244
idea in the complex frame.

670
00:40:08,244 --> 00:40:09,240
STUDENT: [INAUDIBLE]

671
00:40:09,240 --> 00:40:10,610
PROFESSOR: Yes, very good.

672
00:40:10,610 --> 00:40:14,460
To form a triangle in
the complex frame, right?

673
00:40:14,460 --> 00:40:21,150
So what we can do is now
choose the phase difference

674
00:40:21,150 --> 00:40:29,630
delta to be such that
E1, E2, and E3 actually

675
00:40:29,630 --> 00:40:32,410
form a triangle.

676
00:40:32,410 --> 00:40:34,930
You see what I mean?

677
00:40:34,930 --> 00:40:37,570
Therefore, you can
actually already get

678
00:40:37,570 --> 00:40:41,650
what would be the
required delta value.

679
00:40:41,650 --> 00:40:49,110
The required delta value is
going to be 2 pi divided by 3.

680
00:40:49,110 --> 00:40:50,520
Right?

681
00:40:50,520 --> 00:40:52,350
OK?

682
00:40:52,350 --> 00:40:53,030
So very good.

683
00:40:53,030 --> 00:40:55,320
So now, we are not
afraid anymore.

684
00:40:55,320 --> 00:40:57,720
So how about four
slit experiment?

685
00:40:57,720 --> 00:41:01,890
I just add another slit,
d essentially the distance

686
00:41:01,890 --> 00:41:04,670
between the fourth slit
and the third slit.

687
00:41:04,670 --> 00:41:13,430
What will be the
delta required to have

688
00:41:13,430 --> 00:41:15,114
destructive interference?

689
00:41:19,090 --> 00:41:21,386
Anybody can help me?

690
00:41:21,386 --> 00:41:23,240
STUDENT: [INAUDIBLE]

691
00:41:23,240 --> 00:41:24,820
YEN-JIE LEE: Very good.

692
00:41:24,820 --> 00:41:31,150
So if you have four slit,
based on this intuition,

693
00:41:31,150 --> 00:41:37,460
which we developed from
the complex notation vector

694
00:41:37,460 --> 00:41:42,010
sum, what is going to happen
is that if you have four slit,

695
00:41:42,010 --> 00:41:49,251
the delta will be equal
to 2 pi divided by 4.

696
00:41:49,251 --> 00:41:49,750
OK?

697
00:41:49,750 --> 00:41:52,450
So what does this tell us?

698
00:41:52,450 --> 00:41:55,950
So remember, the
sine theta, sine

699
00:41:55,950 --> 00:41:58,360
theta is telling you
the location where

700
00:41:58,360 --> 00:41:59,710
you get the minima.

701
00:41:59,710 --> 00:42:00,640
OK?

702
00:42:00,640 --> 00:42:04,630
So this is actually the
power profile, or, say,

703
00:42:04,630 --> 00:42:07,101
the intensity profile.

704
00:42:07,101 --> 00:42:07,600
OK?

705
00:42:07,600 --> 00:42:10,330
And this is actually equal to 0.

706
00:42:10,330 --> 00:42:11,940
And this is actually delta.

707
00:42:11,940 --> 00:42:13,030
OK?

708
00:42:13,030 --> 00:42:19,410
The place which you
get zero intensity

709
00:42:19,410 --> 00:42:25,790
is actually becoming
closer and closer to zero.

710
00:42:25,790 --> 00:42:26,290
Right?

711
00:42:26,290 --> 00:42:29,290
Because sine theta,
which is the angle

712
00:42:29,290 --> 00:42:33,850
between horizontal direction
and this observer P,

713
00:42:33,850 --> 00:42:36,340
is proportional to delta.

714
00:42:36,340 --> 00:42:40,510
When you have destructive
interference at angle

715
00:42:40,510 --> 00:42:45,400
which is smaller, smaller,
and smaller, that means what?

716
00:42:45,400 --> 00:42:51,310
That means the central
Gaussian-like structure

717
00:42:51,310 --> 00:42:55,315
is going to be becoming
narrower and narrower.

718
00:42:58,730 --> 00:43:00,125
Does that make sense?

719
00:43:02,980 --> 00:43:03,650
Very good.

720
00:43:03,650 --> 00:43:07,270
So at least we found
something interesting now.

721
00:43:07,270 --> 00:43:13,330
That means, ha, one
idea to get very narrow

722
00:43:13,330 --> 00:43:16,870
electromagnetic wave
pointing to some direction

723
00:43:16,870 --> 00:43:22,180
is to have a huge number
of point light source

724
00:43:22,180 --> 00:43:26,830
and slit experiment
such that I can actually

725
00:43:26,830 --> 00:43:32,200
construct something which is
actually very narrow in angle.

726
00:43:32,200 --> 00:43:36,070
And I can use that to
shoot the object which

727
00:43:36,070 --> 00:43:38,282
I would like to detect.

728
00:43:38,282 --> 00:43:40,690
You see what I mean?

729
00:43:40,690 --> 00:43:43,800
Does that make sense?

730
00:43:43,800 --> 00:43:46,551
OK?

731
00:43:46,551 --> 00:43:47,050
All right.

732
00:43:47,050 --> 00:43:47,920
So that's very good.

733
00:43:47,920 --> 00:43:53,901
So now, let's actually consider
an N slit interference pattern

734
00:43:53,901 --> 00:43:54,400
OK?

735
00:43:54,400 --> 00:43:58,720
So suppose, now, I have not
only 1, 2, 3, and then many

736
00:43:58,720 --> 00:44:01,610
more until N slit.

737
00:44:01,610 --> 00:44:03,010
All right?

738
00:44:03,010 --> 00:44:07,600
I can now go ahead and
calculate the E total, which

739
00:44:07,600 --> 00:44:15,130
is the total electric field
coming from all of the slit

740
00:44:15,130 --> 00:44:17,260
we have.

741
00:44:17,260 --> 00:44:24,430
Basically, this will be equal
to E0 exponential i omega t

742
00:44:24,430 --> 00:44:36,110
minus kR where I define r1
is roughly capital R. OK?

743
00:44:36,110 --> 00:44:37,920
That's essentially
the contribution

744
00:44:37,920 --> 00:44:41,980
from slit number 1 OK?

745
00:44:41,980 --> 00:44:44,170
And this contribution
from slit number 1

746
00:44:44,170 --> 00:44:51,790
is going to be looking like
exponential i omega t minus kR

747
00:44:51,790 --> 00:44:54,670
minus delta, right,
because there is a phase

748
00:44:54,670 --> 00:44:57,640
difference between
the light coming

749
00:44:57,640 --> 00:45:02,440
from first slit and the second
slit, which is actually delta.

750
00:45:02,440 --> 00:45:03,640
All right?

751
00:45:03,640 --> 00:45:05,150
So what would be the third term?

752
00:45:05,150 --> 00:45:07,652
So these actually coming
from slit number 2.

753
00:45:07,652 --> 00:45:08,860
What would be the third term?

754
00:45:08,860 --> 00:45:15,310
Exponential i omega t
minus kR minus what?

755
00:45:15,310 --> 00:45:16,130
STUDENT: 2 delta.

756
00:45:16,130 --> 00:45:18,370
YEN-JIE LEE: 2 delta,
yeah, because you

757
00:45:18,370 --> 00:45:21,730
can see that coming
from here, seems

758
00:45:21,730 --> 00:45:25,190
the distance between theta
as constant, which is d.

759
00:45:25,190 --> 00:45:30,510
Therefore, the phase
difference between nearby slits

760
00:45:30,510 --> 00:45:32,440
is actually a constant.

761
00:45:32,440 --> 00:45:36,910
Therefore, I accumulating
the phase difference now.

762
00:45:36,910 --> 00:45:39,682
I get 2 delta here.

763
00:45:39,682 --> 00:45:41,140
And this is actually
a contribution

764
00:45:41,140 --> 00:45:42,040
from the first slit.

765
00:45:42,040 --> 00:45:48,140
And the et cetera, et
cetera, until the Nth slit,

766
00:45:48,140 --> 00:45:50,350
which is actually
going to be exponential

767
00:45:50,350 --> 00:45:58,810
i omega t minus kR
minus N minus 1 delta.

768
00:45:58,810 --> 00:46:01,830
And summing all those things
together, and all of them

769
00:46:01,830 --> 00:46:05,700
are in the Z direction.

770
00:46:05,700 --> 00:46:08,030
OK?

771
00:46:08,030 --> 00:46:10,520
So I'm now going to
calculate this dimension.

772
00:46:10,520 --> 00:46:17,280
So basically, you are getting E0
exponential i omega t minus kR.

773
00:46:17,280 --> 00:46:21,820
I can actually factorize
these factor out.

774
00:46:21,820 --> 00:46:28,910
And what am I going to get is 1
plus exponential minus i delta

775
00:46:28,910 --> 00:46:32,220
plus exponential minus
exponential minus i

776
00:46:32,220 --> 00:46:35,430
2 delta plus blah, blah, blah.

777
00:46:35,430 --> 00:46:39,160
And basically, you will
get exponential minus i

778
00:46:39,160 --> 00:46:42,730
minus 1 delta in the first term.

779
00:46:42,730 --> 00:46:48,050
And all those things are
pointing to the Z direction.

780
00:46:48,050 --> 00:46:50,830
And this, I know how
to actually calculate.

781
00:46:50,830 --> 00:46:52,040
Right?

782
00:46:52,040 --> 00:46:56,120
Just a reminder, basically,
if you calculate summation

783
00:46:56,120 --> 00:47:01,130
N equal to 0 to N
minus 1 r to the Nth.

784
00:47:01,130 --> 00:47:03,530
And these will
give you 1 minus r

785
00:47:03,530 --> 00:47:08,510
to the N divided by phi minus r.

786
00:47:08,510 --> 00:47:09,440
OK?

787
00:47:09,440 --> 00:47:13,010
So basically, I can now go
ahead and calculate this.

788
00:47:13,010 --> 00:47:22,640
And this will basically
give you 1 minus--

789
00:47:22,640 --> 00:47:26,220
OK, so the small r here has
been replaced by exponential

790
00:47:26,220 --> 00:47:28,550
minus i delta, right?

791
00:47:28,550 --> 00:47:30,770
So therefore, what
I'm going to get

792
00:47:30,770 --> 00:47:40,070
is 1 minus exponential minus
i delta N for the upper part.

793
00:47:40,070 --> 00:47:44,320
And then I have 1
minus exponential

794
00:47:44,320 --> 00:47:47,530
minus i delta in the lower part.

795
00:47:47,530 --> 00:47:48,950
OK?

796
00:47:48,950 --> 00:47:53,710
So that actually make use of
this formula, which are here.

797
00:47:53,710 --> 00:47:57,321
And, again, it should be
simplify these series.

798
00:47:57,321 --> 00:47:57,820
All right?

799
00:48:00,330 --> 00:48:02,550
As usual, what
I'm going to do is

800
00:48:02,550 --> 00:48:08,050
to use the trick similar
to what I have done there

801
00:48:08,050 --> 00:48:11,040
to actually get
cosine function out

802
00:48:11,040 --> 00:48:13,500
of the exponential functions.

803
00:48:13,500 --> 00:48:14,250
All right?

804
00:48:14,250 --> 00:48:17,460
So what I'm going to
do is to factorize out

805
00:48:17,460 --> 00:48:23,470
exponential minus i delta N
over 2 for the upper part.

806
00:48:23,470 --> 00:48:26,870
So basically, I get
exponential minus i delta

807
00:48:26,870 --> 00:48:34,320
N divided by 2, exponential
i delta N divided by 2

808
00:48:34,320 --> 00:48:39,683
minus exponential minus
i delta N divided by 2.

809
00:48:39,683 --> 00:48:40,182
OK?

810
00:48:43,360 --> 00:48:46,980
This is actually
divided by exponential

811
00:48:46,980 --> 00:48:52,620
minus i delta over 2
exponential i delta

812
00:48:52,620 --> 00:48:58,908
over 2 minus exponential
minus i delta over 2.

813
00:48:58,908 --> 00:49:00,270
All right?

814
00:49:00,270 --> 00:49:02,460
The reason I'm doing
this is because I

815
00:49:02,460 --> 00:49:06,600
would like to actually make
this a cosine function.

816
00:49:06,600 --> 00:49:08,550
OK?

817
00:49:08,550 --> 00:49:10,020
Any questions so far?

818
00:49:14,830 --> 00:49:16,150
OK.

819
00:49:16,150 --> 00:49:18,340
So if no question,
then basically,

820
00:49:18,340 --> 00:49:22,010
this expression can
be, again, rewritten

821
00:49:22,010 --> 00:49:28,030
as exponential minus i
delta N minus 1 divided

822
00:49:28,030 --> 00:49:33,340
by 2, because I have this
denominator nominator

823
00:49:33,340 --> 00:49:38,020
exponential i delta N over 2 and
that exponential minus i delta

824
00:49:38,020 --> 00:49:39,321
divided by 2.

825
00:49:39,321 --> 00:49:39,820
OK?

826
00:49:39,820 --> 00:49:42,460
Therefore, I can combine
them all together

827
00:49:42,460 --> 00:49:45,950
and then get this
expression here.

828
00:49:45,950 --> 00:49:49,180
And this is actually
exponential minus exponential.

829
00:49:49,180 --> 00:49:52,640
Therefore, I am going
to get sine out of it.

830
00:49:52,640 --> 00:49:56,520
And basically, I
get sine and delta

831
00:49:56,520 --> 00:50:02,265
divided by 2 divided
by sine delta over 2.

832
00:50:06,510 --> 00:50:07,030
OK.

833
00:50:07,030 --> 00:50:09,670
So now, I can actually
go ahead and calculate

834
00:50:09,670 --> 00:50:13,270
what will be the
resulting intensity.

835
00:50:13,270 --> 00:50:14,200
Right?

836
00:50:14,200 --> 00:50:19,290
The resulting intensity
is going to be

837
00:50:19,290 --> 00:50:24,710
proportional to the square
of the electric field.

838
00:50:24,710 --> 00:50:25,210
Right?

839
00:50:25,210 --> 00:50:30,510
So basically, the intensity will
be proportional to E square.

840
00:50:30,510 --> 00:50:36,166
And that is actually
equal to E times E star.

841
00:50:36,166 --> 00:50:39,300
E and the E is a
complex conjugate.

842
00:50:39,300 --> 00:50:41,070
And basically, you
will see that this

843
00:50:41,070 --> 00:50:49,810
will be proportional to sine
and delta divided by 2 divided

844
00:50:49,810 --> 00:50:56,160
by sine delta over 2 square.

845
00:50:56,160 --> 00:51:01,950
Therefore, the intensity
will be equal to i

846
00:51:01,950 --> 00:51:08,880
0 times sine and
delta divided by 2

847
00:51:08,880 --> 00:51:12,860
divided by sine delta over 2.

848
00:51:12,860 --> 00:51:16,256
And then square that.

849
00:51:16,256 --> 00:51:17,684
Any questions?

850
00:51:21,020 --> 00:51:26,090
So after all this work, we have
arrived at expression which

851
00:51:26,090 --> 00:51:28,592
is very hard to understand.

852
00:51:28,592 --> 00:51:29,092
Right?

853
00:51:29,092 --> 00:51:33,080
[LAUGHS] So what I'm
going to do to help you

854
00:51:33,080 --> 00:51:38,830
is to really plot the result
as a function of delta

855
00:51:38,830 --> 00:51:40,440
on the screen.

856
00:51:40,440 --> 00:51:44,050
You can see there
are four plots here.

857
00:51:44,050 --> 00:51:46,380
The first one is N equal to 3.

858
00:51:46,380 --> 00:51:48,860
The upper left one
is N equal to 3.

859
00:51:48,860 --> 00:51:52,270
So you can see that the
pattern looks like this.

860
00:51:52,270 --> 00:51:56,140
So at delta equal to
0, surprise nobody,

861
00:51:56,140 --> 00:51:57,700
you are going to get maxima.

862
00:51:57,700 --> 00:51:58,200
Right?

863
00:51:58,200 --> 00:52:02,850
Because delta is equal to
0, you are adding N vectors

864
00:52:02,850 --> 00:52:04,700
the most efficient way.

865
00:52:04,700 --> 00:52:07,020
Therefore, you are going
to get the maxima, which

866
00:52:07,020 --> 00:52:09,440
is i equal to i 0.

867
00:52:09,440 --> 00:52:10,980
OK?

868
00:52:10,980 --> 00:52:16,290
And if you move away from
the center, delta equal to 0,

869
00:52:16,290 --> 00:52:20,970
and you see that is a
small bump in between.

870
00:52:20,970 --> 00:52:22,800
Then you can continue
and continue.

871
00:52:22,800 --> 00:52:26,820
And you see that there's
another big peak again.

872
00:52:26,820 --> 00:52:27,540
You see?

873
00:52:27,540 --> 00:52:29,010
So that's essentially
the structure

874
00:52:29,010 --> 00:52:33,660
if you plot this result, i
equal to something proportional

875
00:52:33,660 --> 00:52:37,890
to sine square this
expression there.

876
00:52:37,890 --> 00:52:43,850
And that's essentially what you
will get when N is equal to 3.

877
00:52:43,850 --> 00:52:45,510
OK?

878
00:52:45,510 --> 00:52:49,380
And this is essentially how
I remember this pattern.

879
00:52:49,380 --> 00:52:50,760
OK?

880
00:52:50,760 --> 00:52:55,710
So when N is equal to
3, you have a family

881
00:52:55,710 --> 00:52:58,935
of two adult and one child.

882
00:52:58,935 --> 00:52:59,920
[LAUGHTER]

883
00:52:59,920 --> 00:53:00,420
Right?

884
00:53:00,420 --> 00:53:03,170
So basically, you
have two big peak.

885
00:53:03,170 --> 00:53:06,920
And between them,
there's a small peak.

886
00:53:06,920 --> 00:53:07,420
OK?

887
00:53:07,420 --> 00:53:09,850
That's actually how I
remember this pattern.

888
00:53:09,850 --> 00:53:12,880
And I think it's
pretty nice, right?

889
00:53:12,880 --> 00:53:15,555
So you can have N equal to 4.

890
00:53:15,555 --> 00:53:17,560
It's a bigger family.

891
00:53:17,560 --> 00:53:19,570
You have two adults.

892
00:53:19,570 --> 00:53:22,680
The adults are slimmer, OK?

893
00:53:22,680 --> 00:53:23,626
All right?

894
00:53:23,626 --> 00:53:25,810
[LAUGHTER]

895
00:53:25,810 --> 00:53:28,780
Because they have a
lot of work to do.

896
00:53:28,780 --> 00:53:30,600
Then they have two child.

897
00:53:30,600 --> 00:53:32,286
All right?

898
00:53:32,286 --> 00:53:37,002
N equal to 5, how many
children do we have?

899
00:53:37,002 --> 00:53:37,960
STUDENT: We have three.

900
00:53:37,960 --> 00:53:39,260
YEN-JIE LEE: Three.

901
00:53:39,260 --> 00:53:43,910
Therefore, the adults
are really frustrated.

902
00:53:43,910 --> 00:53:49,560
So they are even slimmer in a
happy way, making it positive.

903
00:53:49,560 --> 00:53:52,020
And N equal to 6, woo.

904
00:53:52,020 --> 00:53:55,830
Oh my god, I have four
children in the family.

905
00:53:55,830 --> 00:53:56,670
All right?

906
00:53:56,670 --> 00:54:00,610
So there are two things
which we learned from here.

907
00:54:00,610 --> 00:54:06,540
The first one is that the
number of big peak, which

908
00:54:06,540 --> 00:54:13,770
I would call it principal
maxima, the number

909
00:54:13,770 --> 00:54:16,580
of principal maxima
is actually pretty

910
00:54:16,580 --> 00:54:22,116
similar as a function of delta.

911
00:54:22,116 --> 00:54:26,630
But the number of
secondary maxima

912
00:54:26,630 --> 00:54:30,710
increase as a
function of N value.

913
00:54:30,710 --> 00:54:35,150
N value is actually
telling you how many slits

914
00:54:35,150 --> 00:54:38,020
you have in the experiment.

915
00:54:38,020 --> 00:54:44,060
And also, you can see that the
delta is actually becoming--

916
00:54:44,060 --> 00:54:48,130
the first minima,
the delta value

917
00:54:48,130 --> 00:54:51,580
is actually decreasing
as a function of N value.

918
00:54:51,580 --> 00:54:52,580
Right?

919
00:54:52,580 --> 00:54:55,660
So the parents are
getting slimmer.

920
00:54:55,660 --> 00:54:56,390
All right?

921
00:54:56,390 --> 00:54:59,120
So therefore, you
can see that if I

922
00:54:59,120 --> 00:55:04,130
would like to have a radar
which is actually pointing

923
00:55:04,130 --> 00:55:06,920
to a very specific
direction, what

924
00:55:06,920 --> 00:55:12,870
essentially the choice of
N value which we will need?

925
00:55:12,870 --> 00:55:14,870
Infinity or a very large number.

926
00:55:14,870 --> 00:55:15,420
OK?

927
00:55:15,420 --> 00:55:18,300
For sure in your life,
we cannot do infinity.

928
00:55:18,300 --> 00:55:22,410
But now, we have found
a way to actually design

929
00:55:22,410 --> 00:55:28,890
our radar since sine theta is
actually proportional to delta.

930
00:55:28,890 --> 00:55:30,990
Therefore, what we
actually really need

931
00:55:30,990 --> 00:55:36,390
to do is to really maximize
the number of slits

932
00:55:36,390 --> 00:55:39,650
we have so that actually
we can create a radar which

933
00:55:39,650 --> 00:55:45,390
would really point toward the
direction of the enemy, which

934
00:55:45,390 --> 00:55:48,700
is shown there,
invading the earth.

935
00:55:48,700 --> 00:55:49,200
OK.

936
00:55:49,200 --> 00:55:50,670
[LAUGHTER]

937
00:55:50,670 --> 00:55:52,630
And we can actually detect it.

938
00:55:52,630 --> 00:55:53,130
OK.

939
00:55:53,130 --> 00:55:56,880
So we will take a five minute
break before we actually

940
00:55:56,880 --> 00:56:01,530
go to the last part of the
course, which is the connection

941
00:56:01,530 --> 00:56:04,360
to quantum mechanics.

942
00:56:04,360 --> 00:56:05,880
So we come back at 35.

943
00:56:05,880 --> 00:56:09,880
[SIDE CONVERSATIONS]

944
00:56:12,380 --> 00:56:13,880
[SIDE CONVERSATIONS]

945
00:56:13,880 --> 00:56:17,080
YEN-JIE LEE: OK so welcome
come back from the break.

946
00:56:17,080 --> 00:56:21,370
So before we move
to the connection

947
00:56:21,370 --> 00:56:24,250
to quantum mechanics,
I would like

948
00:56:24,250 --> 00:56:27,085
to talk some more about
what we have learned

949
00:56:27,085 --> 00:56:29,110
from the design of the radar.

950
00:56:29,110 --> 00:56:30,040
OK?

951
00:56:30,040 --> 00:56:33,940
So this essentially
what we actually get.

952
00:56:33,940 --> 00:56:40,410
The position of the minima that
required the phase difference

953
00:56:40,410 --> 00:56:45,100
delta is actually equal to
2 pi divided by N value,

954
00:56:45,100 --> 00:56:48,820
because it was this delta value.

955
00:56:48,820 --> 00:56:53,080
The N vectors is going
to cancel each other.

956
00:56:53,080 --> 00:56:56,600
And you are going to form
something like a circle

957
00:56:56,600 --> 00:57:02,920
if you choose delta equal to
2 pi divided by capital N. OK?

958
00:57:02,920 --> 00:57:05,090
And don't forget why
this is actually delta.

959
00:57:05,090 --> 00:57:12,600
The delta is actually d sine
theta divided by lambda.

960
00:57:12,600 --> 00:57:13,650
Right?

961
00:57:13,650 --> 00:57:14,470
OK?

962
00:57:14,470 --> 00:57:17,900
And times 2 pi.

963
00:57:17,900 --> 00:57:19,221
OK?

964
00:57:19,221 --> 00:57:19,720
Right?

965
00:57:19,720 --> 00:57:24,100
So therefore, you can see that
the sine theta is actually

966
00:57:24,100 --> 00:57:28,580
proportional to lambda
divided by N times d.

967
00:57:28,580 --> 00:57:31,030
OK?

968
00:57:31,030 --> 00:57:34,960
And in this case, you can
see that if you increase

969
00:57:34,960 --> 00:57:38,900
N value, the
resolution or the width

970
00:57:38,900 --> 00:57:43,270
of the central
principal maxima is

971
00:57:43,270 --> 00:57:46,180
going to be decreasing
as a function, though,

972
00:57:46,180 --> 00:57:47,860
N value you're putting.

973
00:57:47,860 --> 00:57:53,530
So in short, how do I actually
design a high-resolution radar?

974
00:57:53,530 --> 00:57:59,720
What I really need is to
have lambda to be small.

975
00:57:59,720 --> 00:58:00,310
OK?

976
00:58:00,310 --> 00:58:04,930
So that means I need to use
high-frequency electromagnetic

977
00:58:04,930 --> 00:58:05,920
wave.

978
00:58:05,920 --> 00:58:09,310
I can maximize the N value.

979
00:58:09,310 --> 00:58:11,960
I can actually
make d very large.

980
00:58:11,960 --> 00:58:15,980
That means I'm going to have
a very large radar design.

981
00:58:15,980 --> 00:58:16,840
Right?

982
00:58:16,840 --> 00:58:20,480
Then I can have a
very good resolution.

983
00:58:20,480 --> 00:58:21,110
OK.

984
00:58:21,110 --> 00:58:23,070
So we are almost
done with radar.

985
00:58:23,070 --> 00:58:25,900
But there's a problem.

986
00:58:25,900 --> 00:58:30,680
The problem is that if you look
at this, if this is actually

987
00:58:30,680 --> 00:58:34,760
the position of the
principal minima,

988
00:58:34,760 --> 00:58:36,950
you can see that
is always pointing

989
00:58:36,950 --> 00:58:43,520
to the center of the radar
where the delta is equal to 0.

990
00:58:43,520 --> 00:58:44,240
OK?

991
00:58:44,240 --> 00:58:49,360
And then that means I can
only scan in one direction.

992
00:58:49,360 --> 00:58:54,970
There is a reason why those
radar are called phased radar.

993
00:58:54,970 --> 00:58:57,160
That is because
now I can actually

994
00:58:57,160 --> 00:59:02,020
change the relative phase of
all those point source emitted

995
00:59:02,020 --> 00:59:05,680
from the radar so
that I can shift

996
00:59:05,680 --> 00:59:09,711
the direction of the
central principal maxima.

997
00:59:09,711 --> 00:59:10,210
OK?

998
00:59:10,210 --> 00:59:13,630
So what is actually
done here is like this.

999
00:59:13,630 --> 00:59:17,500
So basically, I
can have introduced

1000
00:59:17,500 --> 00:59:21,760
before emitting the
electromagnetic wave,

1001
00:59:21,760 --> 00:59:26,550
I can introduce a zero
additional phase difference.

1002
00:59:26,550 --> 00:59:29,830
And for the second one, I
introduce additional phase

1003
00:59:29,830 --> 00:59:31,690
difference of phi.

1004
00:59:31,690 --> 00:59:32,360
OK?

1005
00:59:32,360 --> 00:59:35,290
And for the third
one, I introduce

1006
00:59:35,290 --> 00:59:40,630
additional phase difference
between the third slit--

1007
00:59:40,630 --> 00:59:44,430
or say the third emitter and
the first emitter by 2 delta.

1008
00:59:44,430 --> 00:59:48,730
And for N's emitter, I
introduce a phase difference

1009
00:59:48,730 --> 00:59:51,720
of N minus 1 phi.

1010
00:59:51,720 --> 00:59:53,560
OK?

1011
00:59:53,560 --> 01:00:01,040
If I add this phase difference
into the setup, what

1012
01:00:01,040 --> 01:00:03,440
I'm going to get is like this.

1013
01:00:03,440 --> 01:00:11,280
So basically, delta will become
2 pi divided by lambda d sine

1014
01:00:11,280 --> 01:00:15,892
theta minus phi angle.

1015
01:00:15,892 --> 01:00:17,720
All right?

1016
01:00:17,720 --> 01:00:23,180
And this phi is actually
the artificial eddy phase

1017
01:00:23,180 --> 01:00:25,490
difference between those source.

1018
01:00:25,490 --> 01:00:26,330
OK?

1019
01:00:26,330 --> 01:00:29,270
And that means I will require--

1020
01:00:29,270 --> 01:00:40,030
and this will be equal to 2
pi divided by N value, such

1021
01:00:40,030 --> 01:00:42,790
as you have completely
destructive interference.

1022
01:00:42,790 --> 01:00:43,930
OK?

1023
01:00:43,930 --> 01:00:47,620
I can now make this phi
to be time-dependent.

1024
01:00:47,620 --> 01:00:49,390
For example, it's
increasing as a function

1025
01:00:49,390 --> 01:00:53,530
of time, phi times t, right?

1026
01:00:53,530 --> 01:01:00,180
Then what is going to happen
is that as a function of time,

1027
01:01:00,180 --> 01:01:03,400
I'm going to change
the sine theta value

1028
01:01:03,400 --> 01:01:07,690
so that I can get a complete
cancellation, 2 pi over N.

1029
01:01:07,690 --> 01:01:08,620
Right?

1030
01:01:08,620 --> 01:01:12,220
So effectively, I'm
changing the angle

1031
01:01:12,220 --> 01:01:19,840
of the central principal
maxima by introducing

1032
01:01:19,840 --> 01:01:23,860
additional artificial phase
difference between all

1033
01:01:23,860 --> 01:01:25,590
those point source.

1034
01:01:25,590 --> 01:01:26,290
OK?

1035
01:01:26,290 --> 01:01:28,630
And this is actually
the way we can actually

1036
01:01:28,630 --> 01:01:34,180
rotate the place we are
scanning up and down

1037
01:01:34,180 --> 01:01:39,320
and get a very nice result
to detect the enemy.

1038
01:01:39,320 --> 01:01:40,620
OK?

1039
01:01:40,620 --> 01:01:41,513
Any questions?

1040
01:01:44,411 --> 01:01:45,821
No?

1041
01:01:45,821 --> 01:01:46,320
OK.

1042
01:01:46,320 --> 01:01:50,230
So now, I'm going to
move on and discuss

1043
01:01:50,230 --> 01:01:54,280
a very interesting experiment.

1044
01:01:54,280 --> 01:01:59,250
So this is very exciting
experiment content,

1045
01:01:59,250 --> 01:02:02,640
billiard balls
and the two slits.

1046
01:02:02,640 --> 01:02:03,996
OK?

1047
01:02:03,996 --> 01:02:05,370
And we will wonder,
then, what is

1048
01:02:05,370 --> 01:02:08,040
going to happen when
those balls especially

1049
01:02:08,040 --> 01:02:09,300
pass through the slit.

1050
01:02:09,300 --> 01:02:12,220
Can anybody actually tell me
what she is going to happen?

1051
01:02:12,220 --> 01:02:15,060
And what will be the
statistics, or say,

1052
01:02:15,060 --> 01:02:19,740
the count, which I am going to
go on to get in the receiver

1053
01:02:19,740 --> 01:02:20,710
later?

1054
01:02:20,710 --> 01:02:23,930
Anybody can actually tell me?

1055
01:02:23,930 --> 01:02:27,950
If I actually shoot a lot
of balls through this slit--

1056
01:02:27,950 --> 01:02:30,410
don't be shy, right?

1057
01:02:30,410 --> 01:02:31,730
It's easy.

1058
01:02:31,730 --> 01:02:34,210
No?

1059
01:02:34,210 --> 01:02:35,664
Nobody wants--

1060
01:02:35,664 --> 01:02:37,452
STUDENT: They make [INAUDIBLE]

1061
01:02:37,452 --> 01:02:39,180
YEN-JIE LEE: Yeah, that's right.

1062
01:02:39,180 --> 01:02:40,630
Right?

1063
01:02:40,630 --> 01:02:42,628
Doesn't surprise nobody, right?

1064
01:02:42,628 --> 01:02:46,500
[LAUGHS] Yeah, too afraid
of answering questions.

1065
01:02:46,500 --> 01:02:51,980
OK, you can see that they
make two path, right?

1066
01:02:51,980 --> 01:02:52,820
No?

1067
01:02:52,820 --> 01:02:53,450
Right?

1068
01:02:53,450 --> 01:02:54,050
OK.

1069
01:02:54,050 --> 01:02:55,190
Very good.

1070
01:02:55,190 --> 01:02:59,630
So now, this is
the exciting part.

1071
01:02:59,630 --> 01:03:06,110
Now, instead of shooting
billiard balls, what I'm going

1072
01:03:06,110 --> 01:03:09,500
to do is to shoot electrons.

1073
01:03:09,500 --> 01:03:12,680
So I can actually prepare
an electron source

1074
01:03:12,680 --> 01:03:16,160
and heat it up, such that
it start to emit electrons.

1075
01:03:16,160 --> 01:03:20,510
And I have two slits and have
them pass through this slits.

1076
01:03:20,510 --> 01:03:22,670
And I have a screen,
which actually

1077
01:03:22,670 --> 01:03:25,670
have an electron
detector to count

1078
01:03:25,670 --> 01:03:30,630
the number of electron which I
am going to get on the screen.

1079
01:03:30,630 --> 01:03:34,200
The reason why I call it
single electron source

1080
01:03:34,200 --> 01:03:41,040
is because each time I control
my experiment such that it only

1081
01:03:41,040 --> 01:03:45,524
emit one electron every time.

1082
01:03:45,524 --> 01:03:46,940
OK?

1083
01:03:46,940 --> 01:03:52,750
The question I'm trying
to ask is, will I

1084
01:03:52,750 --> 01:03:55,330
see some pattern,
which is actually

1085
01:03:55,330 --> 01:04:04,460
light like billiard balls, and
they form two piles in a pack?

1086
01:04:04,460 --> 01:04:07,420
That's actually
option number one.

1087
01:04:07,420 --> 01:04:12,410
Or I'm going to see
really something crazy?

1088
01:04:12,410 --> 01:04:16,480
It's the electron is
going to be interfere--

1089
01:04:16,480 --> 01:04:21,150
it's going through the
interference with itself.

1090
01:04:21,150 --> 01:04:23,950
And that essentially
option number two.

1091
01:04:23,950 --> 01:04:24,450
OK?

1092
01:04:24,450 --> 01:04:27,900
The lure of 8.03 is that
everybody had to choose one.

1093
01:04:27,900 --> 01:04:28,830
OK?

1094
01:04:28,830 --> 01:04:36,640
So how many of you think what is
going to happen is number one?

1095
01:04:36,640 --> 01:04:38,410
Come on.

1096
01:04:38,410 --> 01:04:41,680
I have only one
electron each time.

1097
01:04:41,680 --> 01:04:43,445
Nobody think so?

1098
01:04:43,445 --> 01:04:43,945
Wow.

1099
01:04:47,620 --> 01:04:49,283
Maybe all of you are wrong.

1100
01:04:49,283 --> 01:04:55,110
[LAUGHS] How about
the second option?

1101
01:04:55,110 --> 01:04:55,867
STUDENT: [LAUGHS]

1102
01:04:55,867 --> 01:04:57,450
YEN-JIE LEE: Hey,
some of you actually

1103
01:04:57,450 --> 01:04:58,580
didn't raise your hand.

1104
01:04:58,580 --> 01:04:59,080
Come on.

1105
01:04:59,080 --> 01:04:59,580
Come on.

1106
01:04:59,580 --> 01:05:00,130
[LAUGHTER]

1107
01:05:00,130 --> 01:05:02,260
OK, everybody.

1108
01:05:02,260 --> 01:05:03,630
Wow.

1109
01:05:03,630 --> 01:05:06,080
What is actually
happening to you brain?

1110
01:05:06,080 --> 01:05:08,310
[LAUGHTER]

1111
01:05:08,310 --> 01:05:10,410
My brain is not
functional like this.

1112
01:05:10,410 --> 01:05:11,140
OK.

1113
01:05:11,140 --> 01:05:16,200
So I really hope that I can
bring the experiment to here.

1114
01:05:16,200 --> 01:05:17,630
But unfortunately,
that's actually

1115
01:05:17,630 --> 01:05:19,910
going to be difficult. OK?

1116
01:05:19,910 --> 01:05:21,440
So what I'm going
to do is that I'm

1117
01:05:21,440 --> 01:05:25,500
going to show you the
experimental result,

1118
01:05:25,500 --> 01:05:26,870
this video.

1119
01:05:26,870 --> 01:05:30,680
And we are going to see
what is going to happen.

1120
01:05:30,680 --> 01:05:33,660
You see that there
are dots popping out.

1121
01:05:33,660 --> 01:05:34,830
What are those?

1122
01:05:34,830 --> 01:05:40,340
Those are the detected
electron one-by-one on screen.

1123
01:05:40,340 --> 01:05:41,090
OK?

1124
01:05:41,090 --> 01:05:45,630
So basically, you can see
that the number of dots

1125
01:05:45,630 --> 01:05:47,810
are increasing as
a function of time.

1126
01:05:47,810 --> 01:05:52,010
And I actually-- I mean,
speeding up things a bit

1127
01:05:52,010 --> 01:05:54,480
so that actually you can
see the pattern quicker.

1128
01:05:54,480 --> 01:05:54,980
OK.

1129
01:05:54,980 --> 01:05:57,021
So you can see that there
are more and more dots.

1130
01:05:57,021 --> 01:05:59,000
And each time, you can
see that I only get

1131
01:05:59,000 --> 01:06:04,373
one electron per image here.

1132
01:06:04,373 --> 01:06:05,260
Right?

1133
01:06:05,260 --> 01:06:07,010
So you can see now
there are more and more

1134
01:06:07,010 --> 01:06:09,880
and more and more, and
accumulating more data,

1135
01:06:09,880 --> 01:06:12,800
like what we actually done
in The Large Hadron Collider.

1136
01:06:12,800 --> 01:06:15,590
We wait there,
collect more data.

1137
01:06:15,590 --> 01:06:18,410
And we are speeding things up.

1138
01:06:18,410 --> 01:06:21,320
And you can see that,
wow, something's

1139
01:06:21,320 --> 01:06:24,250
actually developing.

1140
01:06:24,250 --> 01:06:24,960
What is that?

1141
01:06:28,410 --> 01:06:30,120
Can you see it?

1142
01:06:30,120 --> 01:06:34,270
Now, you are speeding up
like 1,000 times faster.

1143
01:06:34,270 --> 01:06:37,026
You can see what pattern?

1144
01:06:37,026 --> 01:06:38,874
STUDENT: Interference pattern.

1145
01:06:38,874 --> 01:06:40,290
YEN-JIE LEE:
Interference pattern.

1146
01:06:40,290 --> 01:06:43,510
What is going on?

1147
01:06:43,510 --> 01:06:44,660
You are not surprised?

1148
01:06:44,660 --> 01:06:45,620
STUDENT: No.

1149
01:06:45,620 --> 01:06:46,600
YEN-JIE LEE: Oh my god.

1150
01:06:46,600 --> 01:06:47,320
What is going on?

1151
01:06:47,320 --> 01:06:50,250
[LAUGHTER]

1152
01:06:50,250 --> 01:06:53,490
I'm so surprised.

1153
01:06:53,490 --> 01:06:54,750
Look at this.

1154
01:06:54,750 --> 01:07:00,300
So I have emission of
one electron each time.

1155
01:07:00,300 --> 01:07:04,815
And that is actually the
four snapshot which I took--

1156
01:07:04,815 --> 01:07:07,480
which actually this
experiment, Hitachi Group

1157
01:07:07,480 --> 01:07:08,940
actually did this experiment.

1158
01:07:08,940 --> 01:07:13,880
You can actually click on
this link to the more detail.

1159
01:07:13,880 --> 01:07:17,600
And they took four
snapshots of the experiment.

1160
01:07:17,600 --> 01:07:20,240
And you can see that
in the beginning,

1161
01:07:20,240 --> 01:07:23,570
you can see clearly
each time you only get

1162
01:07:23,570 --> 01:07:27,230
one electron out of the source.

1163
01:07:27,230 --> 01:07:28,760
OK?

1164
01:07:28,760 --> 01:07:31,140
But as a function
of time, you're

1165
01:07:31,140 --> 01:07:33,420
accumulating more and more.

1166
01:07:33,420 --> 01:07:35,580
And you see that
clearly, there's

1167
01:07:35,580 --> 01:07:43,410
a pattern forming, which, is
actually consistent with what

1168
01:07:43,410 --> 01:07:47,540
we see in this calculation.

1169
01:07:47,540 --> 01:07:48,040
OK?

1170
01:07:48,040 --> 01:07:52,470
So I think that's
actually truly amazing.

1171
01:07:52,470 --> 01:07:55,050
And what does that mean?

1172
01:07:55,050 --> 01:08:02,011
That means the electron
is playing with itself.

1173
01:08:02,011 --> 01:08:04,115
It's interfering with itself.

1174
01:08:06,620 --> 01:08:07,220
Right?

1175
01:08:07,220 --> 01:08:08,960
That's really strange.

1176
01:08:08,960 --> 01:08:09,980
What is going to happen?

1177
01:08:09,980 --> 01:08:11,130
What is going on?

1178
01:08:11,130 --> 01:08:17,630
So one single electron pass
through both slit, which is

1179
01:08:17,630 --> 01:08:19,050
actually the option you choose.

1180
01:08:19,050 --> 01:08:21,220
Surprise me.

1181
01:08:21,220 --> 01:08:25,630
And then they
interfere like waves.

1182
01:08:25,630 --> 01:08:31,020
And they produce the pattern
which we see on the screen.

1183
01:08:31,020 --> 01:08:35,850
That is actually
really crazy to me.

1184
01:08:35,850 --> 01:08:40,359
What is actually even more
crazy is this situation.

1185
01:08:40,359 --> 01:08:47,160
So now, if I make measurement in
front of the slit, OK, so now,

1186
01:08:47,160 --> 01:08:50,970
I puts on a little device.

1187
01:08:50,970 --> 01:08:54,750
When the electron pass
through one of the slit,

1188
01:08:54,750 --> 01:08:57,701
I say, send me a signal.

1189
01:08:57,701 --> 01:08:58,200
OK?

1190
01:08:58,200 --> 01:09:01,950
So now, I can clearly
know that which

1191
01:09:01,950 --> 01:09:05,939
slit the electron is
actually going through

1192
01:09:05,939 --> 01:09:07,200
in the experiment.

1193
01:09:07,200 --> 01:09:08,220
OK?

1194
01:09:08,220 --> 01:09:13,170
And the crazy thing is
that if I do that, then it

1195
01:09:13,170 --> 01:09:16,359
becomes two piles.

1196
01:09:16,359 --> 01:09:17,054
OK?

1197
01:09:17,054 --> 01:09:19,220
Of course, maybe there are
some diffraction pattern.

1198
01:09:19,220 --> 01:09:22,370
But it really
changes the pattern

1199
01:09:22,370 --> 01:09:25,279
of the experimental result.
And that is actually

1200
01:09:25,279 --> 01:09:27,319
really very strange.

1201
01:09:27,319 --> 01:09:30,500
And we are going to
talk about that briefly

1202
01:09:30,500 --> 01:09:33,960
in the next lecture.

1203
01:09:33,960 --> 01:09:37,365
So before the end,
I'm going to show you

1204
01:09:37,365 --> 01:09:39,920
an additional
demonstration which

1205
01:09:39,920 --> 01:09:43,189
motivate the discussion
what we are going

1206
01:09:43,189 --> 01:09:47,109
to have in the next lecture.

1207
01:09:47,109 --> 01:09:55,920
So now, I can actually turn off
the light again and also hide

1208
01:09:55,920 --> 01:09:57,950
the image.

1209
01:09:57,950 --> 01:09:58,460
OK.

1210
01:09:58,460 --> 01:10:00,978
I hope I can find the pattern.

1211
01:10:00,978 --> 01:10:04,620
[LAUGHS] All right.

1212
01:10:04,620 --> 01:10:08,290
So here, I have two laser.

1213
01:10:08,290 --> 01:10:11,940
So I'm going to turn
up the first laser.

1214
01:10:11,940 --> 01:10:17,970
And this laser is going to
pass through a two slit--

1215
01:10:17,970 --> 01:10:24,480
a two really nearby slit and
form an interference pattern.

1216
01:10:24,480 --> 01:10:26,490
As you can see on the wall--

1217
01:10:26,490 --> 01:10:29,850
I hope you can see, I don't
know if you can see clearly--

1218
01:10:29,850 --> 01:10:35,760
that you can see there are
many, many dots, nearby dots,

1219
01:10:35,760 --> 01:10:38,670
which actually shows
you the position

1220
01:10:38,670 --> 01:10:43,270
of the principal maximas,
right, because are actually

1221
01:10:43,270 --> 01:10:45,120
two slit experiment.

1222
01:10:45,120 --> 01:10:49,880
Therefore, how many children
do we have in the family?

1223
01:10:49,880 --> 01:10:50,890
Zero, right?

1224
01:10:50,890 --> 01:10:52,720
Because they are--

1225
01:10:52,720 --> 01:10:54,580
OK, they just got
married, maybe.

1226
01:10:54,580 --> 01:10:56,460
[LAUGHS] All right.

1227
01:10:56,460 --> 01:10:59,470
So therefore, you
will see only adults.

1228
01:10:59,470 --> 01:11:04,210
And that is actually
the principal maximas.

1229
01:11:04,210 --> 01:11:07,420
You can see many,
many nearby dots.

1230
01:11:07,420 --> 01:11:10,000
They are almost equally bright.

1231
01:11:10,000 --> 01:11:10,900
OK?

1232
01:11:10,900 --> 01:11:15,050
But there's something happening
to this pattern as well.

1233
01:11:15,050 --> 01:11:17,620
And you can see that--
wait, wait, wait a second.

1234
01:11:17,620 --> 01:11:21,760
In the calculation we
get the principle maxima

1235
01:11:21,760 --> 01:11:24,040
to have the same height, right?

1236
01:11:24,040 --> 01:11:28,250
That means you are going to get
exactly those same intensity

1237
01:11:28,250 --> 01:11:30,790
for all the maximas.

1238
01:11:30,790 --> 01:11:33,440
But you don't see that here.

1239
01:11:33,440 --> 01:11:38,940
You can see that if you move
away from the center too much,

1240
01:11:38,940 --> 01:11:42,210
the intensity is decreasing.

1241
01:11:42,210 --> 01:11:43,470
You see at the edge?

1242
01:11:43,470 --> 01:11:49,440
It actually even goes to zero.

1243
01:11:49,440 --> 01:11:50,750
Right?

1244
01:11:50,750 --> 01:11:52,350
What is actually happening?

1245
01:11:52,350 --> 01:11:57,490
Something clearly is actually
missing in our calculation.

1246
01:11:57,490 --> 01:12:01,780
And that missing
part is actually

1247
01:12:01,780 --> 01:12:06,270
diffraction, which we will talk
about that in the next lecture.

1248
01:12:06,270 --> 01:12:14,800
So if you compare this
pattern to the second demo,

1249
01:12:14,800 --> 01:12:17,410
you can see in the
right hand side

1250
01:12:17,410 --> 01:12:20,560
setup, which I have here,
which I should give you

1251
01:12:20,560 --> 01:12:22,540
a projection on the
wall, which is actually

1252
01:12:22,540 --> 01:12:30,190
lower part of the demo, you can
see that this laser actually

1253
01:12:30,190 --> 01:12:32,800
pass through a single slit.

1254
01:12:32,800 --> 01:12:36,340
But this slit is
actually pretty wide.

1255
01:12:36,340 --> 01:12:37,120
OK?

1256
01:12:37,120 --> 01:12:42,400
And you can see that indeed,
you see the laser coming out,

1257
01:12:42,400 --> 01:12:46,730
but essentially,
not a single spot.

1258
01:12:46,730 --> 01:12:49,160
And it has some kind
of pattern, which

1259
01:12:49,160 --> 01:12:52,130
is actually popping out there.

1260
01:12:52,130 --> 01:12:56,000
And this is also
related to interference

1261
01:12:56,000 --> 01:12:58,740
between infinite
number of source.

1262
01:12:58,740 --> 01:12:59,240
OK?

1263
01:12:59,240 --> 01:13:04,700
And you can see that the
pattern seems to really pretty

1264
01:13:04,700 --> 01:13:11,060
similar to the pattern
we see in the upper demo,

1265
01:13:11,060 --> 01:13:15,380
except that upper demo have
individual similar structure,

1266
01:13:15,380 --> 01:13:19,820
which is the principal maxima
from the two slit interference.

1267
01:13:19,820 --> 01:13:25,400
And we are going to solve
the mystery in the lecture

1268
01:13:25,400 --> 01:13:26,830
next time.

1269
01:13:26,830 --> 01:13:27,330
OK.

1270
01:13:27,330 --> 01:13:29,170
So thank you very much.

1271
01:13:29,170 --> 01:13:33,300
And if you have any questions
related to the lecture today,

1272
01:13:33,300 --> 01:13:35,206
I will be here to
answer your questions.

1273
01:13:43,850 --> 01:13:46,920
So this is a demo
which we would like

1274
01:13:46,920 --> 01:13:52,080
to show you, Single Slit and
the Double Slit Interference

1275
01:13:52,080 --> 01:13:52,991
Pattern.

1276
01:13:52,991 --> 01:13:53,490
OK?

1277
01:13:53,490 --> 01:13:56,730
So the first scene is the setup.

1278
01:13:56,730 --> 01:14:00,210
So we have a laser
beam, which is actually

1279
01:14:00,210 --> 01:14:10,730
passing through this either
single slit or double slit

1280
01:14:10,730 --> 01:14:11,790
experiment.

1281
01:14:11,790 --> 01:14:17,030
And then the laser beam
will be going through this

1282
01:14:17,030 --> 01:14:20,550
and interfere and show
interesting pattern

1283
01:14:20,550 --> 01:14:22,410
on the screen.

1284
01:14:22,410 --> 01:14:25,050
And there are two setup.

1285
01:14:25,050 --> 01:14:30,130
The left-hand side one is two
slit interference experiment.

1286
01:14:30,130 --> 01:14:36,940
And right-hand side is a single
slit diffraction experiment.

1287
01:14:36,940 --> 01:14:40,860
So you can see left-hand side
one, I already turned it on.

1288
01:14:40,860 --> 01:14:43,290
Laser beam passed
through two slits.

1289
01:14:43,290 --> 01:14:47,990
And they form complicated
pattern on the screen.

1290
01:14:47,990 --> 01:14:51,400
And you can see there are
two kinds of structure here.

1291
01:14:51,400 --> 01:14:54,000
The first one is the
very fine structure,

1292
01:14:54,000 --> 01:14:58,070
which you can see that
it's like some row of dots

1293
01:14:58,070 --> 01:15:00,120
in the center of the pattern.

1294
01:15:00,120 --> 01:15:05,740
And there are larger
scale pattern as well,

1295
01:15:05,740 --> 01:15:10,100
which you can see that the
overall intensity of all

1296
01:15:10,100 --> 01:15:13,160
those little dots
are also variating

1297
01:15:13,160 --> 01:15:17,880
as a function of distance
with respect to the center.

1298
01:15:17,880 --> 01:15:21,190
So during the lecture, we
were wondering what actually

1299
01:15:21,190 --> 01:15:23,500
cause this kind of pattern.

1300
01:15:23,500 --> 01:15:25,230
And the answer is
that this is actually

1301
01:15:25,230 --> 01:15:30,390
coming from the effect of
single slit interference.

1302
01:15:30,390 --> 01:15:33,400
The reason why we
have this pattern

1303
01:15:33,400 --> 01:15:37,000
is because the two
slit is actually not

1304
01:15:37,000 --> 01:15:41,060
infinitely narrow in my setup.

1305
01:15:41,060 --> 01:15:45,360
Therefore, within a
single slit, there

1306
01:15:45,360 --> 01:15:49,800
is already a interference
pattern coming out of it.

1307
01:15:49,800 --> 01:15:55,710
Therefore, the compound effect,
results in a very complicated

1308
01:15:55,710 --> 01:15:57,570
structure we see on the screen.

1309
01:15:57,570 --> 01:16:00,600
So to demonstrate
this effect, now, I'm

1310
01:16:00,600 --> 01:16:05,160
going to turn on the
right-hand side setup.

1311
01:16:05,160 --> 01:16:06,870
In the right-hand
side setup, I am

1312
01:16:06,870 --> 01:16:10,140
going to have the
laser beam, which

1313
01:16:10,140 --> 01:16:15,840
you see emitting from here,
pass through a single slit.

1314
01:16:15,840 --> 01:16:19,500
I actually set it
up so that they

1315
01:16:19,500 --> 01:16:24,300
have the same width between
the single slit experiment

1316
01:16:24,300 --> 01:16:26,730
and double slit experiment.

1317
01:16:26,730 --> 01:16:35,960
And then you can see
after I turn it on,

1318
01:16:35,960 --> 01:16:41,450
you can see that now, we
have two sets of pattern.

1319
01:16:41,450 --> 01:16:46,580
The lower set is actually coming
from a single slit interference

1320
01:16:46,580 --> 01:16:47,540
experiment.

1321
01:16:47,540 --> 01:16:52,760
And you can see very nicely
that first of all, it

1322
01:16:52,760 --> 01:16:56,690
has a similar pattern, like
what we see in the double slit

1323
01:16:56,690 --> 01:16:58,080
experiment.

1324
01:16:58,080 --> 01:17:02,460
Secondly, you can see that
basically, we carefully tune

1325
01:17:02,460 --> 01:17:05,060
these two experiments
so that the distance

1326
01:17:05,060 --> 01:17:09,750
between the slit and the
screen is roughly the same.

1327
01:17:09,750 --> 01:17:12,920
Finally, we also set it up,
as I've mentioned before,

1328
01:17:12,920 --> 01:17:16,120
such that the width
of the individual slit

1329
01:17:16,120 --> 01:17:19,490
in the double and the single
slit experiment are the same.

1330
01:17:19,490 --> 01:17:22,850
And you can see that with
single slit experiment,

1331
01:17:22,850 --> 01:17:27,140
we also see a very
similar pattern

1332
01:17:27,140 --> 01:17:29,900
that you have a central maxima.

1333
01:17:29,900 --> 01:17:40,850
You have a high-intensity
light going toward the center

1334
01:17:40,850 --> 01:17:42,590
of the pattern.

1335
01:17:42,590 --> 01:17:49,320
And the intensity actually
decrease dramatically really

1336
01:17:49,320 --> 01:17:52,250
quickly as a
function of distance.

1337
01:17:52,250 --> 01:17:55,460
And also, you can see
that the pattern actually

1338
01:17:55,460 --> 01:17:59,780
matches with what you see in
the double slit experiment

1339
01:17:59,780 --> 01:18:00,680
very well.

1340
01:18:00,680 --> 01:18:03,710
And that is actually
pretty remarkable.

1341
01:18:03,710 --> 01:18:08,240
And from these
two experiment, we

1342
01:18:08,240 --> 01:18:12,510
understand why we have also
a complicated structure

1343
01:18:12,510 --> 01:18:15,620
in the double slit
experiment, not

1344
01:18:15,620 --> 01:18:18,700
just like many,
many little maximas,

1345
01:18:18,700 --> 01:18:20,510
many, many little dots.

1346
01:18:20,510 --> 01:18:23,620
But also, you have
this overall modulation

1347
01:18:23,620 --> 01:18:25,370
in the light intensity.

1348
01:18:25,370 --> 01:18:29,060
And that is actually mainly
coming from the single slit

1349
01:18:29,060 --> 01:18:30,910
diffraction pattern.