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PROFESSOR: Today we are going
to continue discussion about two

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00:00:27,400 --> 00:00:29,420
very important issues.

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00:00:29,420 --> 00:00:31,780
The first one is
the understanding

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00:00:31,780 --> 00:00:34,700
of so-called quarter wave plate.

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00:00:34,700 --> 00:00:38,170
That may not mean anything
to you in the beginning,

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00:00:38,170 --> 00:00:40,590
but I hope after
this lecture, you

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00:00:40,590 --> 00:00:43,810
will know what does that
mean and why that is actually

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00:00:43,810 --> 00:00:46,010
interesting.

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00:00:46,010 --> 00:00:49,630
The second thing is that--

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00:00:49,630 --> 00:00:52,600
the second topic we want to
talk about in the lecture today

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00:00:52,600 --> 00:00:56,620
is, OK, we have been talking
about electromagnetic waves

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00:00:56,620 --> 00:01:01,130
for a long time already,
since the last few lectures.

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00:01:01,130 --> 00:01:04,250
But we have never
touched the topic,

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00:01:04,250 --> 00:01:09,180
how do we actually create
electromagnetic wave, right?

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00:01:09,180 --> 00:01:12,530
And we are going to answer
that in the lecture today.

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00:01:12,530 --> 00:01:15,560
So that's my plan
about these two topics.

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00:01:15,560 --> 00:01:18,940
OK, so before we
start, it's a reminder

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00:01:18,940 --> 00:01:21,370
about why we have
learned last time.

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00:01:21,370 --> 00:01:24,790
So we have learned
several situations

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00:01:24,790 --> 00:01:27,280
related to polarization.

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00:01:27,280 --> 00:01:30,520
So we have learned
linearly polarized wave.

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00:01:30,520 --> 00:01:32,080
What is linearly polarized wave?

30
00:01:32,080 --> 00:01:37,060
If you plot the wave amplitude
as a function of time

31
00:01:37,060 --> 00:01:40,750
as a function of space, it's
going up and down, up and down,

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00:01:40,750 --> 00:01:43,150
up and down.

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00:01:43,150 --> 00:01:45,580
And the direction
of the field doesn't

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00:01:45,580 --> 00:01:47,410
change as a function of time.

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00:01:47,410 --> 00:01:51,640
So that is actually called
linearly polarized light.

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00:01:51,640 --> 00:01:56,110
And we also learned circularly
polarized light, right?

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00:01:56,110 --> 00:02:00,500
When you have two components,
one is in the x direction,

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00:02:00,500 --> 00:02:03,520
the other one is in the
y direction, if the two

39
00:02:03,520 --> 00:02:08,560
components are out of
phase, say, they differ

40
00:02:08,560 --> 00:02:17,290
by 90 degrees, for example,
and they the same amplitude,

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00:02:17,290 --> 00:02:20,770
then the superposition
of these two waves

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00:02:20,770 --> 00:02:23,500
will be a circularly
polarized wave.

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00:02:23,500 --> 00:02:27,530
So basically, the wave
propagation looks like this.

44
00:02:27,530 --> 00:02:31,390
So basically, the pointy
angle of the electric field

45
00:02:31,390 --> 00:02:34,060
is rotating as a
function over time

46
00:02:34,060 --> 00:02:37,060
as a function of the
distance it travels.

47
00:02:37,060 --> 00:02:40,300
And the other case, which
is also interesting,

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00:02:40,300 --> 00:02:42,205
is that when you have--

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00:02:42,205 --> 00:02:45,760
OK, for example, different
phase difference.

50
00:02:45,760 --> 00:02:49,912
Like delta phi different
from 90 degree, or say

51
00:02:49,912 --> 00:02:52,370
you have different amplitude,
although the phase difference

52
00:02:52,370 --> 00:02:55,220
is 90 degree but you
have different amplitude

53
00:02:55,220 --> 00:02:58,210
in the x and the y direction.

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00:02:58,210 --> 00:03:04,540
If that's the case, then you
have a situation which not only

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00:03:04,540 --> 00:03:06,820
the direction is changing,
but also the amplitude

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00:03:06,820 --> 00:03:09,220
is changing as a
function of time.

57
00:03:09,220 --> 00:03:12,520
And that we call it
elliptically polarized.

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00:03:12,520 --> 00:03:16,120
So that's actually the
three situations we learned.

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00:03:16,120 --> 00:03:22,460
And also we learned about
how to make polarized light

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00:03:22,460 --> 00:03:23,630
during the class.

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00:03:23,630 --> 00:03:27,540
So usually, the light
source we are talking about,

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00:03:27,540 --> 00:03:31,750
or even present in this
room, like the light

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00:03:31,750 --> 00:03:34,880
from the light bulb,
et cetera, those

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00:03:34,880 --> 00:03:36,410
are unpolarized light, right?

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00:03:36,410 --> 00:03:42,790
So that means you have a lot
of electromagnetic wave emitted

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00:03:42,790 --> 00:03:47,740
from the light with different
initial time, emission time.

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00:03:47,740 --> 00:03:51,940
And those are in slightly
different angular frequency,

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00:03:51,940 --> 00:03:55,200
slightly different
pointing direction.

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00:03:55,200 --> 00:03:58,780
So you can have all kinds
of different emissions.

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00:03:58,780 --> 00:04:01,660
And the sum of all
those emissions

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00:04:01,660 --> 00:04:04,830
is unpolarized light,
which is actually

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00:04:04,830 --> 00:04:08,180
the light source I have here.

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00:04:08,180 --> 00:04:11,440
And you can use
so-called polarizer.

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00:04:11,440 --> 00:04:18,910
So the polarizer can actually
kill one of the direction,

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00:04:18,910 --> 00:04:23,500
and only keep all the
projection to the easy axis.

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00:04:23,500 --> 00:04:25,630
And in this presentation,
the easy axis

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00:04:25,630 --> 00:04:27,320
is in the x direction.

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00:04:27,320 --> 00:04:30,750
And you can see that if you
start with unpolarized light,

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00:04:30,750 --> 00:04:34,870
and basically, you have that
pass through a polarizer,

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00:04:34,870 --> 00:04:37,180
then the resulting
electric field

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00:04:37,180 --> 00:04:41,340
will be pointing toward
the so-called easy axis.

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00:04:41,340 --> 00:04:43,990
So the easier axis
to pass, right?

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00:04:43,990 --> 00:04:48,730
So therefore, all the
electric field perpendicular

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00:04:48,730 --> 00:04:52,360
to the easy axis is illuminated.

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00:04:52,360 --> 00:04:55,360
And what is left over
is the electric field,

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00:04:55,360 --> 00:05:00,520
which is actually
parallel to the easy axis.

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00:05:00,520 --> 00:05:06,200
And of course, you can
rotate this polarizer

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00:05:06,200 --> 00:05:09,070
and you would see
that, OK, if you

89
00:05:09,070 --> 00:05:13,800
have a linearly polarized wave
passing through polarizer,

90
00:05:13,800 --> 00:05:15,940
because easy axis
is actually now

91
00:05:15,940 --> 00:05:19,630
in line with the polarization,
what is going to happen

92
00:05:19,630 --> 00:05:24,940
is, as I said, still only the
component which is actually

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00:05:24,940 --> 00:05:27,730
parallel to the easy
axis will passed through.

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00:05:27,730 --> 00:05:30,165
And the resulting
electric field will still

95
00:05:30,165 --> 00:05:33,520
be pointing to the
direction of the easy axis.

96
00:05:33,520 --> 00:05:36,920
So that's actually what
we have learned last time.

97
00:05:36,920 --> 00:05:40,370
OK, so that means we
know how to generate

98
00:05:40,370 --> 00:05:42,490
linearly polarized wave, right?

99
00:05:42,490 --> 00:05:45,070
Because you just
need a polarizer

100
00:05:45,070 --> 00:05:47,200
and put it in front
of your light source,

101
00:05:47,200 --> 00:05:50,230
then you produce a
linearly polarized save.

102
00:05:50,230 --> 00:05:54,400
But we didn't talk about
how to produce a circularly

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00:05:54,400 --> 00:05:56,200
polarized wave, right?

104
00:05:56,200 --> 00:05:58,150
OK, so that is actually
the topic which

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00:05:58,150 --> 00:06:01,510
I would like to talk about.

106
00:06:01,510 --> 00:06:05,700
So let's take a look
at the diagram here.

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00:06:05,700 --> 00:06:12,560
So assuming that I have
a single layer of sheet,

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00:06:12,560 --> 00:06:14,750
which I call wave plate.

109
00:06:14,750 --> 00:06:18,420
This is actually the zoom in
and zoom in of that sheet.

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00:06:18,420 --> 00:06:24,410
And the interesting property
of this wave plate sheet

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00:06:24,410 --> 00:06:31,280
is that the refraction
index in the x direction

112
00:06:31,280 --> 00:06:35,930
and the refraction
index for the linearly

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00:06:35,930 --> 00:06:40,390
polarized wave in the y
direction, they are different.

114
00:06:40,390 --> 00:06:41,360
That can happen, right?

115
00:06:41,360 --> 00:06:44,450
Because when we were
discussing two-dimensional and

116
00:06:44,450 --> 00:06:49,490
three-dimensional waves,
the dispersion relation

117
00:06:49,490 --> 00:06:53,930
can be dependent on
the k vector, right?

118
00:06:53,930 --> 00:06:56,660
So that should not
surprise you by now.

119
00:06:56,660 --> 00:07:02,390
And it depends on the
structure of the material you

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00:07:02,390 --> 00:07:04,940
use to make this wave plate.

121
00:07:04,940 --> 00:07:09,830
So therefore, you can
have different velocity

122
00:07:09,830 --> 00:07:13,400
when you have an incident where
pointing in the x direction,

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00:07:13,400 --> 00:07:15,530
and compared to
an incident where

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00:07:15,530 --> 00:07:17,840
pointing in the y direction.

125
00:07:17,840 --> 00:07:21,390
So in short, we can
actually summarize

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00:07:21,390 --> 00:07:24,760
this kind of information,
the dispersion relation,

127
00:07:24,760 --> 00:07:25,840
into two components.

128
00:07:25,840 --> 00:07:29,460
One is the velocity, the phase
velocity in the x direction,

129
00:07:29,460 --> 00:07:32,270
which is denoted as nx.

130
00:07:32,270 --> 00:07:35,810
Just a reminder, the
speed of the light

131
00:07:35,810 --> 00:07:39,260
will be equal to c
divided by nx, right?

132
00:07:39,260 --> 00:07:45,230
So larger n means smaller
speed of light in material.

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00:07:45,230 --> 00:07:50,060
And if that happens, if nx
is different from ny, what

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00:07:50,060 --> 00:07:56,570
is going to happen is that if
you have an incident wave, when

135
00:07:56,570 --> 00:08:00,440
it passes through this wave
plate, what is going to happen

136
00:08:00,440 --> 00:08:04,070
is that the x component,
the delay in phase

137
00:08:04,070 --> 00:08:07,910
in the x component, would
be different from the delay

138
00:08:07,910 --> 00:08:11,480
in phase in the y component.

139
00:08:11,480 --> 00:08:14,210
And that is, essentially,
how we can actually

140
00:08:14,210 --> 00:08:16,990
make use of that to
create elliptically

141
00:08:16,990 --> 00:08:21,410
polarized wave or circularly
polarized wave, OK?

142
00:08:21,410 --> 00:08:23,970
So let's take a look at
this example together.

143
00:08:23,970 --> 00:08:29,840
So suppose I have incident light
with angular frequency omega,

144
00:08:29,840 --> 00:08:30,830
OK?

145
00:08:30,830 --> 00:08:34,880
Since I give you already the
omega, what I really need

146
00:08:34,880 --> 00:08:38,030
is the speed of light, then
I can calculate the resulting

147
00:08:38,030 --> 00:08:40,250
wave number and wave lengths.

148
00:08:40,250 --> 00:08:44,570
So this is actually the
incident wave angular frequency.

149
00:08:44,570 --> 00:08:49,970
And the lens of the-- or say
the thickness of the wave plate

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00:08:49,970 --> 00:08:52,070
is called little l.

151
00:08:52,070 --> 00:08:54,860
And we can actually
check immediately

152
00:08:54,860 --> 00:08:57,380
what would be the
corresponding wave

153
00:08:57,380 --> 00:09:04,580
number in the median for
the linearly polarized wave

154
00:09:04,580 --> 00:09:07,640
in the x direction and linearly
polarized wave in the y

155
00:09:07,640 --> 00:09:08,460
direction.

156
00:09:08,460 --> 00:09:10,770
So we can actually
calculate Kx will

157
00:09:10,770 --> 00:09:15,965
be equal to nx over c omega,
because this is actually

158
00:09:15,965 --> 00:09:18,800
just omega divided
by v, which is

159
00:09:18,800 --> 00:09:24,950
the phase velocity in the median
for waves in the x direction.

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00:09:24,950 --> 00:09:29,080
And that would be equal
to 2 pi over lambda x.

161
00:09:29,080 --> 00:09:32,180
Similarly, you can
also conclude that Ky

162
00:09:32,180 --> 00:09:37,260
can be written as ny
divided by c times omega,

163
00:09:37,260 --> 00:09:39,783
which is 2 pi over lambda u.

164
00:09:39,783 --> 00:09:45,050
Kx and Ky are the
wave numbers inside

165
00:09:45,050 --> 00:09:50,510
for the progressing harmonic
waves inside the median, OK?

166
00:09:50,510 --> 00:09:51,700
One is in the x direction.

167
00:09:51,700 --> 00:09:54,290
The other one's in
the y direction.

168
00:09:54,290 --> 00:09:58,140
So if we keep those in
mind, you will see that,

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00:09:58,140 --> 00:10:04,820
huh, if I have different nx
and ny, when the same frequency

170
00:10:04,820 --> 00:10:10,010
light goes through this
median, its x component

171
00:10:10,010 --> 00:10:13,650
will travel through
different amount of period,

172
00:10:13,650 --> 00:10:17,150
where is a different
amount of phase difference.

173
00:10:17,150 --> 00:10:20,180
Compared to the
light polarized--

174
00:10:20,180 --> 00:10:24,000
compared to the component
in the y direction,

175
00:10:24,000 --> 00:10:26,210
as you can see from
this demonstration.

176
00:10:26,210 --> 00:10:29,240
Therefore, we can
actually conclude

177
00:10:29,240 --> 00:10:31,730
that there must be
a phase difference

178
00:10:31,730 --> 00:10:33,860
between the x component
and y component.

179
00:10:33,860 --> 00:10:35,570
And we can calculate that--

180
00:10:35,570 --> 00:10:38,390
this is actually delta
phi, the phase difference

181
00:10:38,390 --> 00:10:42,740
between the x direction and y
direction will be equal to 2 pi

182
00:10:42,740 --> 00:10:46,070
times l divided by lambda x.

183
00:10:46,070 --> 00:10:50,680
So basically, it's the
number of waves times 2 pi.

184
00:10:50,680 --> 00:10:54,770
l over lambda x is
number of periods past.

185
00:10:54,770 --> 00:11:00,110
And the times 2 pi
translates that to phase.

186
00:11:00,110 --> 00:11:02,840
And we are taking the
difference between the x

187
00:11:02,840 --> 00:11:05,090
and the y direction.

188
00:11:05,090 --> 00:11:09,480
And we can conclude that based
on what we have written here.

189
00:11:09,480 --> 00:11:12,920
As you see that this
is just nx minus ny

190
00:11:12,920 --> 00:11:19,380
divided by c times
omega times l, OK?

191
00:11:19,380 --> 00:11:23,790
So this is actually how
the wave plate works.

192
00:11:23,790 --> 00:11:29,320
Suppose I have a
linearly polarizer

193
00:11:29,320 --> 00:11:32,580
wave coming into this plate.

194
00:11:32,580 --> 00:11:37,080
And the direction
of the polarization

195
00:11:37,080 --> 00:11:39,050
is not in the x
direction or y direction.

196
00:11:39,050 --> 00:11:41,140
So they are positioned--

197
00:11:41,140 --> 00:11:44,820
they are components in the
x direction and y direction.

198
00:11:44,820 --> 00:11:50,100
For example, I can have an
incoming polarizer like this.

199
00:11:50,100 --> 00:11:52,400
And this is actually
the x direction.

200
00:11:52,400 --> 00:11:54,290
This is actually
the y direction.

201
00:11:54,290 --> 00:11:59,580
And I can now decompose this
kind of linearly polarized wave

202
00:11:59,580 --> 00:12:00,900
into two components.

203
00:12:00,900 --> 00:12:07,160
And after this wave passes
through the wave plate,

204
00:12:07,160 --> 00:12:10,200
x component will be--

205
00:12:10,200 --> 00:12:13,210
the phase difference
between x and y

206
00:12:13,210 --> 00:12:16,320
will be increased by delta phi.

207
00:12:16,320 --> 00:12:19,320
So if originally there
were no phase difference

208
00:12:19,320 --> 00:12:22,410
because this is actually
a linearly polarized wave,

209
00:12:22,410 --> 00:12:24,990
and after it passes
through the wave plate,

210
00:12:24,990 --> 00:12:26,220
it will be increased.

211
00:12:26,220 --> 00:12:28,500
And then the phase
difference between x and y

212
00:12:28,500 --> 00:12:31,560
will be delta phi.

213
00:12:31,560 --> 00:12:35,420
All right, so that's
really nice tour.

214
00:12:35,420 --> 00:12:39,120
And the so-called
quarter wave plate

215
00:12:39,120 --> 00:12:45,450
is a device which we
intentionally set the delta phi

216
00:12:45,450 --> 00:12:48,090
to be pi over 2.

217
00:12:48,090 --> 00:12:49,580
Why is that interesting?

218
00:12:49,580 --> 00:12:52,140
That is because
initially you have

219
00:12:52,140 --> 00:13:05,420
Ex equal to E0 cosine
omega t minus Kz,

220
00:13:05,420 --> 00:13:10,230
and this is actually
the y component.

221
00:13:10,230 --> 00:13:14,720
If initially you have this
kind of incident wave,

222
00:13:14,720 --> 00:13:19,170
now it corresponds
to a polarization

223
00:13:19,170 --> 00:13:25,189
which is actually 45 degree
with respect to the x-axis.

224
00:13:25,189 --> 00:13:26,480
So this is actually the x-axis.

225
00:13:29,190 --> 00:13:31,000
And this is actually the y-axis.

226
00:13:33,540 --> 00:13:39,030
When I have this kind of
linearly polarized wave pass

227
00:13:39,030 --> 00:13:43,680
through the quarter wave
plate, what is going to happen?

228
00:13:43,680 --> 00:13:46,440
What is going to happen is
that one of the components

229
00:13:46,440 --> 00:13:50,100
will be delayed by
delta phi or pi over 2.

230
00:13:50,100 --> 00:13:54,360
That will make you a
circularly polarized wave.

231
00:13:54,360 --> 00:13:58,030
Because that will
become sine and cosine.

232
00:13:58,030 --> 00:14:02,510
Therefore, if you plot the
locus of the electric field

233
00:14:02,510 --> 00:14:07,410
in two-dimensional xy plane,
you will see a circle.

234
00:14:07,410 --> 00:14:10,740
So that is actually
why we want are

235
00:14:10,740 --> 00:14:14,130
interested in a special
setup which delta phi is

236
00:14:14,130 --> 00:14:17,460
equal to pi over 2, OK?

237
00:14:17,460 --> 00:14:20,550
So let me go through
a few examples

238
00:14:20,550 --> 00:14:24,990
so that actually you get some
feelings about what is actually

239
00:14:24,990 --> 00:14:27,780
a quarter wave plate.

240
00:14:27,780 --> 00:14:32,910
Usually, instead of drawing
this complicated diagram,

241
00:14:32,910 --> 00:14:35,670
we actually simplify
the presentation

242
00:14:35,670 --> 00:14:38,280
into a diagram like this.

243
00:14:38,280 --> 00:14:42,160
So basically, you
have a fast axis,

244
00:14:42,160 --> 00:14:47,160
which is the axis with
smaller phase shift.

245
00:14:47,160 --> 00:14:53,490
And you have slow axis, which
is actually the axis with larger

246
00:14:53,490 --> 00:14:54,990
phase shift.

247
00:14:54,990 --> 00:14:58,670
So basically, we just reduce
the whole complicated setup

248
00:14:58,670 --> 00:15:02,520
into a simple diagram like that.

249
00:15:02,520 --> 00:15:10,060
So suppose I have an incident
wave which is actually linearly

250
00:15:10,060 --> 00:15:14,140
polarized in this direction.

251
00:15:14,140 --> 00:15:17,570
In this direction, which
I can call it x direction.

252
00:15:17,570 --> 00:15:21,000
And this is actually
y direction.

253
00:15:21,000 --> 00:15:26,190
And I have that pass through
a quarter wave plate,

254
00:15:26,190 --> 00:15:30,350
where the fast axis
is in the x direction,

255
00:15:30,350 --> 00:15:33,465
and there's a slow axis
in the y direction.

256
00:15:36,080 --> 00:15:41,660
Can somebody tell me, what would
be the resulting polarization

257
00:15:41,660 --> 00:15:45,620
after this electromagnetic wave
passes through this quarter

258
00:15:45,620 --> 00:15:47,240
wave plate?

259
00:15:47,240 --> 00:15:49,550
Somebody want to try it?

260
00:15:49,550 --> 00:15:50,417
Yes.

261
00:15:50,417 --> 00:15:53,550
STUDENT: It would be
polarized in the y direction.

262
00:15:53,550 --> 00:15:55,178
PROFESSOR: Polarized in what?

263
00:15:55,178 --> 00:15:58,507
STUDENT: In the y direction.

264
00:15:58,507 --> 00:15:59,090
PROFESSOR: No.

265
00:15:59,090 --> 00:16:04,390
Basically-- OK, maybe I
didn't explain that clearly.

266
00:16:04,390 --> 00:16:10,810
So initially, in this example,
all the electric field

267
00:16:10,810 --> 00:16:13,320
is in the x direction.

268
00:16:13,320 --> 00:16:17,140
Therefore, in the y direction,
there's nothing there.

269
00:16:17,140 --> 00:16:20,252
So that's actually a
linearly polarized wave.

270
00:16:20,252 --> 00:16:22,480
The direction in actually
in the x direction.

271
00:16:22,480 --> 00:16:25,030
And this quarter
wave plate is going

272
00:16:25,030 --> 00:16:31,900
to slow down the y component
by a phase of pi over 2.

273
00:16:31,900 --> 00:16:34,831
So what would be the
resulting polarization?

274
00:16:34,831 --> 00:16:35,330
Yes.

275
00:16:35,330 --> 00:16:39,160
STUDENT: Very similar
to [INAUDIBLE]..

276
00:16:39,160 --> 00:16:40,450
PROFESSOR: Yes, that's right.

277
00:16:40,450 --> 00:16:44,780
So because we are dividing
something which is zero.

278
00:16:44,780 --> 00:16:46,660
But zero is zero.

279
00:16:46,660 --> 00:16:49,730
So zero is zero is zero, right?

280
00:16:49,730 --> 00:16:54,060
So therefore, what you
are going to get is this.

281
00:16:54,060 --> 00:16:57,100
It's still a linearly
polarized wave, right?

282
00:16:57,100 --> 00:17:01,420
OK, doesn't surprise you after
I explain to you more clearly.

283
00:17:01,420 --> 00:17:05,609
And then you can see
that if you have this--

284
00:17:05,609 --> 00:17:08,750
OK, now I change the situation.

285
00:17:08,750 --> 00:17:10,500
So this is the x direction.

286
00:17:10,500 --> 00:17:12,099
This is the y direction.

287
00:17:12,099 --> 00:17:14,230
And I have something
which is 45 degrees.

288
00:17:17,450 --> 00:17:21,870
And I have that pass
through the same setup.

289
00:17:21,870 --> 00:17:25,840
Slow axis is in the y
direction and the fast axis

290
00:17:25,840 --> 00:17:27,980
is in the x direction.

291
00:17:27,980 --> 00:17:29,300
What will we get?

292
00:17:29,300 --> 00:17:32,000
What kind of polarized
light will we

293
00:17:32,000 --> 00:17:38,240
get after it passed through
this quarter wave plate?

294
00:17:38,240 --> 00:17:39,676
Somebody can help me?

295
00:17:39,676 --> 00:17:40,509
STUDENT: Circular.

296
00:17:40,509 --> 00:17:41,550
PROFESSOR: Circular, yes.

297
00:17:41,550 --> 00:17:42,660
Thank you very much.

298
00:17:42,660 --> 00:17:44,610
So that's actually
exactly what I was

299
00:17:44,610 --> 00:17:46,470
talking about in the beginning.

300
00:17:46,470 --> 00:17:50,610
The y component will be
delayed by pi over 2.

301
00:17:50,610 --> 00:17:55,230
Therefore, it would become
a circularly polarized wave.

302
00:17:55,230 --> 00:17:59,520
How about I change
this to 30 degrees?

303
00:17:59,520 --> 00:18:00,950
What is going to happen?

304
00:18:00,950 --> 00:18:02,024
STUDENT: [INAUDIBLE].

305
00:18:02,024 --> 00:18:04,440
PROFESSOR: Yeah, it will be
elliptically polarized, right?

306
00:18:04,440 --> 00:18:08,190
Because now the projection
to a different component

307
00:18:08,190 --> 00:18:09,050
is different.

308
00:18:09,050 --> 00:18:12,870
So therefore, it would be
elliptically polarized wave.

309
00:18:12,870 --> 00:18:13,680
Very good.

310
00:18:13,680 --> 00:18:15,900
It seems to me that
most of you actually

311
00:18:15,900 --> 00:18:17,880
understand what we are doing.

312
00:18:17,880 --> 00:18:23,641
And now it's time to do some
experiment to actually show you

313
00:18:23,641 --> 00:18:24,390
what we have done.

314
00:18:24,390 --> 00:18:25,147
Yes.

315
00:18:25,147 --> 00:18:26,772
STUDENT: It's a little
more complicated

316
00:18:26,772 --> 00:18:29,123
than that because the
slope the refraction

317
00:18:29,123 --> 00:18:42,050
is [INAUDIBLE] be much, much
slower than the fast axis.

318
00:18:42,050 --> 00:18:43,925
PROFESSOR: Yeah.

319
00:18:43,925 --> 00:18:47,050
Yeah, that's right.

320
00:18:47,050 --> 00:18:48,570
You are absolutely right.

321
00:18:48,570 --> 00:18:51,150
So it depends on the
delta phi, right?

322
00:18:51,150 --> 00:18:54,740
So if delta phi
is not pi over 2,

323
00:18:54,740 --> 00:18:58,430
then it can be
elliptically polarized.

324
00:18:58,430 --> 00:19:01,610
And in this setup, I say that
this is actually a quarter wave

325
00:19:01,610 --> 00:19:03,800
plate, therefore,
the delay is always

326
00:19:03,800 --> 00:19:05,570
delta phi equal to pi over 2.

327
00:19:05,570 --> 00:19:07,120
Yeah.

328
00:19:07,120 --> 00:19:09,410
So then-- thank you for that.

329
00:19:09,410 --> 00:19:11,480
This is what we
have been discussing

330
00:19:11,480 --> 00:19:13,610
is always quarter wave plate.

331
00:19:13,610 --> 00:19:17,120
Therefore, the delta phi
between the slow and fast axis

332
00:19:17,120 --> 00:19:18,800
is always pi over 2, OK?

333
00:19:18,800 --> 00:19:21,900
So that everybody
is on the same page.

334
00:19:21,900 --> 00:19:22,568
Yes.

335
00:19:22,568 --> 00:19:24,480
STUDENT: How can
you have a material

336
00:19:24,480 --> 00:19:28,310
that has a different refraction
index for different directions?

337
00:19:28,310 --> 00:19:33,170
PROFESSOR: For example, we
were talking about materials--

338
00:19:33,170 --> 00:19:36,950
or say the two-dimensional
discrete case, right?

339
00:19:36,950 --> 00:19:41,690
So we can have
little mass arranged

340
00:19:41,690 --> 00:19:43,370
in the x and y direction.

341
00:19:43,370 --> 00:19:50,450
But the space between mass in
the x direction and y direction

342
00:19:50,450 --> 00:19:53,690
are different, then you
have a dispersion relation

343
00:19:53,690 --> 00:19:56,840
which is actually
different for the harmonic

344
00:19:56,840 --> 00:19:59,780
wave in the x direction
compared to y direction.

345
00:19:59,780 --> 00:20:01,440
And that's just
some random example.

346
00:20:01,440 --> 00:20:04,700
And that can be
achieved by engineering

347
00:20:04,700 --> 00:20:09,150
the material we will use
for the wave plate, OK?

348
00:20:09,150 --> 00:20:10,580
Good question.

349
00:20:10,580 --> 00:20:12,460
All right, so we will
go ahead and I'll

350
00:20:12,460 --> 00:20:15,440
show you some demonstration.

351
00:20:15,440 --> 00:20:17,360
We prepare.

352
00:20:17,360 --> 00:20:22,840
The first thing I have to
do is to turn off the light

353
00:20:22,840 --> 00:20:24,630
to have some more excitement.

354
00:20:27,810 --> 00:20:31,050
I cannot even see where
is my experiment now.

355
00:20:31,050 --> 00:20:33,060
Oh, right here, yeah.

356
00:20:33,060 --> 00:20:34,910
OK, woo.

357
00:20:34,910 --> 00:20:38,190
OK, so look at
what we have here.

358
00:20:38,190 --> 00:20:41,820
This is a projector.

359
00:20:41,820 --> 00:20:44,095
So what is the
polarization of that light?

360
00:20:44,095 --> 00:20:44,970
STUDENT: Unpolarized.

361
00:20:44,970 --> 00:20:46,190
PROFESSOR: Unpolarized.

362
00:20:46,190 --> 00:20:47,480
Yeah, very good.

363
00:20:47,480 --> 00:20:50,900
OK, I'm very happy to hear that.

364
00:20:50,900 --> 00:20:55,520
All right, so now I have the
polarizer and I put it on it.

365
00:20:55,520 --> 00:20:58,184
What is the polarization
of this light?

366
00:20:58,184 --> 00:21:01,490
STUDENT: [INAUDIBLE].

367
00:21:01,490 --> 00:21:03,003
PROFESSOR: I couldn't hear you.

368
00:21:03,003 --> 00:21:04,160
STUDENT: It's linear.

369
00:21:04,160 --> 00:21:04,670
PROFESSOR: Linear, yeah.

370
00:21:04,670 --> 00:21:06,410
Linearly of-- don't be afraid.

371
00:21:06,410 --> 00:21:07,400
OK, you can say that.

372
00:21:07,400 --> 00:21:08,570
No, this is not linear.

373
00:21:08,570 --> 00:21:10,310
The edge is not linear, right?

374
00:21:10,310 --> 00:21:11,430
But it's OK.

375
00:21:11,430 --> 00:21:15,830
I'm talking about everything
inside of this material.

376
00:21:15,830 --> 00:21:17,000
Very good.

377
00:21:17,000 --> 00:21:22,070
So now what I'm going to
do is to put two polarizers

378
00:21:22,070 --> 00:21:24,380
on top of each other.

379
00:21:24,380 --> 00:21:29,960
And of course, I can rotate such
that the polarizer, the easy

380
00:21:29,960 --> 00:21:33,170
axis is perpendicular
to each other, OK?

381
00:21:33,170 --> 00:21:37,700
So you see that ha, I almost
black most of that light.

382
00:21:37,700 --> 00:21:41,120
So the first thing
which I have been doing

383
00:21:41,120 --> 00:21:46,820
is that I first turn this
unpolarized light polarized.

384
00:21:46,820 --> 00:21:49,760
And it's actually
oscillating in one direction.

385
00:21:49,760 --> 00:21:53,340
And I block it again
with the second one.

386
00:21:53,340 --> 00:21:55,220
And then you see
that it's black.

387
00:21:55,220 --> 00:21:57,900
It's consistent
with what we expect.

388
00:21:57,900 --> 00:22:00,032
So we are happy.

389
00:22:00,032 --> 00:22:00,740
We are not happy?

390
00:22:00,740 --> 00:22:01,400
No?

391
00:22:01,400 --> 00:22:03,530
Yes, we are happy.

392
00:22:03,530 --> 00:22:08,100
All right, so remember the
discussion we had before.

393
00:22:08,100 --> 00:22:15,440
So what I could do is to add a
third one, a third polarizer.

394
00:22:15,440 --> 00:22:18,430
So I can have the
first polarizer

395
00:22:18,430 --> 00:22:21,920
which actually makes the
direction of the oscillation

396
00:22:21,920 --> 00:22:24,330
in this direction.

397
00:22:24,330 --> 00:22:28,760
Then I put a second
polarizer, where the easy axis

398
00:22:28,760 --> 00:22:30,380
is in this direction.

399
00:22:30,380 --> 00:22:35,840
Then I actually-- I'm going
to extract all the components

400
00:22:35,840 --> 00:22:37,950
which projected to this axis.

401
00:22:37,950 --> 00:22:44,270
Therefore, after passing
the second polarizer,

402
00:22:44,270 --> 00:22:48,860
the oscillation of the wave
will be in this direction.

403
00:22:48,860 --> 00:22:55,130
Therefore, aha, now I put
the third polarizer on,

404
00:22:55,130 --> 00:23:00,050
you can see that in the
middle, because it changed

405
00:23:00,050 --> 00:23:03,110
the direction of the
polarization by 45 degrees

406
00:23:03,110 --> 00:23:06,610
already by this
polarizer, therefore

407
00:23:06,610 --> 00:23:11,372
you can see that there's
some residual light survived.

408
00:23:11,372 --> 00:23:12,830
And then you can
actually calculate

409
00:23:12,830 --> 00:23:20,100
what will be the intensity of
the light surviving these three

410
00:23:20,100 --> 00:23:21,020
polarizers.

411
00:23:21,020 --> 00:23:22,610
And you can see
that the ones which

412
00:23:22,610 --> 00:23:29,450
didn't pass the second polarizer
is actually completely blocked

413
00:23:29,450 --> 00:23:33,410
by the two polarizers,
which their easy axes are

414
00:23:33,410 --> 00:23:35,880
perpendicular to each other.

415
00:23:35,880 --> 00:23:38,420
So now, the interesting
thing is that now I

416
00:23:38,420 --> 00:23:41,360
have a quarter wave plate here.

417
00:23:41,360 --> 00:23:42,270
OK, it's here.

418
00:23:42,270 --> 00:23:44,010
Hope you can see it.

419
00:23:44,010 --> 00:23:48,220
And I'm going to insert
this into this experiment

420
00:23:48,220 --> 00:23:50,830
and see what is going to happen.

421
00:23:50,830 --> 00:23:53,660
Look at what we have here.

422
00:23:53,660 --> 00:23:57,920
Oh, this is actually
much brighter, right?

423
00:23:57,920 --> 00:24:01,860
So basically, this water--

424
00:24:01,860 --> 00:24:04,690
this quarter wave plate--
sorry, it's not water--

425
00:24:04,690 --> 00:24:07,320
quarter wave plate, OK?

426
00:24:07,320 --> 00:24:10,390
Quarter wave plate actually
turned the polarized light

427
00:24:10,390 --> 00:24:14,170
into a circularly
polarized light.

428
00:24:14,170 --> 00:24:20,100
And after this circularly
polarized light

429
00:24:20,100 --> 00:24:25,180
continued and passed
through the third polarizer,

430
00:24:25,180 --> 00:24:27,760
you can see that,
huh, the light passed

431
00:24:27,760 --> 00:24:31,510
through this kind
of combination is

432
00:24:31,510 --> 00:24:39,310
a lot more than this experiment
which was three polarizers.

433
00:24:39,310 --> 00:24:41,320
And we can also
calculate what would

434
00:24:41,320 --> 00:24:43,330
be the expected intensity.

435
00:24:43,330 --> 00:24:46,360
And the good news is that we
are not going to calculate that

436
00:24:46,360 --> 00:24:48,820
now, but in your P set.

437
00:24:48,820 --> 00:24:52,840
So you will be able to show
that, indeed, the intensity you

438
00:24:52,840 --> 00:24:57,690
expect with quarter wave plate
will be higher than why you

439
00:24:57,690 --> 00:25:01,630
expect with three polarizers.

440
00:25:01,630 --> 00:25:03,650
So that's actually
the first experiment

441
00:25:03,650 --> 00:25:04,700
I would like to show you.

442
00:25:07,460 --> 00:25:11,270
The second experiment is
also very interesting.

443
00:25:11,270 --> 00:25:13,810
So I have here--

444
00:25:13,810 --> 00:25:20,370
OK, first I need to see if
I can turn on the light.

445
00:25:20,370 --> 00:25:22,890
I have to turn on this light.

446
00:25:22,890 --> 00:25:25,130
Very good.

447
00:25:25,130 --> 00:25:27,060
So look at this tube.

448
00:25:27,060 --> 00:25:33,140
This tube is made
of water and sugar.

449
00:25:33,140 --> 00:25:35,440
So we all love sugar.

450
00:25:35,440 --> 00:25:39,980
And I love it too much, so I
add too much into this tube.

451
00:25:39,980 --> 00:25:45,070
So it's actually
oversaturated sugar water.

452
00:25:45,070 --> 00:25:50,270
And so there is sugar inside
and there are some animal

453
00:25:50,270 --> 00:25:52,610
or whatever living inside.

454
00:25:52,610 --> 00:25:54,540
But we don't care.

455
00:25:54,540 --> 00:25:57,500
We are not studying biology.

456
00:25:57,500 --> 00:26:02,510
But what is actually
interesting is that, OK, now I

457
00:26:02,510 --> 00:26:06,350
have a light source from
the lamp inside emitting

458
00:26:06,350 --> 00:26:09,040
what kind of polarized light?

459
00:26:09,040 --> 00:26:10,310
Unpolarized light, right?

460
00:26:10,310 --> 00:26:15,590
And I have that pass through
a polarizer, which is here.

461
00:26:15,590 --> 00:26:17,120
There's a polarizer here.

462
00:26:17,120 --> 00:26:19,400
And therefore,
what I want to say

463
00:26:19,400 --> 00:26:26,720
is that the incident light
into this tube is polarized.

464
00:26:26,720 --> 00:26:28,790
That's the first
thing I want to say.

465
00:26:28,790 --> 00:26:32,090
The second thing I want
to say is that, OK,

466
00:26:32,090 --> 00:26:36,880
a linearly polarized light,
due to superposition principle,

467
00:26:36,880 --> 00:26:41,300
actually you can
decompose that into two

468
00:26:41,300 --> 00:26:44,630
circularly polarized light.

469
00:26:44,630 --> 00:26:46,970
Both of them are
actually rotating

470
00:26:46,970 --> 00:26:49,100
in different directions.

471
00:26:49,100 --> 00:26:50,540
You can actually
work on the mass

472
00:26:50,540 --> 00:26:53,060
and you will see that,
ha, indeed, it works.

473
00:26:53,060 --> 00:26:57,220
So our linearly polarized
light you can always rewrite it

474
00:26:57,220 --> 00:27:00,010
as a superposition
of two circularly

475
00:27:00,010 --> 00:27:04,810
polarized light, but rotating
in different directions.

476
00:27:04,810 --> 00:27:07,400
The interesting
thing is the material

477
00:27:07,400 --> 00:27:12,830
which we use in this
demonstration is oversaturated

478
00:27:12,830 --> 00:27:13,910
sugar.

479
00:27:13,910 --> 00:27:19,610
And we know that the molecule
for the sugar and those kind

480
00:27:19,610 --> 00:27:26,630
of material is asymmetric
under mirror transformation.

481
00:27:26,630 --> 00:27:27,860
It's asymmetric.

482
00:27:27,860 --> 00:27:30,050
It's a chiral material.

483
00:27:30,050 --> 00:27:31,850
OK, chiral is actually
just some name,

484
00:27:31,850 --> 00:27:33,470
but it doesn't mean
anything to you.

485
00:27:33,470 --> 00:27:37,640
But what is actually interesting
is that this material

486
00:27:37,640 --> 00:27:39,470
is asymmetric.

487
00:27:39,470 --> 00:27:41,750
If you have a mirror
and this material

488
00:27:41,750 --> 00:27:45,390
is looking at the mirror, in
the other side of the mirror,

489
00:27:45,390 --> 00:27:47,480
it looks different.

490
00:27:47,480 --> 00:27:52,150
It's like your hand, right?

491
00:27:52,150 --> 00:27:56,300
So in a mirror, it's asymmetric.

492
00:27:56,300 --> 00:27:59,960
So what is interesting is that
due to this kind of structure

493
00:27:59,960 --> 00:28:04,860
in the material that the
light passed through,

494
00:28:04,860 --> 00:28:09,530
the circularly polarized light,
counterclockwise polarized

495
00:28:09,530 --> 00:28:13,070
light, will have
different refractive index

496
00:28:13,070 --> 00:28:15,680
compared to clockwise.

497
00:28:15,680 --> 00:28:18,800
Clockwise and
counterclockwise light

498
00:28:18,800 --> 00:28:21,860
will have different
refractive index.

499
00:28:21,860 --> 00:28:29,420
Therefore, you see that now you
can see some kind of rotation

500
00:28:29,420 --> 00:28:32,840
or some kind of change
in the polarization

501
00:28:32,840 --> 00:28:36,830
as a function of distance
the light travels through.

502
00:28:36,830 --> 00:28:39,320
So basically, this
material would

503
00:28:39,320 --> 00:28:42,530
rotate the linearly
polarized light,

504
00:28:42,530 --> 00:28:46,280
because the refractive
index for the clockwise and

505
00:28:46,280 --> 00:28:49,920
counterclockwise are different.

506
00:28:49,920 --> 00:28:51,830
So if you accept
that, I would like

507
00:28:51,830 --> 00:28:54,200
to add another complication.

508
00:28:54,200 --> 00:28:58,520
In addition to that,
the refractive index

509
00:28:58,520 --> 00:29:04,250
also depends on the frequency
of the incident light.

510
00:29:04,250 --> 00:29:09,020
Therefore, you will have
different amount of rotation

511
00:29:09,020 --> 00:29:11,330
for different color.

512
00:29:11,330 --> 00:29:13,760
So therefore, you
can see that once I

513
00:29:13,760 --> 00:29:16,670
have incident light which
is linearly polarized,

514
00:29:16,670 --> 00:29:19,370
all the colors are lined up.

515
00:29:19,370 --> 00:29:21,410
You can see that here.

516
00:29:21,410 --> 00:29:24,160
What is the color here?

517
00:29:24,160 --> 00:29:27,760
It's kind of bluish or
white, essentially, right?

518
00:29:27,760 --> 00:29:32,030
But if you move slightly more,
then it becomes pretty blue.

519
00:29:32,030 --> 00:29:35,800
And then if you move more,
because of the dependence

520
00:29:35,800 --> 00:29:40,360
of the refractive index as
a function of wavelength,

521
00:29:40,360 --> 00:29:42,790
therefore, you can see that
this whole thing is actually

522
00:29:42,790 --> 00:29:44,260
changing color.

523
00:29:44,260 --> 00:29:48,700
And in the end, I have
another polarizer which

524
00:29:48,700 --> 00:29:51,980
filter one of the directions.

525
00:29:51,980 --> 00:29:54,010
And I can change the
direction, and you

526
00:29:54,010 --> 00:29:59,320
will see that I can filter
out different colors.

527
00:29:59,320 --> 00:30:02,130
Which color do you like?

528
00:30:02,130 --> 00:30:02,990
Now it's red.

529
00:30:05,900 --> 00:30:09,770
And of course, I can
rotate this polarizer,

530
00:30:09,770 --> 00:30:12,080
and I am sampling
different color.

531
00:30:12,080 --> 00:30:16,070
Because at the time
different color of light

532
00:30:16,070 --> 00:30:18,170
passes through
this material, they

533
00:30:18,170 --> 00:30:21,650
are rotated by different
amount of degree.

534
00:30:21,650 --> 00:30:25,370
Therefore, I can filter
out and create all kinds

535
00:30:25,370 --> 00:30:27,820
of different color on the wall.

536
00:30:27,820 --> 00:30:31,120
The other thing which is
interesting which I can do

537
00:30:31,120 --> 00:30:36,200
is that I can now change that
direction of the incident

538
00:30:36,200 --> 00:30:39,950
light, or the direction of the
polarization of the incident

539
00:30:39,950 --> 00:30:41,960
light, by rotating this one.

540
00:30:44,720 --> 00:30:51,350
You can see that the whole tube
is changing color, like why you

541
00:30:51,350 --> 00:30:54,190
see in the barber shop, right?

542
00:30:57,400 --> 00:31:02,700
OK, so maybe this is a fancy
way to make that kind of tube.

543
00:31:02,700 --> 00:31:03,200
No?

544
00:31:03,200 --> 00:31:06,330
A physics barber shop.

545
00:31:06,330 --> 00:31:07,910
Maybe we should do that.

546
00:31:07,910 --> 00:31:10,335
OK, so I hope you enjoyed
this demonstration.

547
00:31:10,335 --> 00:31:13,420
And we will take a five minute
break to take questions.

548
00:31:13,420 --> 00:31:15,430
And the next topic we
are going to talk about

549
00:31:15,430 --> 00:31:21,620
is how do we actually create
electromagnetic wave at all.

550
00:31:21,620 --> 00:31:24,670
So let's come back in 15.

551
00:31:31,070 --> 00:31:35,030
OK, so I hope you can hear me.

552
00:31:35,030 --> 00:31:39,140
All right, so welcome
back from the break.

553
00:31:39,140 --> 00:31:42,440
So we are going to talk about
the second topic we would like

554
00:31:42,440 --> 00:31:45,150
to cover in the lecture today.

555
00:31:45,150 --> 00:31:48,640
The question we are asking
is, how do we actually

556
00:31:48,640 --> 00:31:54,680
create electromagnetic waves
and so-called radiation?

557
00:31:54,680 --> 00:31:59,300
So this is actually a picture
from Hubble telescope.

558
00:31:59,300 --> 00:32:02,540
And you can see that
light can travel

559
00:32:02,540 --> 00:32:07,280
through billions, or tens
of billions, of light years

560
00:32:07,280 --> 00:32:09,260
and arrive at Earth.

561
00:32:09,260 --> 00:32:11,790
And you can actually
measure them

562
00:32:11,790 --> 00:32:16,770
and see you what is actually
going on in the past.

563
00:32:16,770 --> 00:32:20,300
And that means if
you have a source

564
00:32:20,300 --> 00:32:22,890
and you have some
kind of radiation,

565
00:32:22,890 --> 00:32:29,360
and this source is going to emit
energy towards somewhere, which

566
00:32:29,360 --> 00:32:32,960
is actually really, really
far away toward the edge

567
00:32:32,960 --> 00:32:34,730
of the universe.

568
00:32:34,730 --> 00:32:39,980
So that is actually what we
call electromagnetic wave

569
00:32:39,980 --> 00:32:44,090
and radiation.

570
00:32:44,090 --> 00:32:47,290
But the what is actually
requirement for that to happen?

571
00:32:47,290 --> 00:32:49,730
What is the requirement
for us to be

572
00:32:49,730 --> 00:32:53,390
able to see the stars
which are so far away?

573
00:32:53,390 --> 00:32:55,460
That's the question.

574
00:32:55,460 --> 00:33:00,670
So let me actually make
a simple argument here.

575
00:33:00,670 --> 00:33:03,410
Suppose I have some
kind of a light source.

576
00:33:03,410 --> 00:33:06,180
It's a source in the center.

577
00:33:06,180 --> 00:33:09,420
And we have learned about
pointing vector, right?

578
00:33:09,420 --> 00:33:11,610
So what this actually
pointing vector?

579
00:33:11,610 --> 00:33:13,800
It's not really the
pointing vector, right?

580
00:33:13,800 --> 00:33:20,730
So it's rate of energy
transfer per unit area.

581
00:33:20,730 --> 00:33:22,530
So it's kind of
pointing, but it's

582
00:33:22,530 --> 00:33:27,660
pointing to the direction
of the energy transfer.

583
00:33:27,660 --> 00:33:29,420
So this is a vector.

584
00:33:29,420 --> 00:33:32,280
And it's actually highly
related to the direction

585
00:33:32,280 --> 00:33:36,220
of the electric field
and the magnetic field.

586
00:33:36,220 --> 00:33:38,540
And now, if I--

587
00:33:38,540 --> 00:33:42,690
since this is essentially
the energy transfer per area,

588
00:33:42,690 --> 00:33:50,820
I can now capture the average
pointing vector times area.

589
00:33:50,820 --> 00:33:55,820
And what is going to happen is
that if I do this calculation

590
00:33:55,820 --> 00:33:56,760
at this surface--

591
00:33:56,760 --> 00:34:02,740
this is actually a sphere
which is covering this source.

592
00:34:02,740 --> 00:34:05,990
I can do this at
sphere number 1.

593
00:34:05,990 --> 00:34:10,739
And I can actually also do
that in the sphere number 2.

594
00:34:10,739 --> 00:34:13,949
Since there are absolutely
no other source--

595
00:34:13,949 --> 00:34:16,530
I'm assuming that there's
only one source here.

596
00:34:16,530 --> 00:34:19,889
There's only one light
source in the universe,

597
00:34:19,889 --> 00:34:21,870
which is kind of lonely.

598
00:34:21,870 --> 00:34:26,370
Apparently it's not my universe,
but somebody else's problem.

599
00:34:26,370 --> 00:34:31,770
And then I will conclude that
since there's nothing outside,

600
00:34:31,770 --> 00:34:36,880
I will conclude that S
times A, if I evaluate that

601
00:34:36,880 --> 00:34:40,199
in the first surface,
will be equal to S

602
00:34:40,199 --> 00:34:42,199
times A in the second surface.

603
00:34:42,199 --> 00:34:44,639
That's equal to power, OK?

604
00:34:44,639 --> 00:34:48,260
So that should not
surprise anybody.

605
00:34:48,260 --> 00:34:51,440
So that means the
pointing vector

606
00:34:51,440 --> 00:34:57,620
will be proportional to 1/A,
which is the surface area.

607
00:34:57,620 --> 00:35:01,250
And that means, based on
simple mathematics, that

608
00:35:01,250 --> 00:35:03,810
would be proportional
to 1 over r

609
00:35:03,810 --> 00:35:10,760
squared for this constant
power transfer to happen.

610
00:35:10,760 --> 00:35:13,640
So this means that
there's a source.

611
00:35:13,640 --> 00:35:18,050
And if I integrate all
the energy transfer

612
00:35:18,050 --> 00:35:20,270
from some kind of
surface, it's going

613
00:35:20,270 --> 00:35:26,000
to be a constant, no matter
what surface you are choosing.

614
00:35:26,000 --> 00:35:29,630
So that means if I look
at the structure of the S

615
00:35:29,630 --> 00:35:32,300
vector, the pointing
vector, we can

616
00:35:32,300 --> 00:35:36,010
conclude that at least
the electric field

617
00:35:36,010 --> 00:35:41,610
and magnetic field has to
be proportional to 1/r,

618
00:35:41,610 --> 00:35:44,600
which is the distance with
respect to the source.

619
00:35:44,600 --> 00:35:49,790
Otherwise, it's going to be
decaying faster, or reducing

620
00:35:49,790 --> 00:35:56,720
faster than 1/r, then the
total power will approach zero

621
00:35:56,720 --> 00:35:58,760
when you increase r enough.

622
00:35:58,760 --> 00:36:01,910
Then that means if
you have that happen,

623
00:36:01,910 --> 00:36:06,710
you will not see anything
if you are far enough.

624
00:36:06,710 --> 00:36:10,390
So if that's
actually the case, we

625
00:36:10,390 --> 00:36:16,670
can now come back and
discuss two situations which

626
00:36:16,670 --> 00:36:18,980
we are very familiar with.

627
00:36:18,980 --> 00:36:22,070
For example, you
can say, how about I

628
00:36:22,070 --> 00:36:23,420
have a stationary charge?

629
00:36:27,220 --> 00:36:28,710
So I can have a
stationary charge

630
00:36:28,710 --> 00:36:30,330
and see what will happen.

631
00:36:30,330 --> 00:36:33,390
And apparently, if
I have a charge here

632
00:36:33,390 --> 00:36:37,250
without actually moving
it, it's going to emit--

633
00:36:37,250 --> 00:36:42,750
basically, it is going to have
an electric field around this.

634
00:36:42,750 --> 00:36:46,980
But electric field, based on
what we learned from 8.02,

635
00:36:46,980 --> 00:36:54,690
is going to be 2 divided by 4
pi epsilon zero r squared r hat.

636
00:36:54,690 --> 00:36:59,090
It's going to be proportional
to 1 over r squared.

637
00:36:59,090 --> 00:37:02,130
It's already not very good news,
because it's proportional to 1

638
00:37:02,130 --> 00:37:03,330
over r squared.

639
00:37:03,330 --> 00:37:05,530
And it's hitted by this.

640
00:37:05,530 --> 00:37:07,365
The magnetic field is zero.

641
00:37:10,551 --> 00:37:14,360
If I have something
times zero it's zero.

642
00:37:14,360 --> 00:37:16,650
Then there will be
no energy transfer

643
00:37:16,650 --> 00:37:20,970
if you have a stationary
charge just sitting there.

644
00:37:20,970 --> 00:37:22,830
So apparently, this
is not a good way

645
00:37:22,830 --> 00:37:27,320
to create electromagnetic
wave, based on our argument.

646
00:37:27,320 --> 00:37:32,050
The pointing vector is
actually equal to zero.

647
00:37:32,050 --> 00:37:34,940
So now you can say, OK,
this is actually too boring,

648
00:37:34,940 --> 00:37:36,760
so let's introduce
some excitement.

649
00:37:36,760 --> 00:37:42,780
How about we make this charge
moving at a constant speed?

650
00:37:42,780 --> 00:37:44,380
What we can do is like this.

651
00:37:44,380 --> 00:37:47,950
Basically, if you have a
positively charged particle,

652
00:37:47,950 --> 00:37:51,780
you can actually make it
move at a constant speed,

653
00:37:51,780 --> 00:37:56,060
velocity equal to v. And what
you are going to see is that,

654
00:37:56,060 --> 00:37:59,560
oh, indeed, there will be some
changes in the electric field

655
00:37:59,560 --> 00:38:00,940
and the magnetic field.

656
00:38:00,940 --> 00:38:03,880
And I'm not going to go
through the calculation

657
00:38:03,880 --> 00:38:05,590
of this kind of situation.

658
00:38:05,590 --> 00:38:07,390
And I will leave
that as an exercise.

659
00:38:07,390 --> 00:38:11,230
But I would like to tell you
what would be the conclusion.

660
00:38:11,230 --> 00:38:15,190
So if you have a single
charge, which is essentially

661
00:38:15,190 --> 00:38:19,900
moving at a constant speed,
and what is going to happen

662
00:38:19,900 --> 00:38:26,860
is that the electric field
density, or the field line

663
00:38:26,860 --> 00:38:28,720
density will change.

664
00:38:28,720 --> 00:38:32,180
And you will be more
concentrated in the direction,

665
00:38:32,180 --> 00:38:34,890
which is essentially
perpendicular to the direction

666
00:38:34,890 --> 00:38:40,450
of the motion of this charge.

667
00:38:40,450 --> 00:38:42,830
And we can actually
calculate what

668
00:38:42,830 --> 00:38:44,980
would be the electric field.

669
00:38:44,980 --> 00:38:52,360
The electric field will be equal
to q divided by 4 pi epsilon0 r

670
00:38:52,360 --> 00:38:55,540
squared, 1 minus beta squared.

671
00:38:55,540 --> 00:38:57,580
I will define bet in a moment.

672
00:38:57,580 --> 00:39:00,870
1 minus beta
squared sine squared

673
00:39:00,870 --> 00:39:07,270
theta 3/2 in the r direction.

674
00:39:07,270 --> 00:39:15,030
And where the beta is actually
defined as u/c, which is u

675
00:39:15,030 --> 00:39:22,070
is actually the velocity
of this little charge.

676
00:39:22,070 --> 00:39:24,740
And of course, you
can also calculate

677
00:39:24,740 --> 00:39:27,710
what would be the
corresponding B, right?

678
00:39:27,710 --> 00:39:33,445
The magnetic field will be
actually equal to u plus E

679
00:39:33,445 --> 00:39:36,430
divided by c squared.

680
00:39:36,430 --> 00:39:39,080
And that is actually
proportional to 1

681
00:39:39,080 --> 00:39:42,830
over r squared.

682
00:39:42,830 --> 00:39:46,100
As you can see from
here, the bad news

683
00:39:46,100 --> 00:39:50,420
is that, OK, you indeed now
have both electric field

684
00:39:50,420 --> 00:39:51,540
and the magnetic field.

685
00:39:51,540 --> 00:39:52,940
There is some improvement.

686
00:39:52,940 --> 00:39:57,497
But the problem is
that the reduction

687
00:39:57,497 --> 00:39:59,330
of the electric field
and the magnetic field

688
00:39:59,330 --> 00:40:00,970
is a function of distance.

689
00:40:00,970 --> 00:40:02,450
It's too large.

690
00:40:02,450 --> 00:40:06,920
Both of them are proportional
to 1 over r squared,

691
00:40:06,920 --> 00:40:09,020
proportional to
1 over r squared.

692
00:40:09,020 --> 00:40:13,150
Therefore, the magnitude
of S will be proportional 1

693
00:40:13,150 --> 00:40:16,510
over r to the fourth.

694
00:40:16,510 --> 00:40:20,140
So if you are far
enough, you can

695
00:40:20,140 --> 00:40:26,200
conclude that the total
power will approach zero,

696
00:40:26,200 --> 00:40:30,780
even if you integrate
over the whole surface

697
00:40:30,780 --> 00:40:34,570
surrounding this moving charge.

698
00:40:34,570 --> 00:40:38,380
So apparently, that's
actually not the solution

699
00:40:38,380 --> 00:40:42,600
we are seeking.

700
00:40:42,600 --> 00:40:45,060
Therefore, we have
to do something

701
00:40:45,060 --> 00:40:50,230
more aggressive to
accelerate the charge.

702
00:40:50,230 --> 00:40:53,810
So you can now have a charge
moving at a constant speed.

703
00:40:53,810 --> 00:40:55,520
We see that it
didn't do anything.

704
00:40:55,520 --> 00:40:59,890
Therefore, we have to
make the velocity increase

705
00:40:59,890 --> 00:41:02,080
and see what'll happen.

706
00:41:02,080 --> 00:41:06,870
So what I am going to do
now requires concentration.

707
00:41:06,870 --> 00:41:09,890
So I will hope that
you don't take notes.

708
00:41:09,890 --> 00:41:14,920
Just follow me so that you
get what I am trying to argue.

709
00:41:14,920 --> 00:41:18,190
And of course, if you are
really good in mathematics,

710
00:41:18,190 --> 00:41:23,470
you can actually also go
through page 356 to 360

711
00:41:23,470 --> 00:41:24,730
in George's book.

712
00:41:24,730 --> 00:41:27,180
There are some really
mathematical deviations

713
00:41:27,180 --> 00:41:30,460
of the radiation from
an accelerated charge.

714
00:41:33,100 --> 00:41:40,160
So let's try to see how
can we actually understand

715
00:41:40,160 --> 00:41:42,560
an accelerated charge
and what is actually

716
00:41:42,560 --> 00:41:47,150
the associated
electromagnetic field.

717
00:41:47,150 --> 00:41:52,590
So my goal is to have
some kind of acceleration.

718
00:41:52,590 --> 00:41:54,830
So I would like to
set up the stage.

719
00:41:54,830 --> 00:41:58,210
So let's take a look
at the slide here.

720
00:41:58,210 --> 00:42:01,970
At t equal to zero,
time equal to zero,

721
00:42:01,970 --> 00:42:05,510
before I introduce
any excitement,

722
00:42:05,510 --> 00:42:11,270
I have a charged particle
initially at rest.

723
00:42:11,270 --> 00:42:13,890
And it's sitting there.

724
00:42:13,890 --> 00:42:17,360
What I'm going to do is that at
some point, at t equal to zero,

725
00:42:17,360 --> 00:42:24,170
I try to accelerate this charge
until t equal to delta t.

726
00:42:24,170 --> 00:42:30,770
The original position of that
charged particle is at a.

727
00:42:30,770 --> 00:42:38,490
And I try to accelerate this
charge by acceleration a.

728
00:42:38,490 --> 00:42:42,440
And that only happened in a
very small amount of time,

729
00:42:42,440 --> 00:42:44,720
which is delta t.

730
00:42:44,720 --> 00:42:46,810
So what is going to
happen is that this charge

731
00:42:46,810 --> 00:42:48,680
will get accelerated.

732
00:42:48,680 --> 00:42:52,640
And you can see that the
velocity of the charge--

733
00:42:52,640 --> 00:42:55,450
you can see velocity as
a function of time here--

734
00:42:55,450 --> 00:42:59,590
is increasing linearly in
this period, and reaching

735
00:42:59,590 --> 00:43:04,030
maxima, which is a delta t.

736
00:43:04,030 --> 00:43:08,350
So after that, I stop
the acceleration.

737
00:43:08,350 --> 00:43:11,210
So originally, the
charge is at rest.

738
00:43:11,210 --> 00:43:14,170
Then I accelerate it
for some period of time.

739
00:43:14,170 --> 00:43:19,690
And I stop the acceleration at
A prime, or t equal to delta t.

740
00:43:19,690 --> 00:43:23,840
And what is going to happen
afterwards to the charge?

741
00:43:23,840 --> 00:43:25,210
Everybody is following?

742
00:43:25,210 --> 00:43:28,420
You will be moving
at constant velocity.

743
00:43:28,420 --> 00:43:30,030
Very good.

744
00:43:30,030 --> 00:43:32,090
So that's actually
what you see here.

745
00:43:32,090 --> 00:43:36,860
And the wave can actually--
this information can propagate

746
00:43:36,860 --> 00:43:38,290
as a function of time.

747
00:43:38,290 --> 00:43:40,600
So that's actually
the whole setup,

748
00:43:40,600 --> 00:43:43,840
which I would like to discuss.

749
00:43:43,840 --> 00:43:46,930
Before that, I would like
to bring your attention

750
00:43:46,930 --> 00:43:50,790
to the graph I was
trying to draw here.

751
00:43:50,790 --> 00:43:52,290
So you can see that
originally there

752
00:43:52,290 --> 00:43:57,560
is a line which is pointing
up, like 45 degree with respect

753
00:43:57,560 --> 00:44:00,040
to this charge.

754
00:44:00,040 --> 00:44:04,360
So that's one of the field
lines I was drawing here.

755
00:44:04,360 --> 00:44:08,380
That's actually the
electric field line.

756
00:44:08,380 --> 00:44:12,970
And as you can see that as
I manipulate this charged

757
00:44:12,970 --> 00:44:16,180
particle, this is a sphere--

758
00:44:16,180 --> 00:44:18,300
or a circle I should--

759
00:44:18,300 --> 00:44:23,500
on this slide, which
is actually telling you

760
00:44:23,500 --> 00:44:28,930
where this information already
propagated in the space.

761
00:44:28,930 --> 00:44:32,740
So for example, if
I am sitting here

762
00:44:32,740 --> 00:44:35,122
in the position of
my little mouse here.

763
00:44:35,122 --> 00:44:35,830
Can you see that?

764
00:44:35,830 --> 00:44:37,990
No, you cannot see it.

765
00:44:37,990 --> 00:44:46,060
If I'm sitting in the upper
right corner of the slide,

766
00:44:46,060 --> 00:44:48,340
and I try to--

767
00:44:48,340 --> 00:44:54,030
then the experiment starts
and I move the charge,

768
00:44:54,030 --> 00:45:00,240
the observer at the upper right
corner would not feel anything.

769
00:45:00,240 --> 00:45:05,070
Because it takes time for the
field, or for the changes,

770
00:45:05,070 --> 00:45:11,430
or for the information to
be sent from the position A

771
00:45:11,430 --> 00:45:17,580
to the observer, which are far
away from the charged particle.

772
00:45:17,580 --> 00:45:21,060
And the surface which--

773
00:45:21,060 --> 00:45:26,520
the surface is actually where
the information has propagated.

774
00:45:26,520 --> 00:45:32,100
So this information that
my charge is accelerated,

775
00:45:32,100 --> 00:45:34,740
this information has
already propagated

776
00:45:34,740 --> 00:45:40,950
to a sphere, which is actually
far away by c times delta t

777
00:45:40,950 --> 00:45:46,550
away from the center,
which is the location

778
00:45:46,550 --> 00:45:47,820
of the charged particle.

779
00:45:47,820 --> 00:45:50,640
And you can see that
as time goes on,

780
00:45:50,640 --> 00:45:56,290
this black circle is actually
becoming larger and larger,

781
00:45:56,290 --> 00:45:58,070
which contains the
information that,

782
00:45:58,070 --> 00:46:01,520
OK, I accelerated the charge.

783
00:46:01,520 --> 00:46:04,620
This is actually where you can
see that out of this circle

784
00:46:04,620 --> 00:46:08,340
is as if the charge
is stationary.

785
00:46:08,340 --> 00:46:11,380
So you can see the field
line is still linear.

786
00:46:11,380 --> 00:46:16,280
And passing through this
line, or say, this surface,

787
00:46:16,280 --> 00:46:18,640
the information is
already propagated.

788
00:46:18,640 --> 00:46:22,840
If you standing inside this
line, like for example,

789
00:46:22,840 --> 00:46:26,380
next to the question
mark, if you are there,

790
00:46:26,380 --> 00:46:30,700
you feel, aha, now I
observe the acceleration

791
00:46:30,700 --> 00:46:33,610
to the charged particle.

792
00:46:33,610 --> 00:46:39,940
Finally, if I go toward the
charged particle even more,

793
00:46:39,940 --> 00:46:44,560
and I will see, aha, if I am
now inside the green circle,

794
00:46:44,560 --> 00:46:46,660
I know that this
charged particle already

795
00:46:46,660 --> 00:46:48,430
stopped the acceleration.

796
00:46:48,430 --> 00:46:50,920
It's now moving
at constant speed.

797
00:46:50,920 --> 00:46:54,760
So that's the meaning of
these two little circles.

798
00:46:54,760 --> 00:47:00,570
And now I am looking at
the situation at time

799
00:47:00,570 --> 00:47:07,920
equal to t where the
charge is at position B.

800
00:47:07,920 --> 00:47:12,550
And I should see something
really interesting.

801
00:47:12,550 --> 00:47:17,400
As I mentioned before, if you
have a constantly propagating

802
00:47:17,400 --> 00:47:24,830
charge, the field
line is actually still

803
00:47:24,830 --> 00:47:29,500
a straight line, actually,
right there in the equation.

804
00:47:29,500 --> 00:47:31,510
If you have a
stationary charge, it's

805
00:47:31,510 --> 00:47:34,780
also a linear straight line.

806
00:47:34,780 --> 00:47:38,080
And you can see that you
have two straight lines,

807
00:47:38,080 --> 00:47:44,850
but in between, there's a kink
which connects these two lines.

808
00:47:44,850 --> 00:47:49,680
So between these two
lines, basically this

809
00:47:49,680 --> 00:47:51,360
is actually what we have here.

810
00:47:51,360 --> 00:47:54,200
So we have the
original particle.

811
00:47:54,200 --> 00:47:58,370
And this is actually where
the particle have the field

812
00:47:58,370 --> 00:48:01,220
line as a moving charge.

813
00:48:01,220 --> 00:48:04,890
And there's another
surface, which

814
00:48:04,890 --> 00:48:07,250
actually out of
the surface, it's

815
00:48:07,250 --> 00:48:11,930
like there is no
acceleration at all.

816
00:48:11,930 --> 00:48:15,320
The charge is still
stationary at A.

817
00:48:15,320 --> 00:48:20,840
You can see that these two
field lines are linear,

818
00:48:20,840 --> 00:48:25,020
and also essentially in
the radial direction.

819
00:48:25,020 --> 00:48:28,220
But the excitement is that
since the field line has

820
00:48:28,220 --> 00:48:34,760
to be continuous, the excitement
is that I have successfully

821
00:48:34,760 --> 00:48:39,210
created a kink, which
is actually propagating

822
00:48:39,210 --> 00:48:42,210
in the radial direction.

823
00:48:42,210 --> 00:48:48,390
And this kink is going to be our
electromagnetic wave because it

824
00:48:48,390 --> 00:48:53,760
has a component which is
perpendicular to the direction

825
00:48:53,760 --> 00:48:54,600
of propagation.

826
00:48:54,600 --> 00:48:56,670
Just a reminder,
what is actually

827
00:48:56,670 --> 00:48:59,010
an electromagnetic
field looks like, it

828
00:48:59,010 --> 00:49:01,350
looks like this, right?

829
00:49:01,350 --> 00:49:03,120
So basically, you have
the electric field

830
00:49:03,120 --> 00:49:07,920
oscillating up and down
in one of the directions,

831
00:49:07,920 --> 00:49:09,690
the polarization--

832
00:49:09,690 --> 00:49:12,780
linearly polarized
electromagnetic wave.

833
00:49:12,780 --> 00:49:15,000
And the whole wave is
actually propagating

834
00:49:15,000 --> 00:49:17,010
toward the right-hand
side of the board.

835
00:49:17,010 --> 00:49:20,490
And the electric field is in
the perpendicular direction

836
00:49:20,490 --> 00:49:22,120
of the direction of propagation.

837
00:49:22,120 --> 00:49:26,550
And this kink is actually
what we are looking for, OK?

838
00:49:26,550 --> 00:49:32,600
And that really becomes
the electromagnetic wave

839
00:49:32,600 --> 00:49:37,130
right there from
the point source.

840
00:49:37,130 --> 00:49:40,080
Any questions so far?

841
00:49:40,080 --> 00:49:42,090
Everybody's following?

842
00:49:42,090 --> 00:49:45,060
OK, so now, that's good.

843
00:49:45,060 --> 00:49:49,260
We have managed to
create this situation.

844
00:49:49,260 --> 00:49:51,660
And I would like
to be more concrete

845
00:49:51,660 --> 00:49:53,740
about several settings.

846
00:49:53,740 --> 00:49:57,630
The first one is actually we
have a constant acceleration a,

847
00:49:57,630 --> 00:50:01,140
and this delta t
is really small.

848
00:50:01,140 --> 00:50:05,000
Very small delta t,
very small acceleration.

849
00:50:05,000 --> 00:50:11,700
Therefore, I would assume
that u defined as delta t,

850
00:50:11,700 --> 00:50:15,450
the resulting velocity
is much, much smaller

851
00:50:15,450 --> 00:50:17,700
than the speed of light.

852
00:50:17,700 --> 00:50:23,100
So that's actually the setup
which I would like to use.

853
00:50:23,100 --> 00:50:26,280
Then the question now
is, how do we actually

854
00:50:26,280 --> 00:50:29,490
evaluate what will
be the magnitude

855
00:50:29,490 --> 00:50:33,750
of this so-called
kink electric field?

856
00:50:33,750 --> 00:50:38,640
So for this, it's
actually also pretty easy.

857
00:50:38,640 --> 00:50:43,770
So now I would like to copy the
geometry which I have there.

858
00:50:43,770 --> 00:50:50,040
I am trying to draw a copy
of that to my board here.

859
00:50:50,040 --> 00:50:55,140
So basically, originally the
charge is stationary at A.

860
00:50:55,140 --> 00:51:02,580
And it's emitting an electric
field, which is actually only

861
00:51:02,580 --> 00:51:05,520
in the radial direction.

862
00:51:05,520 --> 00:51:09,930
And it got accelerated
by a really small time.

863
00:51:09,930 --> 00:51:12,720
I'm exaggerating
in that figure, OK?

864
00:51:12,720 --> 00:51:18,210
So it got accelerated a
really small amount of time.

865
00:51:18,210 --> 00:51:21,960
And after that, it
reached a prime,

866
00:51:21,960 --> 00:51:25,580
which is the exaggerated version
is actually probably there.

867
00:51:25,580 --> 00:51:31,110
And A and A prime is, in fact,
very, very close to each other,

868
00:51:31,110 --> 00:51:35,040
because this is actually just
a very, very small delta t.

869
00:51:35,040 --> 00:51:38,190
I can have delta t goes to zero.

870
00:51:38,190 --> 00:51:42,510
Then A and A prime would
be very, very similar.

871
00:51:42,510 --> 00:51:49,130
And now I let the time
go on, and now this

872
00:51:49,130 --> 00:51:55,650
charged particle is now at
point B. It's moved to point B.

873
00:51:55,650 --> 00:51:59,670
And I can connect
B to A and A prime.

874
00:51:59,670 --> 00:52:01,860
And I can actually
conclude that, OK,

875
00:52:01,860 --> 00:52:06,160
since the resulting velocity
of the charged particle

876
00:52:06,160 --> 00:52:11,100
up to a prime is actually equal
to u, defined as a times delta

877
00:52:11,100 --> 00:52:17,490
t, and we are now
at time equal to t.

878
00:52:17,490 --> 00:52:20,160
Therefore, the
distance these charged

879
00:52:20,160 --> 00:52:24,090
particles pass through,
or travel through,

880
00:52:24,090 --> 00:52:27,740
is actually u times t.

881
00:52:27,740 --> 00:52:29,100
Doesn't surprise you, right?

882
00:52:29,100 --> 00:52:30,550
So that's velocity times t.

883
00:52:33,630 --> 00:52:39,020
And also, we can actually
calculate this lens.

884
00:52:39,020 --> 00:52:40,390
This lens is actually--

885
00:52:40,390 --> 00:52:43,500
I call it this
point D here, which

886
00:52:43,500 --> 00:52:46,570
is the intersection
between the second surface

887
00:52:46,570 --> 00:52:49,350
and the original field line.

888
00:52:49,350 --> 00:52:54,430
And I call this one E, which is
the intersection of the field

889
00:52:54,430 --> 00:53:00,310
line from the moving charge
and the second surface.

890
00:53:00,310 --> 00:53:04,300
And finally, I also
have the intersection,

891
00:53:04,300 --> 00:53:06,910
which I call it F,
which is actually

892
00:53:06,910 --> 00:53:10,330
where the field line and
the surface actually join,

893
00:53:10,330 --> 00:53:13,270
which is actually the
information about the charge

894
00:53:13,270 --> 00:53:18,910
has moved is actually
the surface, which

895
00:53:18,910 --> 00:53:22,900
within that surface, people
know the charge is actually

896
00:53:22,900 --> 00:53:24,320
already moved.

897
00:53:24,320 --> 00:53:29,070
So once I have all these, I can
now evaluate what will be at D

898
00:53:29,070 --> 00:53:33,970
and F. D and F are actually
pretty straightforward as well,

899
00:53:33,970 --> 00:53:38,460
because all those surfaces are
traveling at the speed of what?

900
00:53:38,460 --> 00:53:40,190
Light, right.

901
00:53:40,190 --> 00:53:44,230
So what is actually the delta
t between these two surfaces?

902
00:53:44,230 --> 00:53:46,630
It's delta t, right?

903
00:53:46,630 --> 00:53:51,550
Because I actually stopped
the acceleration at delta t,

904
00:53:51,550 --> 00:53:55,840
therefore, the distance
between D point and F

905
00:53:55,840 --> 00:53:57,812
is actually just
c times delta t.

906
00:54:01,260 --> 00:54:04,500
And of course, now I have this.

907
00:54:04,500 --> 00:54:11,160
I can connect E and D. And
roughly, because a and a prime

908
00:54:11,160 --> 00:54:14,700
are very, very
close to each other,

909
00:54:14,700 --> 00:54:22,290
and also t is very large,
therefore the BE, this line,

910
00:54:22,290 --> 00:54:27,480
is roughly parallel
to these AF line.

911
00:54:27,480 --> 00:54:32,760
So these two lines are actually
roughly parallel to each other.

912
00:54:32,760 --> 00:54:35,370
Therefore, I can
now evaluate what

913
00:54:35,370 --> 00:54:39,510
will be this line, D and E--

914
00:54:39,510 --> 00:54:43,800
what would be the size of
the distance between D and E.

915
00:54:43,800 --> 00:54:45,190
And that can be evaluated.

916
00:54:45,190 --> 00:54:49,920
And it's actually just u
perpendicular times t--

917
00:54:49,920 --> 00:54:55,410
perpendicular to the
direction of the field.

918
00:54:55,410 --> 00:54:58,560
And I can copy that here.

919
00:54:58,560 --> 00:55:06,880
The distance between D and E is
just u perpendicular times t.

920
00:55:06,880 --> 00:55:10,780
And of course, I can approximate
that is actually just a line.

921
00:55:10,780 --> 00:55:13,930
And I have a theta angle
which is actually DEF.

922
00:55:17,840 --> 00:55:23,960
So now I can actually try
to use this information,

923
00:55:23,960 --> 00:55:28,010
this geometrical
argument information,

924
00:55:28,010 --> 00:55:33,620
to figure out what will be
the electric field, this kink.

925
00:55:33,620 --> 00:55:41,430
So now I can have the electric
field, the same triangle here,

926
00:55:41,430 --> 00:55:43,850
this is angle theta.

927
00:55:43,850 --> 00:55:52,790
And this is the electric
field parallel to the AF line.

928
00:55:52,790 --> 00:55:56,970
And I can have
also E perp, which

929
00:55:56,970 --> 00:56:01,340
is actually the perpendicular
to AF, this line.

930
00:56:01,340 --> 00:56:05,480
And the kink, E
kink, is actually

931
00:56:05,480 --> 00:56:10,010
what we would like to
figure out as well.

932
00:56:10,010 --> 00:56:14,210
And basically, this E kink is
what we want to figure out.

933
00:56:14,210 --> 00:56:18,480
And the E has the
following two components.

934
00:56:18,480 --> 00:56:20,060
One is the E parallel.

935
00:56:20,060 --> 00:56:22,070
The other one is
the E perp, which

936
00:56:22,070 --> 00:56:25,940
is the perpendicular and the
parallel components to the AF

937
00:56:25,940 --> 00:56:28,010
line.

938
00:56:28,010 --> 00:56:31,640
And we can already make use
of the similarity of these two

939
00:56:31,640 --> 00:56:32,990
triangles, right?

940
00:56:32,990 --> 00:56:36,920
Basically, this field line
is actually pure geometrical,

941
00:56:36,920 --> 00:56:38,870
therefore, I know
what is actually

942
00:56:38,870 --> 00:56:41,600
theta from this
geometrical argument.

943
00:56:41,600 --> 00:56:46,880
So what is actually
theta, basically, you

944
00:56:46,880 --> 00:56:50,470
can get that from the
information of c delta t.

945
00:56:50,470 --> 00:56:54,140
And then u perp times t.

946
00:56:54,140 --> 00:56:56,730
So therefore, I can
conclude that the magnitude

947
00:56:56,730 --> 00:57:01,810
of E perp divided by
magnitude of E parallel

948
00:57:01,810 --> 00:57:11,610
will be equal to u perp
t divided by c delta t.

949
00:57:11,610 --> 00:57:15,110
And this E kink is like this.

950
00:57:15,110 --> 00:57:18,290
It actually has a direction.

951
00:57:18,290 --> 00:57:21,710
However, you can see
that, wait a second,

952
00:57:21,710 --> 00:57:23,390
you have this ratio, right?

953
00:57:23,390 --> 00:57:28,430
But the E kink is actually
pointing to this direction.

954
00:57:28,430 --> 00:57:33,980
And this ut is pointing
up to upward direction.

955
00:57:33,980 --> 00:57:37,820
Therefore, if you
take this ratio,

956
00:57:37,820 --> 00:57:41,360
the E kink will be pointing
to the upper left direction.

957
00:57:41,360 --> 00:57:44,350
Therefore, you really need
a minus sign here, right?

958
00:57:44,350 --> 00:57:49,370
Therefore, the E perp
would be pointing downward.

959
00:57:49,370 --> 00:57:53,640
Therefore, that's actually how
you get this minus sign there.

960
00:57:53,640 --> 00:57:56,210
From this pure
geometrical argument,

961
00:57:56,210 --> 00:57:57,780
you can actually
conclude what would

962
00:57:57,780 --> 00:58:01,980
be the ratio between E perp
and the E parallel, which

963
00:58:01,980 --> 00:58:03,770
is actually equal to that.

964
00:58:03,770 --> 00:58:06,190
And I can write it
down explicitly.

965
00:58:06,190 --> 00:58:11,276
Basically, that's going to
be equal to a delta t times

966
00:58:11,276 --> 00:58:14,760
t divided by c delta t.

967
00:58:14,760 --> 00:58:21,350
Remember, u is equal
to a times delta t.

968
00:58:21,350 --> 00:58:24,350
Therefore, I can
now cancel delta t.

969
00:58:24,350 --> 00:58:29,145
Then basically, what I get is
minus a perp t divided by c.

970
00:58:32,380 --> 00:58:34,730
And now this is
actually equal to minus

971
00:58:34,730 --> 00:58:39,050
a perp r divided
by c squared, where

972
00:58:39,050 --> 00:58:42,980
r is actually just c times t.

973
00:58:42,980 --> 00:58:46,640
r is actually the distance
between the position

974
00:58:46,640 --> 00:58:56,220
you are evaluating this field
and the origin, which is A, OK?

975
00:58:56,220 --> 00:58:58,770
So you can now
conclude that-- based

976
00:58:58,770 --> 00:59:01,080
on this geometrical
argument, you

977
00:59:01,080 --> 00:59:04,050
can conclude that E
perp is highly related

978
00:59:04,050 --> 00:59:06,630
to the E parallel.

979
00:59:06,630 --> 00:59:11,400
The E perp is equal to
minus a perp r divided

980
00:59:11,400 --> 00:59:16,462
by c squared E parallel.

981
00:59:16,462 --> 00:59:18,458
Any questions so far?

982
00:59:21,951 --> 00:59:22,949
Yes.

983
00:59:22,949 --> 00:59:24,960
STUDENT: How'd you
get r real quick?

984
00:59:24,960 --> 00:59:27,710
PROFESSOR: R is actually--
yeah, so r is actually

985
00:59:27,710 --> 00:59:29,610
just c times t.

986
00:59:29,610 --> 00:59:36,028
So it's the whole
distance is the r.

987
00:59:36,028 --> 00:59:37,020
Cool.

988
00:59:37,020 --> 00:59:41,590
All right, so you can see that
right now all of those things

989
00:59:41,590 --> 00:59:44,620
are purely geometrical, right?

990
00:59:44,620 --> 00:59:46,200
So this is really no magic.

991
00:59:46,200 --> 00:59:48,790
And no even integration.

992
00:59:48,790 --> 00:59:52,720
So now we are going to
do some integration.

993
00:59:52,720 --> 00:59:55,320
So now we are almost there.

994
00:59:55,320 --> 00:59:58,320
I would like to figure out
what would be the E kink.

995
00:59:58,320 --> 01:00:02,760
And I am especially
interested in E perp,

996
01:00:02,760 --> 01:00:05,070
because E perp is
the direction which

997
01:00:05,070 --> 01:00:08,130
is actually perpendicular to
the direction of propagation.

998
01:00:08,130 --> 01:00:09,210
It's really cool.

999
01:00:09,210 --> 01:00:11,820
So that's actually
related to the magnitude

1000
01:00:11,820 --> 01:00:14,490
of the electromagnetic
field radiating.

1001
01:00:14,490 --> 01:00:16,920
So I would like to
know E perp, but I

1002
01:00:16,920 --> 01:00:19,470
don't know what is E parallel.

1003
01:00:19,470 --> 01:00:25,650
So what we could do is to use
Gauss' law in this example.

1004
01:00:25,650 --> 01:00:28,770
So now what I could
do is that I can

1005
01:00:28,770 --> 01:00:35,140
draw a pillbox,
which is actually

1006
01:00:35,140 --> 01:00:38,350
through the surface number 1.

1007
01:00:38,350 --> 01:00:40,780
This is actually
surface number 1.

1008
01:00:40,780 --> 01:00:45,060
What I could do is I can draw
a pillbox which is actually

1009
01:00:45,060 --> 01:00:48,930
passing through the
surface number 1.

1010
01:00:48,930 --> 01:00:53,320
Out of surface number 1, we
know the physics very well,

1011
01:00:53,320 --> 01:00:55,860
which is actually
the electric field

1012
01:00:55,860 --> 01:00:59,310
of a single stationary charge.

1013
01:00:59,310 --> 01:01:02,470
So therefore, I know what is
actually the electric field

1014
01:01:02,470 --> 01:01:02,970
outside.

1015
01:01:08,550 --> 01:01:12,010
Which is actually
pointing outward

1016
01:01:12,010 --> 01:01:14,640
in the radial direction.

1017
01:01:14,640 --> 01:01:18,870
And the E parallel is actually
what we are stuck with.

1018
01:01:18,870 --> 01:01:20,445
So we don't know
what is actually

1019
01:01:20,445 --> 01:01:23,060
the magnitude of E parallel.

1020
01:01:23,060 --> 01:01:26,950
That's the electric field
inside the surface number 1.

1021
01:01:29,590 --> 01:01:32,250
Makes sense?

1022
01:01:32,250 --> 01:01:36,660
So now we also
have the component

1023
01:01:36,660 --> 01:01:41,130
which is actually
perpendicular to the direction

1024
01:01:41,130 --> 01:01:42,330
of propagation.

1025
01:01:42,330 --> 01:01:46,140
So this is actually the
contribution of the E perp

1026
01:01:46,140 --> 01:01:50,910
and the contribution of E perp,
which they go from the side

1027
01:01:50,910 --> 01:01:52,200
to the site.

1028
01:01:52,200 --> 01:01:58,110
Go in from the side, go out
from the side of this pillbox.

1029
01:01:58,110 --> 01:02:00,720
So I can now
immediately conclude

1030
01:02:00,720 --> 01:02:07,650
that the total contribution
of this surface integral

1031
01:02:07,650 --> 01:02:10,750
will be equal to 0,
because of Gauss' law.

1032
01:02:10,750 --> 01:02:15,060
There's no charge in my pillbox.

1033
01:02:15,060 --> 01:02:18,180
Therefore, all those
things should cancel.

1034
01:02:18,180 --> 01:02:23,720
Apparently, these will
cancel, because side

1035
01:02:23,720 --> 01:02:29,050
in, side out, the same
magnitude, which is E perp.

1036
01:02:29,050 --> 01:02:31,740
Therefore, that
cancel is trivial.

1037
01:02:31,740 --> 01:02:34,650
And the interesting
thing is that we can also

1038
01:02:34,650 --> 01:02:41,610
figure out that e parallel
will have to be equal to E out.

1039
01:02:45,060 --> 01:02:51,180
So that the sum of all the
integral will be equal to 0,

1040
01:02:51,180 --> 01:02:52,970
because of Gauss' law.

1041
01:02:52,970 --> 01:02:55,650
That's actually a very
big amount of information,

1042
01:02:55,650 --> 01:03:01,560
because I know how
to write down E out.

1043
01:03:01,560 --> 01:03:06,210
So E parallel will
be equal to E out.

1044
01:03:06,210 --> 01:03:10,510
We learned from 8.02 this
is actually just q divided

1045
01:03:10,510 --> 01:03:14,605
by 4 pi epsilon0 r squared.

1046
01:03:17,550 --> 01:03:19,110
Does that surprise you?

1047
01:03:19,110 --> 01:03:22,920
Should not, right, because
out of the surface,

1048
01:03:22,920 --> 01:03:25,200
people think nothing
actually really

1049
01:03:25,200 --> 01:03:27,930
happened to the
charged particle.

1050
01:03:27,930 --> 01:03:31,500
So it's actually still
stationary sitting there.

1051
01:03:31,500 --> 01:03:34,590
So therefore, I have the
information of E parallel,

1052
01:03:34,590 --> 01:03:39,660
therefore, I can now conclude
what would be the E perp.

1053
01:03:39,660 --> 01:03:47,700
Now, E perp will be equal to
minus q a perp divided by 4 pi

1054
01:03:47,700 --> 01:03:52,710
epsilon0 c squared r,
because this is actually

1055
01:03:52,710 --> 01:03:55,980
just a perp minus
a perp r divided

1056
01:03:55,980 --> 01:04:00,010
by c squared times E parallel.

1057
01:04:00,010 --> 01:04:02,740
Look at what we have achieved.

1058
01:04:02,740 --> 01:04:04,430
Look at this.

1059
01:04:04,430 --> 01:04:08,060
This is actually
proportional to what?

1060
01:04:08,060 --> 01:04:10,230
1/r, right?

1061
01:04:10,230 --> 01:04:19,020
So that means the decaying
speed of this E perp

1062
01:04:19,020 --> 01:04:23,970
is really slow compared
to the electric field

1063
01:04:23,970 --> 01:04:25,890
from a stationary charge.

1064
01:04:25,890 --> 01:04:27,930
So that's actually
very encouraging.

1065
01:04:27,930 --> 01:04:31,050
And of course, you
can also write down

1066
01:04:31,050 --> 01:04:36,210
what will be the
resulting magnetic field.

1067
01:04:36,210 --> 01:04:39,930
And it's going to be
also proportional to 1/r.

1068
01:04:39,930 --> 01:04:41,970
So what we can
actually conclude is

1069
01:04:41,970 --> 01:04:50,510
that the E rad is a function
of direction of the--

1070
01:04:50,510 --> 01:04:54,450
evaluating this E
radiated electric field is

1071
01:04:54,450 --> 01:04:56,370
a function of t.

1072
01:04:56,370 --> 01:04:58,830
And we can actually--
based on this exercise,

1073
01:04:58,830 --> 01:05:02,640
this will be minus q.

1074
01:05:02,640 --> 01:05:05,390
a is a vector, but
now I only take

1075
01:05:05,390 --> 01:05:08,300
the perpendicular direction.

1076
01:05:08,300 --> 01:05:11,350
And this thing is
actually evaluated

1077
01:05:11,350 --> 01:05:22,570
at t minus r over c divided
by 4 pi epsilon0 c squared r.

1078
01:05:22,570 --> 01:05:24,190
Let's take a look
at this formula

1079
01:05:24,190 --> 01:05:27,880
closely together, since we
have spent a lot of time

1080
01:05:27,880 --> 01:05:29,500
trying to get this result.

1081
01:05:29,500 --> 01:05:31,370
So look at this structure.

1082
01:05:31,370 --> 01:05:35,230
So basically, the
radiated energy

1083
01:05:35,230 --> 01:05:40,000
has a minus sign in
front of q and a perp,

1084
01:05:40,000 --> 01:05:43,960
because the E kink
is actually pointing

1085
01:05:43,960 --> 01:05:45,580
in the opposite
direction compared

1086
01:05:45,580 --> 01:05:49,390
to the directional acceleration,
as you can see from here.

1087
01:05:49,390 --> 01:05:54,280
The E kink and the
E perpendicular

1088
01:05:54,280 --> 01:06:03,640
is pointing to the opposite
direction of the acceleration.

1089
01:06:03,640 --> 01:06:07,450
Therefore, we have
this minus sign there.

1090
01:06:07,450 --> 01:06:11,680
And only the perpendicular
direction motion, acceleration,

1091
01:06:11,680 --> 01:06:14,020
works.

1092
01:06:14,020 --> 01:06:18,670
And there's this little
component here, t minus r/c.

1093
01:06:18,670 --> 01:06:20,510
This is actually--
now multiplying

1094
01:06:20,510 --> 01:06:26,690
this factor is evaluated at
the t equal to t minus r/c.

1095
01:06:26,690 --> 01:06:28,900
It's evaluated at that time.

1096
01:06:28,900 --> 01:06:34,160
So this is actually
evaluated at retarded time.

1097
01:06:34,160 --> 01:06:39,050
So that means I am really slow.

1098
01:06:39,050 --> 01:06:41,150
I need to wait for
the information

1099
01:06:41,150 --> 01:06:46,910
to arrive my detector so that
I know there are acceleration

1100
01:06:46,910 --> 01:06:49,780
happening.

1101
01:06:49,780 --> 01:06:53,750
Finally, I can now
also conclude what

1102
01:06:53,750 --> 01:06:56,060
will be the magnetic field.

1103
01:06:56,060 --> 01:06:59,270
The magnetic field
rad, as I mentioned,

1104
01:06:59,270 --> 01:07:01,660
would be proportional to 1/r.

1105
01:07:01,660 --> 01:07:06,610
And of course, I also give
you the explicit formula

1106
01:07:06,610 --> 01:07:10,330
in the lecture notes.

1107
01:07:10,330 --> 01:07:14,980
And now we can actually conclude
that s will be proportional

1108
01:07:14,980 --> 01:07:17,350
to 1 over r squared.

1109
01:07:17,350 --> 01:07:20,800
So that means I
can now send energy

1110
01:07:20,800 --> 01:07:25,600
to the edge of the universe,
because of all this hard work

1111
01:07:25,600 --> 01:07:28,000
we have been doing here.

1112
01:07:28,000 --> 01:07:31,520
Any questions?

1113
01:07:31,520 --> 01:07:34,760
All right, before the
end of the lecture

1114
01:07:34,760 --> 01:07:38,550
today, I'm going to show
you an experiment here.

1115
01:07:38,550 --> 01:07:41,840
So here I have an
antenna, which you

1116
01:07:41,840 --> 01:07:46,250
can have electron
going back and forth,

1117
01:07:46,250 --> 01:07:52,730
oscillating harmonically
really, really fast like this.

1118
01:07:52,730 --> 01:07:55,910
Therefore, there will
be acceleration, because

1119
01:07:55,910 --> 01:07:57,950
of this harmonic oscillation.

1120
01:07:57,950 --> 01:07:59,952
And I'm going to
turn off the light.

1121
01:08:06,900 --> 01:08:10,620
Also probably hide the image.

1122
01:08:10,620 --> 01:08:14,180
OK, this is good.

1123
01:08:14,180 --> 01:08:21,500
But I have to be able
to see the button.

1124
01:08:21,500 --> 01:08:22,450
Can I see it?

1125
01:08:22,450 --> 01:08:24,390
No.

1126
01:08:24,390 --> 01:08:26,206
Oh, I'm in trouble.

1127
01:08:26,206 --> 01:08:28,290
Ah, here.

1128
01:08:28,290 --> 01:08:31,200
OK, here I have a receiver.

1129
01:08:31,200 --> 01:08:35,100
It's also a metal rod.

1130
01:08:35,100 --> 01:08:38,700
And I have a light
bulb in between,

1131
01:08:38,700 --> 01:08:43,830
which is actually trying to
receive the information from--

1132
01:08:43,830 --> 01:08:47,340
or say that it receives the
electromagnetic wave emitted

1133
01:08:47,340 --> 01:08:49,290
from that source.

1134
01:08:49,290 --> 01:08:51,930
Which you have electrons
going back and forth

1135
01:08:51,930 --> 01:08:53,399
in that direction.

1136
01:08:53,399 --> 01:08:57,810
So now, first, I
am trying to align

1137
01:08:57,810 --> 01:09:01,649
my setup in this direction
so that it's really--

1138
01:09:01,649 --> 01:09:04,972
what would be the polarization
of an electromagnetic wave?

1139
01:09:04,972 --> 01:09:08,689
The polarization is going to
be in a horizontal direction.

1140
01:09:08,689 --> 01:09:10,220
Yes, very good.

1141
01:09:10,220 --> 01:09:14,670
Therefore, if I have
this set up like this,

1142
01:09:14,670 --> 01:09:17,120
it's actually perpendicular
to the direction

1143
01:09:17,120 --> 01:09:21,220
of the polarization,
therefore, I see nothing here,

1144
01:09:21,220 --> 01:09:24,350
It is also possible that the
light bulb is actually broken,

1145
01:09:24,350 --> 01:09:25,970
but let's see.

1146
01:09:25,970 --> 01:09:30,250
So now what I'm going to do
is to change the direction.

1147
01:09:30,250 --> 01:09:31,279
You see that?

1148
01:09:31,279 --> 01:09:35,180
I am moving also closer
really carefully.

1149
01:09:35,180 --> 01:09:37,160
Now you can see what happened.

1150
01:09:37,160 --> 01:09:43,470
You can see that now I receive
the signal from this machine.

1151
01:09:43,470 --> 01:09:47,630
The emitted light is
actually polarized

1152
01:09:47,630 --> 01:09:49,430
in the horizontal direction.

1153
01:09:49,430 --> 01:09:52,470
And now I have also the
electron going back and forth,

1154
01:09:52,470 --> 01:09:56,330
and that actually can
light up the light bulb.

1155
01:09:56,330 --> 01:09:58,926
Now, if I change
the direction, you

1156
01:09:58,926 --> 01:10:01,060
can see that this
is actually gone.

1157
01:10:04,850 --> 01:10:06,460
And I can do this again.

1158
01:10:06,460 --> 01:10:09,410
And I can go farther
away from the source.

1159
01:10:09,410 --> 01:10:13,450
You can see that now the light
is actually disappearing.

1160
01:10:13,450 --> 01:10:14,320
Why?

1161
01:10:14,320 --> 01:10:18,030
That is because you
get the 1/r term.

1162
01:10:18,030 --> 01:10:20,310
Therefore, it's
actually disappearing.

1163
01:10:20,310 --> 01:10:24,030
And if I move closer to the
source, it's reappearing.

1164
01:10:24,030 --> 01:10:29,550
So now I need an assistant
to hold this thing for me.

1165
01:10:29,550 --> 01:10:30,600
Who can volunteer?

1166
01:10:30,600 --> 01:10:33,270
And I would like to rotate that.

1167
01:10:33,270 --> 01:10:35,880
I can actually also
rotate my setup.

1168
01:10:35,880 --> 01:10:36,660
Can you help?

1169
01:10:36,660 --> 01:10:37,550
Yes.

1170
01:10:37,550 --> 01:10:39,710
OK, be careful.

1171
01:10:39,710 --> 01:10:42,160
And I hope you can survive this.

1172
01:10:44,710 --> 01:10:47,230
So now what am I going to do--

1173
01:10:47,230 --> 01:10:48,870
OK, so stay there.

1174
01:10:48,870 --> 01:10:53,040
And what I'm going to do is
I can rotate the whole setup,

1175
01:10:53,040 --> 01:10:56,270
the same concept.

1176
01:10:56,270 --> 01:10:59,690
If I rotate the setup, I have
to be careful so that I am not

1177
01:10:59,690 --> 01:11:01,670
touching this more.

1178
01:11:01,670 --> 01:11:03,690
I want to survive.

1179
01:11:03,690 --> 01:11:05,740
And you can see now
what is actually

1180
01:11:05,740 --> 01:11:07,000
the direction of the emission.

1181
01:11:07,000 --> 01:11:09,590
It's actually in this
direction, right?

1182
01:11:09,590 --> 01:11:13,410
The direction of
the polarization

1183
01:11:13,410 --> 01:11:15,860
is in the back and
forth direction.

1184
01:11:15,860 --> 01:11:19,500
And you see that that the light
bulb is actually turned off.

1185
01:11:19,500 --> 01:11:23,060
And now I can turn it back on.

1186
01:11:23,060 --> 01:11:24,900
And you see that
it's still there.

1187
01:11:24,900 --> 01:11:26,180
OK, thank you very much.

1188
01:11:26,180 --> 01:11:27,050
You survived.

1189
01:11:27,050 --> 01:11:29,030
Not everybody actually
survives this.

1190
01:11:29,030 --> 01:11:31,070
[LAUGHTER]

1191
01:11:31,070 --> 01:11:35,780
So you can see it now I can
move really close to this thing.

1192
01:11:35,780 --> 01:11:37,920
And what is going to happen?

1193
01:11:37,920 --> 01:11:40,490
The amount of energy
will be too high,

1194
01:11:40,490 --> 01:11:44,620
and probably this light
bulb will explode or broken.

1195
01:11:44,620 --> 01:11:46,126
Do you want to see that?

1196
01:11:46,126 --> 01:11:47,100
STUDENT: [INAUDIBLE].

1197
01:11:47,100 --> 01:11:49,540
PROFESSOR: Oh, my god.

1198
01:11:49,540 --> 01:11:50,830
Let's see.

1199
01:11:50,830 --> 01:11:52,288
Ooh, [INAUDIBLE].

1200
01:11:52,288 --> 01:11:54,760
[LAUGHTER]

1201
01:11:54,760 --> 01:11:56,390
OK, very good.

1202
01:11:56,390 --> 01:11:59,210
So now this experiment is dead.

1203
01:11:59,210 --> 01:12:02,610
And then we can--
it's a very good time

1204
01:12:02,610 --> 01:12:04,660
to close the lecture today.

1205
01:12:04,660 --> 01:12:07,530
And thank you very much for
attending the lecture today.

1206
01:12:07,530 --> 01:12:14,130
And I hope now you understand
how we actually create light.

1207
01:12:14,130 --> 01:12:19,860
And enjoy the
homework, because you

1208
01:12:19,860 --> 01:12:27,270
will be able to figure out
why the quarter wave plate

1209
01:12:27,270 --> 01:12:31,500
combination will give you
a higher light intensity.

1210
01:12:31,500 --> 01:12:32,940
OK, so if you have
any questions,

1211
01:12:32,940 --> 01:12:35,460
I will be here and
just standing up here.

1212
01:12:42,732 --> 01:12:44,940
OK, hello everybody.

1213
01:12:44,940 --> 01:12:50,760
Today I'm going to show you a
demonstration, which actually

1214
01:12:50,760 --> 01:12:56,370
demonstrates the effect of
polarizer and quarter wave

1215
01:12:56,370 --> 01:12:58,470
plate.

1216
01:12:58,470 --> 01:12:59,850
Here is the setup.

1217
01:12:59,850 --> 01:13:07,180
I have a projector here, which
emits our polarizer light.

1218
01:13:07,180 --> 01:13:13,810
And if I put a sheet of
polarizer on top of it

1219
01:13:13,810 --> 01:13:21,750
with easy axis in the
vertical direction,

1220
01:13:21,750 --> 01:13:23,630
like what my finger--

1221
01:13:23,630 --> 01:13:27,900
in the direction oscillation
along the direction

1222
01:13:27,900 --> 01:13:29,600
of my finger, then
basically, you

1223
01:13:29,600 --> 01:13:34,710
will see that the intensity
of the light is reduced.

1224
01:13:34,710 --> 01:13:39,830
Because for the
unpolarized light,

1225
01:13:39,830 --> 01:13:41,340
light component
which is actually

1226
01:13:41,340 --> 01:13:46,170
oscillating along the easy axis
can pass through the polarizer,

1227
01:13:46,170 --> 01:13:48,600
but the component
which is actually

1228
01:13:48,600 --> 01:13:54,250
oscillating perpendicular
to the easy axis, like this,

1229
01:13:54,250 --> 01:13:56,190
is not going to
pass the polarizer.

1230
01:13:56,190 --> 01:14:00,340
Therefore, a large fraction
of unpolarized light

1231
01:14:00,340 --> 01:14:04,230
is actually filtered out,
and you will see a reduction

1232
01:14:04,230 --> 01:14:08,440
in the intensity on the screen.

1233
01:14:08,440 --> 01:14:12,990
So what I'm going to do now
is to place another polarizer

1234
01:14:12,990 --> 01:14:16,290
on top of the first one.

1235
01:14:16,290 --> 01:14:18,150
So now we have two sheets.

1236
01:14:18,150 --> 01:14:25,290
And you can see that after
adding the second sheet,

1237
01:14:25,290 --> 01:14:28,550
you see some change
in the intensity.

1238
01:14:28,550 --> 01:14:32,630
But if I rotate this
sheet so that now

1239
01:14:32,630 --> 01:14:36,960
the easy axis of the
first and the second sheet

1240
01:14:36,960 --> 01:14:40,770
are perpendicular to each
other, you can see on the screen

1241
01:14:40,770 --> 01:14:47,520
that all the light which are
emitted from the projector

1242
01:14:47,520 --> 01:14:50,660
is actually filtered out.

1243
01:14:50,660 --> 01:14:51,480
Why is that?

1244
01:14:51,480 --> 01:14:56,870
That is because now the first
sheet actually filters out

1245
01:14:56,870 --> 01:15:02,310
all that light which is actually
oscillating in the direction

1246
01:15:02,310 --> 01:15:05,100
perpendicular to the easy axis.

1247
01:15:05,100 --> 01:15:10,830
If I actually introduce another
filter which has easy axis

1248
01:15:10,830 --> 01:15:16,920
now perpendicular to the
one from the first sheet,

1249
01:15:16,920 --> 01:15:20,250
then I'm going to filter
out both directions.

1250
01:15:20,250 --> 01:15:23,786
Therefore, all the
light are filtered out

1251
01:15:23,786 --> 01:15:28,686
due to this putting
perpendicular setup.

1252
01:15:28,686 --> 01:15:33,420
Now, if I introduce
a third sheet,

1253
01:15:33,420 --> 01:15:36,990
insert that between the
two existing sheets,

1254
01:15:36,990 --> 01:15:39,180
but now I am trying
to actually insert

1255
01:15:39,180 --> 01:15:44,760
that such that the
direction of the easy axis

1256
01:15:44,760 --> 01:15:47,440
is actually 45
degrees with respect

1257
01:15:47,440 --> 01:15:52,230
to the easy axis
of the first sheet.

1258
01:15:52,230 --> 01:15:57,180
According to our calculation in
class, also in your homework,

1259
01:15:57,180 --> 01:16:02,260
you should see some light which
will pass through this setup.

1260
01:16:02,260 --> 01:16:05,130
And let's take a look at
the experimental result.

1261
01:16:05,130 --> 01:16:11,070
You can see that, indeed,
after you insert a third sheet,

1262
01:16:11,070 --> 01:16:14,970
you see that now the
easy axis is actually

1263
01:16:14,970 --> 01:16:18,300
45 degrees with respect
to the first sheet.

1264
01:16:18,300 --> 01:16:25,410
And you do see the intensity
of the light becomes larger,

1265
01:16:25,410 --> 01:16:29,340
or you see a brighter
light output passing

1266
01:16:29,340 --> 01:16:33,250
through these three polarizers.

1267
01:16:33,250 --> 01:16:39,450
And if I rotate it
so that actually

1268
01:16:39,450 --> 01:16:43,380
the easy axis of the second
sheet is actually changing,

1269
01:16:43,380 --> 01:16:45,700
you can see that
it reached maxima

1270
01:16:45,700 --> 01:16:48,360
at roughly 45 degrees,
which is actually

1271
01:16:48,360 --> 01:16:54,150
consistent with what we
predicted from your homework.

1272
01:16:54,150 --> 01:16:57,510
And then the other thing which
you predicted from the homework

1273
01:16:57,510 --> 01:17:03,230
is that if we insert a quarter
wave plate between these two

1274
01:17:03,230 --> 01:17:08,250
sheets, you are going to
see a brighter light passing

1275
01:17:08,250 --> 01:17:10,440
through this setup.

1276
01:17:10,440 --> 01:17:12,170
So let's actually
take a look at what

1277
01:17:12,170 --> 01:17:15,330
will happen by inserting
the quarter wave

1278
01:17:15,330 --> 01:17:18,900
plate between these two sheets.

1279
01:17:18,900 --> 01:17:22,230
And this is actually
the result. You

1280
01:17:22,230 --> 01:17:29,610
can see that, indeed,
the intensity is higher

1281
01:17:29,610 --> 01:17:35,030
compared to the three
polarizer experiment.

1282
01:17:35,030 --> 01:17:40,410
And also, the intensity
actually reached maxima

1283
01:17:40,410 --> 01:17:45,030
when the fast axis
of the polarizer

1284
01:17:45,030 --> 01:17:49,200
is 45 degrees with
respect to the easy axis,

1285
01:17:49,200 --> 01:17:51,850
as we predicted
from your homework.

1286
01:17:51,850 --> 01:17:55,720
And we can actually put both
experimental results side

1287
01:17:55,720 --> 01:17:56,910
by side.

1288
01:17:56,910 --> 01:17:59,430
Indeed, the results from the--

1289
01:17:59,430 --> 01:18:02,170
so now I am inserting
the polarizer also

1290
01:18:02,170 --> 01:18:04,300
between the two sheets.

1291
01:18:04,300 --> 01:18:08,620
And you can see that,
indeed, the light passing

1292
01:18:08,620 --> 01:18:12,160
through three
polarizers, the intensity

1293
01:18:12,160 --> 01:18:16,980
is actually lower than two
polarizers and the one quarter

1294
01:18:16,980 --> 01:18:18,109
wave plate setup.

1295
01:18:25,100 --> 01:18:27,030
Hello, everybody.

1296
01:18:27,030 --> 01:18:29,520
So today, we are going to
show you a demonstration

1297
01:18:29,520 --> 01:18:32,250
of dipole radiation.

1298
01:18:32,250 --> 01:18:33,550
Here is the setup.

1299
01:18:33,550 --> 01:18:38,480
So we have a radiator
here with two antenna.

1300
01:18:38,480 --> 01:18:41,720
And when I turn it down,
there will be current

1301
01:18:41,720 --> 01:18:46,940
going back and forth
through these two antenna.

1302
01:18:46,940 --> 01:18:49,070
And therefore,
this setup is going

1303
01:18:49,070 --> 01:18:55,610
to emit polarized
electromagnetic wave.

1304
01:18:55,610 --> 01:19:00,530
And we are able to detect
those electromagnetic waves

1305
01:19:00,530 --> 01:19:08,600
by using a detector here, which
consists of two antenna and one

1306
01:19:08,600 --> 01:19:09,590
light bulb here.

1307
01:19:09,590 --> 01:19:18,180
When there are current
on this antenna,

1308
01:19:18,180 --> 01:19:21,230
you will see the light
emitting from the light bulb.

1309
01:19:21,230 --> 01:19:24,020
And the intensity
of the light bulb

1310
01:19:24,020 --> 01:19:26,510
actually can help
us to understand

1311
01:19:26,510 --> 01:19:32,510
the structure of the radiation
from the dipole radiator.

1312
01:19:32,510 --> 01:19:39,260
So what I am going to do now
is to turn this setup on.

1313
01:19:39,260 --> 01:19:43,640
You can see now, the setup
is on and the light is on.

1314
01:19:43,640 --> 01:19:49,170
And there will be current
going back and forth

1315
01:19:49,170 --> 01:19:52,340
through these two antenna.

1316
01:19:52,340 --> 01:19:57,170
So since the oscillation
of the charge will

1317
01:19:57,170 --> 01:19:59,540
generate electromagnetic wave--

1318
01:19:59,540 --> 01:20:01,670
since the direction
of oscillation

1319
01:20:01,670 --> 01:20:06,140
is in the horizontal direction,
therefore, the electric field

1320
01:20:06,140 --> 01:20:08,300
of the electromagnetic
wave is going

1321
01:20:08,300 --> 01:20:11,550
to be in the
horizontal direction.

1322
01:20:11,550 --> 01:20:15,890
So this can be actually verified
by using the detector here.

1323
01:20:15,890 --> 01:20:19,610
When my detector-- the
direction of the antenna

1324
01:20:19,610 --> 01:20:24,250
is actually perpendicular to the
direction of the oscillation,

1325
01:20:24,250 --> 01:20:27,140
you basically don't
see any light emitting

1326
01:20:27,140 --> 01:20:29,060
from the light bulb.

1327
01:20:29,060 --> 01:20:32,290
Now I'm going to
rotate my detector.

1328
01:20:32,290 --> 01:20:40,070
You can see that as we actually
rotate so that the antenna is

1329
01:20:40,070 --> 01:20:43,700
parallel to the direction
of the oscillation,

1330
01:20:43,700 --> 01:20:45,260
then you will see
that, huh, we will

1331
01:20:45,260 --> 01:20:50,270
see a large intensity of light
emitted from the light bulb.

1332
01:20:50,270 --> 01:20:53,680
But on the other hand, if
we actually rotate such

1333
01:20:53,680 --> 01:20:57,260
that the direction
of the antenna

1334
01:20:57,260 --> 01:21:00,440
is perpendicular to the
direction of oscillation

1335
01:21:00,440 --> 01:21:03,020
of the charges,
then you will not

1336
01:21:03,020 --> 01:21:07,460
see any light emitted
from the light bulb.

1337
01:21:07,460 --> 01:21:10,640
This can also be demonstrated
from on the other side

1338
01:21:10,640 --> 01:21:12,150
of the experiment.

1339
01:21:12,150 --> 01:21:15,640
So now, instead of standing
in front of the setup,

1340
01:21:15,640 --> 01:21:22,660
I'm going to go to the side
of this dipole radiator.

1341
01:21:22,660 --> 01:21:28,040
So here is actually roughly
90 degrees with respect

1342
01:21:28,040 --> 01:21:30,010
to where I was standing.

1343
01:21:30,010 --> 01:21:32,180
And you can see that
no matter which angle--

1344
01:21:35,375 --> 01:21:42,575
no matter which angle of my
detector is in, basically,

1345
01:21:42,575 --> 01:21:48,810
you will never see light
emitted from the light bulb.

1346
01:21:48,810 --> 01:21:53,230
That is because the
direction of the oscillation

1347
01:21:53,230 --> 01:21:54,910
is in this direction.

1348
01:21:54,910 --> 01:21:58,390
And according to our
formula, our prediction

1349
01:21:58,390 --> 01:22:04,420
is that there will be no
electromagnetic wave traveling

1350
01:22:04,420 --> 01:22:06,870
in this direction.

1351
01:22:06,870 --> 01:22:10,630
And therefore, no matter
which angle you are actually

1352
01:22:10,630 --> 01:22:14,380
trying to detect
the emitted light,

1353
01:22:14,380 --> 01:22:18,970
the light bulb will
never light up.

1354
01:22:18,970 --> 01:22:22,690
So that's essentially
consistent with our declaration.

1355
01:22:22,690 --> 01:22:26,800
The second thing which I would
like to actually show you

1356
01:22:26,800 --> 01:22:31,720
is that we can also
detect the nodal point

1357
01:22:31,720 --> 01:22:36,470
of the emitted
electromagnetic wave

1358
01:22:36,470 --> 01:22:43,910
by moving this detector
around in the classroom.

1359
01:22:43,910 --> 01:22:51,640
For example, if now I move
farther away from the dipole,

1360
01:22:51,640 --> 01:22:56,530
now I am here and you can
see that the intensity goes

1361
01:22:56,530 --> 01:23:00,600
to zero at this point,
because we are actually

1362
01:23:00,600 --> 01:23:06,980
in one of the nodes of the
electromagnetic radiation.

1363
01:23:06,980 --> 01:23:11,080
And if I now move further
away from the setup,

1364
01:23:11,080 --> 01:23:17,090
you can see now the light
is actually emitting again.

1365
01:23:17,090 --> 01:23:20,210
And also, the
intensity increases.

1366
01:23:20,210 --> 01:23:26,935
And again, if I move farther
and farther away from the setup,

1367
01:23:26,935 --> 01:23:30,580
you can see that the light
becomes dimmer and dimmer,

1368
01:23:30,580 --> 01:23:32,370
and disappears again.

1369
01:23:32,370 --> 01:23:35,840
Here is actually another
node in the classroom.

1370
01:23:35,840 --> 01:23:41,390
And also, you can see that
as a function of distance,

1371
01:23:41,390 --> 01:23:46,000
the maxima intensity
emitted by the light bulb

1372
01:23:46,000 --> 01:23:50,200
is also decreasing because of
the larger and larger distance

1373
01:23:50,200 --> 01:23:53,770
with respect to the source.

1374
01:23:53,770 --> 01:23:57,760
So this demonstration
actually shows

1375
01:23:57,760 --> 01:24:01,750
that we can understand
the dipole radiation.

1376
01:24:01,750 --> 01:24:03,700
And the other
experimental results

1377
01:24:03,700 --> 01:24:05,870
are consistent with
the calculation

1378
01:24:05,870 --> 01:24:08,390
we have done in class.