1
00:00:01,063 --> 00:00:02,833
- So I got to be honest with you.

2
00:00:02,833 --> 00:00:05,833
Single slit interference is confusing.

3
00:00:05,833 --> 00:00:08,733
In fact, this argument I gave earlier,

4
00:00:08,733 --> 00:00:10,266
first time I heard about this,

5
00:00:10,266 --> 00:00:13,366
I thought this was just
mathematical mumbo-jumbo.

6
00:00:13,366 --> 00:00:16,600
I was, like, "What are you talking about?

7
00:00:16,600 --> 00:00:17,800
"This makes no sense."

8
00:00:17,800 --> 00:00:20,600
It seems like you could
argue anything like this,

9
00:00:20,600 --> 00:00:21,734
But you can't.

10
00:00:21,734 --> 00:00:23,667
And I'm going to try to
show you that in this video.

11
00:00:23,667 --> 00:00:25,500
Specifically, I'm going
to try to show you that

12
00:00:25,500 --> 00:00:28,966
this same argument that we
made for the destructive points

13
00:00:28,966 --> 00:00:32,436
won't work for the constructive points.

14
00:00:32,436 --> 00:00:33,667
And I think that will help a little bit.

15
00:00:33,667 --> 00:00:37,133
In other words, this half
wavelength relationship

16
00:00:37,133 --> 00:00:39,801
won't give the constructive
points, not exactly.

17
00:00:39,801 --> 00:00:42,100
It'll give it approximately,
but it won't work exactly.

18
00:00:42,100 --> 00:00:43,333
Why?

19
00:00:43,333 --> 00:00:45,467
All right, well, let's look at this.

20
00:00:45,467 --> 00:00:46,838
So let's get rid of all of that.

21
00:00:46,838 --> 00:00:47,933
So let's say we were going to try to

22
00:00:47,933 --> 00:00:51,187
derive the formula for
the constructive points.

23
00:00:51,187 --> 00:00:53,670
The first thing I'd do is,
I'd say, well, all right,

24
00:00:53,670 --> 00:00:57,301
again, each point on here
defracts when it gets to the hole.

25
00:00:57,301 --> 00:00:58,967
I'll have infinitely many sources,

26
00:00:58,967 --> 00:01:00,634
but I can't draw infinitely many

27
00:01:00,634 --> 00:01:03,302
so let's just consider eight again.

28
00:01:03,302 --> 00:01:05,902
One, two, three, four, eight,

29
00:01:05,902 --> 00:01:08,501
I get my interference pattern on the wall,

30
00:01:08,501 --> 00:01:10,701
and this is the graphical representation.

31
00:01:10,701 --> 00:01:13,401
I mean, they're really,
like, smudgy lines over here,

32
00:01:13,401 --> 00:01:18,035
but the graphical representation
looks something like this.

33
00:01:18,035 --> 00:01:21,301
You'd have a big old
bright spot in the middle.

34
00:01:21,301 --> 00:01:23,536
These points on the end,
you keep getting them,

35
00:01:23,536 --> 00:01:25,282
but I can't keep drawing them over here.

36
00:01:25,282 --> 00:01:26,301
So it keeps on going.

37
00:01:26,301 --> 00:01:28,108
And I'd pick a constructive point.

38
00:01:28,108 --> 00:01:30,569
Right here, this is a bright spot.

39
00:01:30,569 --> 00:01:33,002
So this, if I had to give a guess for

40
00:01:33,002 --> 00:01:35,501
what point would be totally
constructive for all the waves,

41
00:01:35,501 --> 00:01:37,067
I'd say it's that point.

42
00:01:37,067 --> 00:01:39,734
So I'd take my topmost wave,

43
00:01:39,734 --> 00:01:42,735
I'd say it travels a certain
distance to this bring spot.

44
00:01:42,735 --> 00:01:44,601
I'd take my wave in the middle,

45
00:01:44,601 --> 00:01:46,836
travels a certain distance to get here.

46
00:01:46,836 --> 00:01:49,766
I'd imagine my line straight down here,

47
00:01:49,766 --> 00:01:52,205
to try to figure out the
path length difference.

48
00:01:52,834 --> 00:01:56,566
Now remember, this here is
the path length difference.

49
00:01:56,566 --> 00:02:00,234
What should that be in order
for these two purple waves

50
00:02:00,234 --> 00:02:02,566
to interfere constructively over here?

51
00:02:02,566 --> 00:02:04,333
It's got to be an integer wavelength.

52
00:02:04,333 --> 00:02:06,433
So one wavelength, two wavelengths ...

53
00:02:06,433 --> 00:02:09,733
since this is the first
one from the center,

54
00:02:09,733 --> 00:02:11,500
we'll just say that's one wavelength.

55
00:02:12,515 --> 00:02:14,100
What's the relationship?

56
00:02:14,100 --> 00:02:15,134
We know that.

57
00:02:15,134 --> 00:02:18,434
Remember, the relationship
for the path length difference

58
00:02:18,434 --> 00:02:21,100
and the theta, the angle that it's at,

59
00:02:21,100 --> 00:02:23,400
was just d sine theta.

60
00:02:23,400 --> 00:02:28,400
D is, well, the whole width
of the hole -- it's a w.

61
00:02:29,633 --> 00:02:32,334
So what width is this?

62
00:02:32,334 --> 00:02:37,069
This width between this source
of light and this source

63
00:02:37,069 --> 00:02:39,267
would be w over two.

64
00:02:39,267 --> 00:02:40,428
And the relationship I'd get?

65
00:02:40,428 --> 00:02:41,134
All right.

66
00:02:41,134 --> 00:02:45,703
D is w over two times sine
of theta, would equal ...

67
00:02:45,703 --> 00:02:48,766
For this first point, I'd
say it's equal to lambda.

68
00:02:48,766 --> 00:02:50,967
So let's just assume
these two are interfering

69
00:02:50,967 --> 00:02:53,634
constructively at this point.

70
00:02:53,634 --> 00:02:55,700
And that would give me:

71
00:02:55,700 --> 00:03:00,533
w times sine theta equals two lambda

72
00:03:00,533 --> 00:03:03,869
gives me a constructive point.

73
00:03:03,869 --> 00:03:06,100
Now, I'm already confused.

74
00:03:06,100 --> 00:03:06,967
What?

75
00:03:06,967 --> 00:03:08,733
W sine theta equals two lambda?

76
00:03:08,733 --> 00:03:10,433
Constructive?

77
00:03:11,466 --> 00:03:14,367
We already proved this
is a destructive point.

78
00:03:14,367 --> 00:03:17,535
Remember our relationship
for the destructive points

79
00:03:17,535 --> 00:03:22,535
that we derived was: w
sine theta equals m lambda

80
00:03:24,200 --> 00:03:28,900
as long as m is not zero, but
one, two, three, four, five.

81
00:03:28,900 --> 00:03:33,900
These are giving destructive
for any m equals one, two,

82
00:03:35,900 --> 00:03:38,835
it could even be negative if
you want to consider down here,

83
00:03:38,835 --> 00:03:40,169
any integer.

84
00:03:40,169 --> 00:03:43,166
Looks like we just proved
these are constructive.

85
00:03:43,166 --> 00:03:44,866
How are these constructive?

86
00:03:44,866 --> 00:03:46,843
Well, they're not, really.

87
00:03:46,843 --> 00:03:49,600
They kind of are, but watch what happens.

88
00:03:49,600 --> 00:03:50,633
Just, here we go.

89
00:03:50,633 --> 00:03:53,005
So if I follow this argument through,

90
00:03:53,533 --> 00:03:54,501
the thing that fails ...

91
00:03:54,501 --> 00:03:56,333
Our previous argument's fine.

92
00:03:56,333 --> 00:03:58,201
The argument that fails
is this current one

93
00:03:58,201 --> 00:03:59,900
with constructive, because yes,

94
00:03:59,900 --> 00:04:02,738
these two are constructive
there, but watch.

95
00:04:03,466 --> 00:04:04,600
This point here, now I ...

96
00:04:04,600 --> 00:04:06,367
just remember the game we played.

97
00:04:06,367 --> 00:04:08,400
We said if these two are constructive,

98
00:04:08,400 --> 00:04:10,400
then the rest of them
should all be constructive.

99
00:04:10,400 --> 00:04:11,533
Is that so?

100
00:04:11,533 --> 00:04:13,533
Well, let's go down
one, let's go down one.

101
00:04:14,533 --> 00:04:16,866
I imagine these two waves getting here.

102
00:04:17,800 --> 00:04:18,976
So far it's looking good.

103
00:04:18,976 --> 00:04:20,932
They're at the same angle.

104
00:04:20,933 --> 00:04:23,000
They're the same distance between them.

105
00:04:23,000 --> 00:04:27,100
I mean, this length here
is still w over two.

106
00:04:27,100 --> 00:04:31,633
So I'd still get w over
2, sine of the same angle,

107
00:04:31,633 --> 00:04:33,700
because it's the same point on the wall.

108
00:04:33,700 --> 00:04:36,669
So if w over two is the same,
sine of the theta's the same,

109
00:04:36,669 --> 00:04:40,266
then that's got to also be path
length difference of lambda,

110
00:04:40,266 --> 00:04:42,833
which means these two blue waves

111
00:04:42,833 --> 00:04:45,333
also interfere constructively.

112
00:04:45,333 --> 00:04:48,233
So this is looking pretty
good, which is kind of bad.

113
00:04:48,233 --> 00:04:49,133
I'll show you why.

114
00:04:49,133 --> 00:04:52,500
These two would also be constructive.

115
00:04:52,869 --> 00:04:55,144
Well, is this a constructive point?

116
00:04:55,144 --> 00:04:57,100
Is m equals two a constructive point

117
00:04:57,100 --> 00:04:58,495
or a destructive point in that end?

118
00:04:58,495 --> 00:05:00,034
It's a destructive point.

119
00:05:00,034 --> 00:05:03,266
This argument's failing,
and it fails because ...

120
00:05:03,266 --> 00:05:04,300
watch this ...

121
00:05:04,300 --> 00:05:05,600
Even though these two purple ones

122
00:05:05,600 --> 00:05:08,800
interfere constructively over
here -- here's a wave cycle.

123
00:05:08,800 --> 00:05:12,134
Even though the two purple
ones meet up constructively,

124
00:05:12,134 --> 00:05:14,166
let's say the top one was there,

125
00:05:14,166 --> 00:05:16,733
that means the one in the
middle, this one here,

126
00:05:16,733 --> 00:05:18,266
was also at the peak.

127
00:05:18,266 --> 00:05:20,038
So those two interfere constructively.

128
00:05:20,038 --> 00:05:21,167
How about the next two?

129
00:05:21,167 --> 00:05:23,234
Well, those two are going to interfere ...

130
00:05:23,234 --> 00:05:25,533
Now maybe those two are,
like, at this point.

131
00:05:26,467 --> 00:05:29,533
They're both constructive,
but they're not necessarily

132
00:05:29,533 --> 00:05:31,267
the same as the two purple ones.

133
00:05:31,267 --> 00:05:33,166
And how about the orange ones?

134
00:05:33,166 --> 00:05:34,700
Orange ones might be constructive,

135
00:05:34,700 --> 00:05:37,133
because they're both at the
same point in the phase,

136
00:05:37,133 --> 00:05:40,100
but they're not at the same
point as all the rest of them.

137
00:05:40,100 --> 00:05:41,300
You can have more.

138
00:05:41,300 --> 00:05:43,479
What about these down here?

139
00:05:43,479 --> 00:05:44,833
Oh, these might be down here.

140
00:05:44,833 --> 00:05:47,800
Those two together are also constructive,

141
00:05:47,800 --> 00:05:49,733
but you see the problem.

142
00:05:49,733 --> 00:05:53,066
Even though these two are constructive,

143
00:05:53,066 --> 00:05:55,733
this one's not constructive with this guy,

144
00:05:55,733 --> 00:05:56,874
and these all add up.

145
00:05:56,874 --> 00:06:00,033
In fact, for the most part, they cancel.

146
00:06:00,033 --> 00:06:01,400
That's why these are so little.

147
00:06:01,400 --> 00:06:06,100
You get these weak, you get
these really weak fringes

148
00:06:06,100 --> 00:06:08,077
on the sides of the single slit,

149
00:06:08,077 --> 00:06:09,634
because you're not going to get points

150
00:06:09,634 --> 00:06:12,500
where they all add up
really well necessarily.

151
00:06:12,500 --> 00:06:15,567
You get points where a lot
of them sort of cancel out.

152
00:06:15,567 --> 00:06:18,367
And it doesn't completely cancel those.

153
00:06:18,367 --> 00:06:21,567
Here's where I lied, for
the diffraction grating.

154
00:06:21,567 --> 00:06:23,125
Remember, for the diffraction grating ...

155
00:06:23,125 --> 00:06:24,353
Let me get rid of this.

156
00:06:24,353 --> 00:06:27,567
For the diffraction grating,
we had a single line

157
00:06:27,567 --> 00:06:29,700
and we made a ton of holes in it.

158
00:06:29,700 --> 00:06:32,034
And I said that diffraction
gratings are great

159
00:06:32,187 --> 00:06:34,466
because, if you come over to here,

160
00:06:34,466 --> 00:06:36,533
you make a ton of holes in here,

161
00:06:36,533 --> 00:06:39,875
instead of getting a
smudgy pattern on the wall,

162
00:06:39,875 --> 00:06:42,666
you get a big bright
spot right in the middle

163
00:06:42,666 --> 00:06:47,403
and then a well-defined,
well-defined, well-defined

164
00:06:47,403 --> 00:06:52,000
on each side of them, evenly
spaced, basically just zero

165
00:06:52,000 --> 00:06:55,000
and then extremely sharp.

166
00:06:56,633 --> 00:06:59,904
And then zero and then extremely sharp.

167
00:07:00,438 --> 00:07:02,933
And then zero and extremely sharp.

168
00:07:02,933 --> 00:07:05,300
And the whole argument I
made for defraction gradings

169
00:07:05,300 --> 00:07:07,903
was that the reason it's zero in between,

170
00:07:09,466 --> 00:07:11,100
the reason these are giving zero

171
00:07:11,100 --> 00:07:13,167
everywhere except these
constructive points

172
00:07:13,167 --> 00:07:15,867
was precisely because ...

173
00:07:16,667 --> 00:07:18,233
we come back over to here ...

174
00:07:20,167 --> 00:07:22,833
was precisely because of
this effect right here.

175
00:07:22,833 --> 00:07:26,367
This effect where they,
for the most part, cancel.

176
00:07:26,367 --> 00:07:27,433
Now I'm saying,

177
00:07:27,433 --> 00:07:32,400
"Eh, they don't actually
completely cancel necessarily."

178
00:07:32,400 --> 00:07:35,968
So these wiggles here are actually

179
00:07:37,206 --> 00:07:39,468
in a defraction grading pattern.

180
00:07:39,468 --> 00:07:41,800
They're just so small and unpronounced,

181
00:07:41,800 --> 00:07:43,940
compared to these, you
don't really notice them.

182
00:07:43,940 --> 00:07:44,567
What I'm saying is,

183
00:07:44,567 --> 00:07:47,605
if I wanted to draw
this more realistically,

184
00:07:47,605 --> 00:07:50,800
I would definitely have
this bright spot right here,

185
00:07:50,800 --> 00:07:55,566
but I'd have this in
between small variations,

186
00:07:55,566 --> 00:07:57,833
small points where it
becomes a little more,

187
00:07:57,833 --> 00:08:00,400
a little less, constructive
or destructive.

188
00:08:00,400 --> 00:08:05,101
What you have for a single slit is this:

189
00:08:05,101 --> 00:08:07,433
just one center bright spot.

190
00:08:07,433 --> 00:08:09,000
It's not going to be as well-defined

191
00:08:09,000 --> 00:08:11,733
because it's a defraction
grading, it's a single slit.

192
00:08:11,733 --> 00:08:14,533
But you still get these.

193
00:08:14,533 --> 00:08:17,267
You get these weird wiggles
that, for the most part,

194
00:08:17,267 --> 00:08:20,433
you ignore for a defraction
grading, but they're there.

195
00:08:20,433 --> 00:08:23,269
And for a single slit,
that's kind of all you got.

196
00:08:23,269 --> 00:08:25,567
So, can't really ignore it so much.

197
00:08:25,567 --> 00:08:26,966
Those are going to be there.

198
00:08:26,966 --> 00:08:29,567
It's because these
don't completely cancel.

199
00:08:29,567 --> 00:08:31,833
Our argument does not work.

200
00:08:31,833 --> 00:08:33,166
It works in the sense that

201
00:08:33,166 --> 00:08:35,445
two of these might be constructive.

202
00:08:35,445 --> 00:08:38,232
That means, you can pair
these off in constructive,

203
00:08:38,232 --> 00:08:42,465
but they won't all be at the
same point on their phase,

204
00:08:42,466 --> 00:08:46,033
which would give you a completely
constructive point there.

205
00:08:46,033 --> 00:08:47,607
So that's why we don't ...

206
00:08:47,607 --> 00:08:50,500
it's hard to find an exact formula.

207
00:08:50,766 --> 00:08:54,000
What's the formula for
the constructive points?

208
00:08:54,000 --> 00:08:57,135
Well, getting this formula
-- not quite as simple.

209
00:08:57,135 --> 00:09:00,342
You need to know a little
bit more physics to do that.

210
00:09:00,342 --> 00:09:03,933
And so, typically, in
introductory physics classes,

211
00:09:03,933 --> 00:09:07,866
you aren't asked to
find the exact locations

212
00:09:07,866 --> 00:09:10,966
of the most constructive points over here.

213
00:09:10,966 --> 00:09:14,734
Even these most constructive
points partially cancel.

214
00:09:14,734 --> 00:09:18,066
You do know how to find
the exact locations

215
00:09:18,066 --> 00:09:20,334
of the destructive points, though.

216
00:09:20,334 --> 00:09:23,500
And, if you wanted an approximate location

217
00:09:23,500 --> 00:09:24,973
of a constructive point,

218
00:09:24,973 --> 00:09:27,433
well, you can find the exact location

219
00:09:27,433 --> 00:09:30,066
of two neighboring destructive points,

220
00:09:30,066 --> 00:09:31,500
which, if you really wanted to,

221
00:09:31,500 --> 00:09:33,400
I mean, the constructive's in there,

222
00:09:33,400 --> 00:09:35,500
approximately in the middle,

223
00:09:35,500 --> 00:09:38,133
if you wanted to get a rough idea.

224
00:09:38,133 --> 00:09:40,200
I can still see some of
you being upset, though.

225
00:09:40,200 --> 00:09:40,733
You might say, "Wait.

226
00:09:40,733 --> 00:09:42,366
"Hold on a minute.

227
00:09:42,366 --> 00:09:44,166
"So we're saying this formula's good

228
00:09:44,166 --> 00:09:47,833
"for the destructive
points, but is this problem

229
00:09:47,833 --> 00:09:49,733
"we ran into for constructive points

230
00:09:49,733 --> 00:09:52,166
"also a problem for destructive points?"

231
00:09:52,166 --> 00:09:53,877
And it's not.

232
00:09:53,877 --> 00:09:55,682
I doesn't matter if
they're at different points

233
00:09:55,682 --> 00:09:57,700
in their phase for the destructive,

234
00:09:57,700 --> 00:09:59,712
because each pair cancels.

235
00:09:59,712 --> 00:10:03,266
In other words, when we
ran through this argument

236
00:10:03,266 --> 00:10:05,113
for the destructive points, look at --

237
00:10:05,113 --> 00:10:09,333
if these two purple ones
cancel, then they cancel.

238
00:10:09,333 --> 00:10:12,400
I mean, if one was at the
peak, and then the other's

239
00:10:12,400 --> 00:10:16,033
at the trough or the valley,
those add up to zero.

240
00:10:16,033 --> 00:10:16,740
They're gone.

241
00:10:16,740 --> 00:10:19,400
Any effect they might have had

242
00:10:19,400 --> 00:10:22,512
on light hitting this point
on the screen is gone,

243
00:10:22,512 --> 00:10:23,800
completely negated.

244
00:10:23,800 --> 00:10:25,533
And so, what about the next two,

245
00:10:25,533 --> 00:10:27,466
These two blue ones?

246
00:10:27,466 --> 00:10:30,133
Well, those two, if these
two purple ones cancel,

247
00:10:30,133 --> 00:10:32,866
remember the argument went
that these two blue ones

248
00:10:32,866 --> 00:10:33,800
would have to cancel.

249
00:10:33,800 --> 00:10:35,433
So no matter where they're at,

250
00:10:35,433 --> 00:10:37,466
they're at some different
point on this cycle,

251
00:10:37,466 --> 00:10:40,200
let's say one's here and the other's ...

252
00:10:40,200 --> 00:10:41,473
well, that looked like the same.

253
00:10:41,473 --> 00:10:43,367
So let's say one's here and the other's

254
00:10:43,367 --> 00:10:48,367
at this corresponding 180
degree out-of-phase point.

255
00:10:48,965 --> 00:10:50,271
Well, they still cancel.

256
00:10:50,271 --> 00:10:51,700
That adds up to zero.

257
00:10:51,700 --> 00:10:53,472
And so it doesn't even matter that they're

258
00:10:53,472 --> 00:10:55,200
at different points in their phase.

259
00:10:55,200 --> 00:10:55,966
It doesn't matter.

260
00:10:55,966 --> 00:10:58,200
No matter where they're
at, one's 180 degrees

261
00:10:58,200 --> 00:11:01,901
out of phase with the other,
every contribution cancels out.

262
00:11:01,901 --> 00:11:05,200
You add up a bunch of zeros, you get zero.

263
00:11:05,200 --> 00:11:07,694
So destructive works fine.

264
00:11:07,694 --> 00:11:10,700
You don't run into the same
problem with constructive.

265
00:11:10,700 --> 00:11:12,667
It's a problem for the constructive points

266
00:11:12,667 --> 00:11:15,767
because these might add
up to some big number,

267
00:11:15,767 --> 00:11:18,033
and then the blue ones add
up to a different number,

268
00:11:18,033 --> 00:11:20,266
and the orange one adds
up to a different number,

269
00:11:20,266 --> 00:11:23,200
and then the red ones might
add up to a negative number,

270
00:11:23,200 --> 00:11:25,066
and you keep getting
these different numbers.

271
00:11:25,066 --> 00:11:27,933
You try to add them all
up, well, what do you get?

272
00:11:27,933 --> 00:11:30,200
That's why this formula's
not so easy to find.

273
00:11:30,723 --> 00:11:33,739
Adding up zeros, that's
easy -- just gives you zero.

274
00:11:33,739 --> 00:11:38,739
So, I hope I showed you that
this crazy mumbo-jumbo argument

275
00:11:38,876 --> 00:11:41,105
can't say anything whatsoever.

276
00:11:41,767 --> 00:11:45,834
And hopefully, that gives you
a little more justification,

277
00:11:45,834 --> 00:11:47,366
hopefully it makes you
believe a little more

278
00:11:47,366 --> 00:11:48,700
into this formula

279
00:11:48,700 --> 00:11:50,800
that we derived for
the destructive points.

280
00:11:50,800 --> 00:11:52,533
Those it does work for.

281
00:11:52,533 --> 00:11:55,247
And so, we can find
destructive points just fine.

282
00:11:55,247 --> 00:11:57,833
One more thing we can find is the width

283
00:11:57,833 --> 00:12:02,194
of this center bright fringe
here, the center bright spot.

284
00:12:02,194 --> 00:12:03,300
It's going to be wide.

285
00:12:03,776 --> 00:12:06,333
And since this goes to m equals one,

286
00:12:06,333 --> 00:12:10,334
now that first destructive
is over here, this is wide.

287
00:12:10,334 --> 00:12:15,334
This is, in fact, twice
as wide as all of these

288
00:12:15,638 --> 00:12:18,334
between these destructive points.

289
00:12:18,334 --> 00:12:21,041
And how wide is this?

290
00:12:21,041 --> 00:12:22,800
Well, you can find the angle

291
00:12:22,800 --> 00:12:26,064
to this first destructive
point up here, m equals one.

292
00:12:26,064 --> 00:12:29,200
You can find it to the
m equals negative one.

293
00:12:29,200 --> 00:12:30,586
You do a little trigonometry,

294
00:12:30,586 --> 00:12:32,359
you can actually get this length.

295
00:12:32,359 --> 00:12:34,225
That's another thing you can find exactly,

296
00:12:34,225 --> 00:12:37,000
is the width of this center bright spot,

297
00:12:37,000 --> 00:12:39,700
and the location is right in the center.

298
00:12:40,173 --> 00:12:42,866
But the location of these
constructive points up here,

299
00:12:42,866 --> 00:12:45,901
the exact location,
that's a little harder.

300
00:12:45,901 --> 00:12:49,069
You can find their width
again, because you can find

301
00:12:49,069 --> 00:12:51,302
the locations where they terminate.

302
00:12:51,302 --> 00:12:55,033
But finding where it
actually peaks in here,

303
00:12:55,033 --> 00:12:56,500
don't have an exact formula.

304
00:12:56,500 --> 00:12:59,435
We do have an exact
formula for the single slit

305
00:12:59,435 --> 00:13:01,369
destructive points.

306
00:13:01,369 --> 00:13:03,833
And that's typically what
you're going to have to find

307
00:13:03,833 --> 00:00:00,000
in these problems.