00:01
In his problem, technically, you have double slit diffraction.
00:07
You have the interference pattern from double slit, but you have a diffraction envelope on top of that.
00:16
This is an intensity pattern.
00:18
So you can see that the intensity is modulated by the envelope.
00:24
So the smaller patterns is from the double slit, and the diffraction is obviously from the diffraction going to take place in any individual slit.
00:37
So it's a combination.
00:40
Now, let's talk about for the double slip.
00:43
So looking at the interference pattern alone, we leave alone the larger envelope.
00:50
So d -sign theta m, m -lamda, m is equal to 0, 1, 2, so on.
00:58
This is the maxima, the brights.
01:03
Now, independently of that, if you look at the diagram here, here's my distance to center distance between the slits.
01:09
That's d what i'm looking for first.
01:11
And i have some angle to the mth bright.
01:15
And ym is measured from the center line, the center maximum, to that bright fringe.
01:23
So you can write independently tangent theta m is equal to ym over l, the screen, the distance to the screen.
01:38
Now, if the angle is small, sine theta and tangent theta are eventually the same thing.
01:46
So i could replace sine theta with tangent theta, which is this.
01:50
I don't, if i go one step farther and replace all of it with theta, then theta must be in radiance, but we don't need to go that far here.
01:57
So if theta m small, sine theta m, basically tangent theta m are the same.
02:09
And like i said, that also means that they're theta m if you, theta, in radiance.
02:16
You have to use radiance then.
02:20
So we can put that in.
02:22
We get to d, y, m over l is equal to m lambda.
02:27
That gives me the d is equal to m lambda l over ym.
02:35
So that's how i could get d.
02:38
Now, let's check that for, let's check the theta small for m equals 5.
02:45
That's the best on your screen.
02:46
That one lines up the best with a line at 0 .8 centimeters.
02:51
That's at 5 .8 centimeters.
02:53
The center maximum is at 5 centimeters, so it's 0 .8 from the center line.
03:00
So now you might say what happens if this angle isn't small? say the angle is 25 degrees.
03:12
I'm not saying it will be.
03:13
And double slit usually there's no problem.
03:16
But what do you do? well, you would calculate the angle from the tangent and stick that angle directly into the formula for the maxima...