00:01
So it looks like we're analyzing the results of a diffraction experiment.
00:05
So a couple things to write down, and then we'll verify the data analysis and see what we have here.
00:13
But the idea is that the diffraction equation looks kind of like double slit, but with some important differences.
00:23
So we have a sine theta is equal to m lambda.
00:27
M is just an integer 0, 1, 2, etc.
00:32
And we'll talk about that.
00:34
Lambda is the wavelength of light used in the experiment, usually a laser or an led.
00:43
A is the slit width, and why don't we just call that w, make it a little bit easier to talk about slit width.
00:53
And the idea is we have laser light going through a slit.
01:02
Of width w, and you look at the pattern on a screen some distance are away.
01:08
Typically, what you measure is the width of what's called the central maximum.
01:15
And what that theta measures is the angle from the center where the slit is positioned out to the positions of the minima.
01:30
Okay, so that's supposedly a bright spot, and then we have minimum, and then we have another bright spot.
01:36
Etc.
01:39
And so there's a series of those spots that get a little bit harder and harder to identify the further out you go.
01:50
In any event, what you can do is you can figure out the theta m to each of the orders for the dark spots m equals 1, 2, etc.
02:07
And usually there's some things that you do with the other side as well, minus one, minus two.
02:17
But that gets into some careful measurements.
02:21
But if you make a plot of sine of theta m, which is usually about equal to theta m for small angles versus m, you should get a straight line with the slope if we rearrange this.
02:41
We have w equals, actually what we have is lambda over the width is equal to sinathea m over m.
03:05
So if we make that plot and we find the slope from it using trendline, say in excel, and we know the wavelength we should be able to find the width.
03:18
So i verified that, yeah, the slope is, in this case, point dot watt 7 .2.
03:26
What are the units? that has no units.
03:35
So the idea is the sign of an angle has no units, as you multiply it by something, but we're not doing that.
03:45
And m is just a counting number, so it has no units.
03:49
So this is very nice.
03:52
So your width, in this case, will have the same units that your lambda does.
03:57
And it looks like we used a helium -deon laser.
04:06
So the lambda is 632 .8 nanometers.
04:11
There's different ways to write that.
04:14
And we'll get that in terms of meters.
04:19
Okay, so the equation turns out to be 0 .0 .072.
04:25
In the denominator with the lambda, the numerator, is equal to w.
04:31
And we can simply put in our numbers, and our w should wind up to be in nanometers as well.
04:40
If we convert the nanometers, it will be a meters.
04:46
Ok, so 10 to the minus 9 is a nano.
04:50
And when we do that, we get 8 .8 times 10 to the minus 5 meters.
05:05
Now, if we compare that to the expected value, so usually you get the slit from a package.
05:13
So the expected w look to be 0 .1 millimeter.
05:23
So we'll say 0 .1 times 10 to the minus 3 meters, or 10 times 10 to the minus 5 meters if we want to compare directly.
05:40
And so there's really the only way to compare the expected to the measured with the information given so far is to do what's called a percent difference.
05:53
And that is typically the expected minus the measured.
06:06
Take an absolute value so you don't worry about plus minus, and then divide by the expected and then multiply by 100%.
06:24
Okay, so that in this case would be 10 minus 8 .8 over 10 times 100%.
06:35
Notice that the common exponent of times 100%.
06:41
10 to the minus 5, and the meters would cancel.
06:47
And that gives about 12%...