WEBVTT 00:00:00.090 --> 00:00:02.490 The following content is provided under a Creative 00:00:02.490 --> 00:00:04.030 Commons license. 00:00:04.030 --> 00:00:06.330 Your support will help MIT OpenCourseWare 00:00:06.330 --> 00:00:10.690 continue to offer high-quality educational resources for free. 00:00:10.690 --> 00:00:13.320 To make a donation or view additional materials 00:00:13.320 --> 00:00:17.260 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.260 --> 00:00:18.220 at ocw.mit.edu. 00:00:21.176 --> 00:00:22.690 SHAOUL EZEKIEL: Now we're all set 00:00:22.690 --> 00:00:26.530 to look at the Fraunhofer diffraction pattern associated 00:00:26.530 --> 00:00:29.830 with the two-dimensional multi slits. 00:00:29.830 --> 00:00:33.500 The setup, again just to remind you, same as before-- 00:00:33.500 --> 00:00:34.990 here's the laser. 00:00:34.990 --> 00:00:39.000 Here's the beam from the laser reflected by this mirror 00:00:39.000 --> 00:00:42.190 and reflected by this mirror into a lens. 00:00:42.190 --> 00:00:45.640 Now, the lens here is used to expand the beam so that we 00:00:45.640 --> 00:00:51.580 can illuminate quite a chunk of a two-dimensional multiple 00:00:51.580 --> 00:00:52.990 slits. 00:00:52.990 --> 00:00:59.780 And then the diffracted light then goes on onto the screen. 00:00:59.780 --> 00:01:04.180 Now let's look at the two-dimensional multiple slits. 00:01:04.180 --> 00:01:06.700 What we have for you-- 00:01:06.700 --> 00:01:10.660 we have two Ronchi rulings. 00:01:10.660 --> 00:01:13.888 Each one has so many lines per inch. 00:01:13.888 --> 00:01:15.430 I'm not going to tell you because I'm 00:01:15.430 --> 00:01:18.890 going to leave that, again, as an exercise. 00:01:18.890 --> 00:01:22.870 So we have two identical Ronchi rulings that are crossed. 00:01:22.870 --> 00:01:25.970 The first one is fixed, which is over here. 00:01:25.970 --> 00:01:29.230 And the second one is attached to a rotation 00:01:29.230 --> 00:01:31.960 stage behind the first. 00:01:31.960 --> 00:01:35.320 So we can rotate the second Ronchi ruling, 00:01:35.320 --> 00:01:38.830 and then we can see what it does to the diffraction pattern. 00:01:38.830 --> 00:01:42.430 So now let's look at the screen. 00:01:42.430 --> 00:01:46.570 And then as we-- 00:01:46.570 --> 00:01:48.820 and as you can see on the screen now, 00:01:48.820 --> 00:01:53.110 you see the two-dimensional diffraction pattern 00:01:53.110 --> 00:01:56.320 of multiple slits. 00:01:56.320 --> 00:02:00.610 You can see that they look different than the single slit. 00:02:00.610 --> 00:02:02.280 We have a lot more dots. 00:02:02.280 --> 00:02:04.030 And again, as I say, I'm going to leave it 00:02:04.030 --> 00:02:06.790 as an exercise for you to figure them all out. 00:02:06.790 --> 00:02:08.590 Again, I'd like to draw attention 00:02:08.590 --> 00:02:13.850 to the dots around here, to all these cross terms 00:02:13.850 --> 00:02:16.190 in this pattern. 00:02:16.190 --> 00:02:22.420 So this pattern, then, is associated with the rulings 00:02:22.420 --> 00:02:24.160 crossed or orthogonal. 00:02:24.160 --> 00:02:26.350 Now what I'm going to do, I'm going 00:02:26.350 --> 00:02:33.880 to rotate the Ronchi ruling or the multiple slits 00:02:33.880 --> 00:02:35.400 in the back of the fixed one. 00:02:35.400 --> 00:02:35.900 See? 00:02:35.900 --> 00:02:38.240 So again you can see that the pattern rotates. 00:02:38.240 --> 00:02:42.130 Now, if we get rid of the insert and then look 00:02:42.130 --> 00:02:45.340 at the entire pattern, now you can 00:02:45.340 --> 00:02:54.400 see what happens as I rotate the Ronchi ruling in the back. 00:02:54.400 --> 00:02:55.200 Here we are. 00:02:55.200 --> 00:02:57.180 I could rotate the other way. 00:02:57.180 --> 00:03:00.660 And I hope you can see all the weak spots, which are 00:03:00.660 --> 00:03:03.900 the cross terms in the pattern. 00:03:03.900 --> 00:03:08.430 Now, in order for you to calculate the line spacings 00:03:08.430 --> 00:03:11.610 in the Ronchi rulings, I will give you 00:03:11.610 --> 00:03:14.220 the information you need. 00:03:14.220 --> 00:03:20.220 We have a plane wave that impinges on the Ronchi ruling. 00:03:20.220 --> 00:03:24.660 And the diameter of it is about a little over a centimeter. 00:03:24.660 --> 00:03:28.350 The screen is about 100 centimeters away 00:03:28.350 --> 00:03:31.560 from the Ronchi rulings. 00:03:31.560 --> 00:03:35.820 And the wavelength of the light, as before, is 6328. 00:03:35.820 --> 00:03:37.850 And with all this information, you 00:03:37.850 --> 00:03:42.480 should be able to calculate the number of lines 00:03:42.480 --> 00:03:45.750 per inch or millimeter of the Ronchi ruling. 00:03:45.750 --> 00:03:47.715 But you need still one more information, 00:03:47.715 --> 00:03:51.300 and that is the scale on the screen. 00:03:51.300 --> 00:03:52.920 And I'm not going to put a scale on. 00:03:52.920 --> 00:03:55.830 But I will tell you that the separation 00:03:55.830 --> 00:04:01.470 between these dots here, these pair of dots, 00:04:01.470 --> 00:04:04.450 is about 6 millimeters. 00:04:04.450 --> 00:04:06.750 So now, you have all the information 00:04:06.750 --> 00:04:11.970 you need to calculate the spacing between the lines 00:04:11.970 --> 00:04:14.400 in the Ronchi ruling. 00:04:14.400 --> 00:04:18.450 Now, just before we quit, if we can pull away-- 00:04:18.450 --> 00:04:22.800 the camera pull away-- and show you the extent of the pattern, 00:04:22.800 --> 00:04:26.310 now you can see the pattern extends quite a bit. 00:04:26.310 --> 00:04:34.010 And now we can come in again and back to where we were before. 00:04:37.300 --> 00:04:39.760 This completes our demonstrations 00:04:39.760 --> 00:04:43.560 of two-dimensional Fraunhofer diffraction pattern. 00:04:43.560 --> 00:04:47.790 Next, what we have for you is Fresnel diffraction. 00:04:47.790 --> 00:04:50.170 So when we come back, we'll have the setup 00:04:50.170 --> 00:04:53.140 rearranged so we can look at some Fresnel diffraction 00:04:53.140 --> 00:04:54.690 patterns.