1 00:00:00,120 --> 00:00:02,490 The following content is provided under a Creative 2 00:00:02,490 --> 00:00:04,059 Commons license. 3 00:00:04,059 --> 00:00:06,350 Your support will help MIT OpenCourseWare 4 00:00:06,350 --> 00:00:10,720 continue to offer high-quality educational resources for free. 5 00:00:10,720 --> 00:00:13,350 To make a donation or view additional materials 6 00:00:13,350 --> 00:00:17,290 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,290 --> 00:00:18,470 at ocw.mit.edu. 8 00:00:21,443 --> 00:00:22,860 PROFESSOR: Now we're ready to look 9 00:00:22,860 --> 00:00:26,550 at 2-dimensional Fraunhofer diffraction bands. 10 00:00:26,550 --> 00:00:28,590 The setup is the same as before. 11 00:00:28,590 --> 00:00:31,530 And just let me remind you of it. 12 00:00:31,530 --> 00:00:33,180 Here is the helium-neon laser. 13 00:00:33,180 --> 00:00:35,700 Here's the beam from the laser. 14 00:00:35,700 --> 00:00:38,670 Gets reflected by this mirror, then 15 00:00:38,670 --> 00:00:42,330 gets reflected by this mirror into this lens. 16 00:00:42,330 --> 00:00:44,580 Then the output of the lens falls 17 00:00:44,580 --> 00:00:47,850 on this 2-dimensional aperture. 18 00:00:47,850 --> 00:00:51,060 And then the diffracted light from this aperture 19 00:00:51,060 --> 00:00:55,620 then goes onto the screen. 20 00:00:55,620 --> 00:00:59,190 Now let's look at this 2-dimensional aperture here. 21 00:00:59,190 --> 00:01:03,720 It's made of two pairs of slits, a fixed 22 00:01:03,720 --> 00:01:07,080 one and an adjustable one. 23 00:01:07,080 --> 00:01:11,010 And the adjustable one is behind the fixed one. 24 00:01:11,010 --> 00:01:14,130 I'm not going to tell you the spacing, because I'm 25 00:01:14,130 --> 00:01:19,410 going to leave it as an exercise for you to find out later. 26 00:01:19,410 --> 00:01:22,140 So what I can do with the adjusted one, 27 00:01:22,140 --> 00:01:28,920 I can adjust the slit width by just moving this translation 28 00:01:28,920 --> 00:01:30,610 stage, OK? 29 00:01:30,610 --> 00:01:33,510 So now we're ready to look at the 2-dimensional Fraunhofer 30 00:01:33,510 --> 00:01:35,020 diffraction pattern on the screen. 31 00:01:35,020 --> 00:01:39,760 So now if we bring in the pattern on the screen, 32 00:01:39,760 --> 00:01:41,472 we can see-- 33 00:01:41,472 --> 00:01:42,930 this is before I do any adjustment. 34 00:01:42,930 --> 00:01:45,912 We can see, now, it's different from what we had before. 35 00:01:45,912 --> 00:01:46,870 It's in two dimensions. 36 00:01:46,870 --> 00:01:51,030 And also, what I'd like to bring to your attention 37 00:01:51,030 --> 00:01:55,660 is the cross terms, the cross terms over here and over here. 38 00:01:55,660 --> 00:01:58,740 I hope you can see it well, because they're very weak. 39 00:01:58,740 --> 00:02:01,530 But they're very important to the 2-dimensional diffraction 40 00:02:01,530 --> 00:02:02,340 band. 41 00:02:02,340 --> 00:02:04,130 As you can see, the diffraction band 42 00:02:04,130 --> 00:02:09,780 looks like the 2-dimensional Fourier transform of the field 43 00:02:09,780 --> 00:02:15,600 at the rectangular aperture. 44 00:02:15,600 --> 00:02:21,900 What I'm going to do now is vary the separation of one 45 00:02:21,900 --> 00:02:22,980 of the slits. 46 00:02:22,980 --> 00:02:25,710 That's the one behind. 47 00:02:25,710 --> 00:02:27,750 As you can see, the pattern changes. 48 00:02:27,750 --> 00:02:31,970 Now if we pull back with the camera-- if we pull back to-- 49 00:02:31,970 --> 00:02:32,890 OK, that's enough. 50 00:02:32,890 --> 00:02:40,140 Fine-- then you can see that I can change the spots-- 51 00:02:40,140 --> 00:02:42,890 the size of the spots on the screen. 52 00:02:47,320 --> 00:02:51,400 Now in order for you to calculate 53 00:02:51,400 --> 00:02:54,340 that we're seeing what we're supposed to be seeing, 54 00:02:54,340 --> 00:03:00,160 and also to get a feel of what the slit widths are, 55 00:03:00,160 --> 00:03:08,190 I'm going to now put in a scale over here. 56 00:03:24,420 --> 00:03:29,550 And the scale here, the markers represent 57 00:03:29,550 --> 00:03:31,630 a 2-centimeter spacing. 58 00:03:31,630 --> 00:03:37,710 Now, the separation between the aperture and the screen 59 00:03:37,710 --> 00:03:40,590 is a meter. 60 00:03:40,590 --> 00:03:46,500 And the wavelength of the laser is 6,328 angstroms. 61 00:03:46,500 --> 00:03:50,100 So now you should be able to calculate 62 00:03:50,100 --> 00:03:53,700 the size of the rectangular aperture 63 00:03:53,700 --> 00:03:58,320 just from the information I've given you. 64 00:03:58,320 --> 00:04:02,190 And here, again, let me do some adjustments 65 00:04:02,190 --> 00:04:04,790 so you can calculate it here. 66 00:04:04,790 --> 00:04:09,816 And then you can calculate the change in this slit width 67 00:04:09,816 --> 00:04:11,430 when I go to this position. 68 00:04:11,430 --> 00:04:13,650 Now you can see the high-order ones. 69 00:04:13,650 --> 00:04:17,279 Also, I'd like you to notice the intensity variations. 70 00:04:17,279 --> 00:04:19,800 It's not that easy to see on video, 71 00:04:19,800 --> 00:04:24,507 because the central spot is so bright. 72 00:04:24,507 --> 00:04:26,340 But at least you can see that, indeed, there 73 00:04:26,340 --> 00:04:28,320 are lots of spots available. 74 00:04:28,320 --> 00:04:34,150 And I hope you can calculate it with ease. 75 00:04:34,150 --> 00:04:37,380 Now that we've looked at the 2-dimensional Fraunhofer 76 00:04:37,380 --> 00:04:40,810 diffraction pattern of a rectangular aperture, 77 00:04:40,810 --> 00:04:44,578 we're now going to look at the circular aperture. 78 00:04:44,578 --> 00:04:46,620 We're going to look at the Fraunhofer diffraction 79 00:04:46,620 --> 00:04:51,540 band associated with various sizes of circular apertures. 80 00:04:51,540 --> 00:04:54,300 So when we come back, we'll have that ready for you 81 00:04:54,300 --> 00:04:57,170 and see what those look like.