1 00:00:00,060 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,030 Your support will help MIT OpenCourseWare 4 00:00:06,030 --> 00:00:10,120 continue to offer high quality educational resources for free. 5 00:00:10,120 --> 00:00:12,660 To make a donation or to view additional materials 6 00:00:12,660 --> 00:00:16,472 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,472 --> 00:00:20,249 at ocw.mit.edu. 8 00:00:20,249 --> 00:00:22,540 MARK HARTMAN: So here, I have just regular white light. 9 00:00:22,540 --> 00:00:24,750 And then I have a blue filter. 10 00:00:24,750 --> 00:00:27,450 And we said that if we put a diffraction grading in front, 11 00:00:27,450 --> 00:00:31,560 we can spread the white light out into its different colors. 12 00:00:31,560 --> 00:00:34,350 This essentially is an energy-- 13 00:00:34,350 --> 00:00:36,955 it detects the energy of the photons 14 00:00:36,955 --> 00:00:38,830 and it makes them go in different directions. 15 00:00:38,830 --> 00:00:43,060 So if I put my grading down in front, 16 00:00:43,060 --> 00:00:44,640 I can see that my white light gets 17 00:00:44,640 --> 00:00:46,650 spread out into all these different colors, 18 00:00:46,650 --> 00:00:48,120 just like we saw before. 19 00:00:48,120 --> 00:00:51,120 My blue light, however-- 20 00:00:51,120 --> 00:00:55,830 I can see this is part of the issue that we had yesterday. 21 00:00:55,830 --> 00:00:58,770 The blue light, if it was a perfect blue filter, 22 00:00:58,770 --> 00:01:00,600 would only let through blue. 23 00:01:00,600 --> 00:01:04,019 But right now, it's letting through some purple, some blue, 24 00:01:04,019 --> 00:01:07,200 some green, maybe a little bit of orange, and there's no red. 25 00:01:07,200 --> 00:01:09,172 So it is blocking out the red. 26 00:01:09,172 --> 00:01:11,130 We can't make a perfect filter that filters out 27 00:01:11,130 --> 00:01:15,480 exactly everything, but this isn't just dark red, 28 00:01:15,480 --> 00:01:17,490 there's actually no light there. 29 00:01:17,490 --> 00:01:20,400 But we're going to think about how could I-- 30 00:01:20,400 --> 00:01:26,610 and could I get a couple of the square grid patterns-- 31 00:01:26,610 --> 00:01:31,560 how could I represent this-- 32 00:01:31,560 --> 00:01:33,420 how can I represent the number of counts 33 00:01:33,420 --> 00:01:36,240 that I'm getting from different colors as a histogram? 34 00:01:39,120 --> 00:01:41,520 How can I represent those different colors? 35 00:01:41,520 --> 00:01:43,860 And ideas? 36 00:01:43,860 --> 00:01:44,670 [? Asif? ?] 37 00:01:44,670 --> 00:01:45,822 AUDIENCE: [INAUDIBLE] 38 00:01:45,822 --> 00:01:47,280 MARK HARTMAN: Again, nice and loud. 39 00:01:47,280 --> 00:01:48,360 I can't hear you. 40 00:01:48,360 --> 00:01:57,827 AUDIENCE: [INAUDIBLE] 41 00:01:57,827 --> 00:01:59,160 MARK HARTMAN: What do you mean-- 42 00:01:59,160 --> 00:02:01,080 what's less-- what's first and last? 43 00:02:01,080 --> 00:02:01,980 Tell me what's first. 44 00:02:01,980 --> 00:02:03,300 AUDIENCE: The first one is purple. 45 00:02:03,300 --> 00:02:04,174 MARK HARTMAN: Purple. 46 00:02:04,174 --> 00:02:05,520 AUDIENCE: Then comes green. 47 00:02:05,520 --> 00:02:06,281 MARK HARTMAN: OK. 48 00:02:06,281 --> 00:02:08,009 AUDIENCE: [INAUDIBLE] blue [INAUDIBLE] 49 00:02:08,009 --> 00:02:11,301 MARK HARTMAN: Well, purple, kind of green, blue, yellow. 50 00:02:11,301 --> 00:02:12,342 AUDIENCE: [INAUDIBLE] 51 00:02:12,342 --> 00:02:13,050 MARK HARTMAN: OK. 52 00:02:13,050 --> 00:02:14,460 And what would I represent? 53 00:02:14,460 --> 00:02:16,521 What would be the thing that I'm counting? 54 00:02:16,521 --> 00:02:18,612 AUDIENCE: [INAUDIBLE] 55 00:02:18,612 --> 00:02:19,320 MARK HARTMAN: OK. 56 00:02:19,320 --> 00:02:21,646 So at first you said, the power. 57 00:02:21,646 --> 00:02:24,270 We don't want to use words that we don't know exactly what they 58 00:02:24,270 --> 00:02:26,920 mean, but Juan? 59 00:02:26,920 --> 00:02:34,895 AUDIENCE: Maybe we can take that thing [INAUDIBLE] and split up 60 00:02:34,895 --> 00:02:39,888 the image and get the number of the counts of [? the protons ?] 61 00:02:39,888 --> 00:02:44,880 and then we can get that data and [? get ?] graph. 62 00:02:44,880 --> 00:02:46,350 MARK HARTMAN: Fantastic. 63 00:02:46,350 --> 00:02:49,350 So what I can do I could put a detector here-- 64 00:02:49,350 --> 00:02:50,836 very well done. 65 00:02:50,836 --> 00:02:52,710 I could put it detector here and I could say, 66 00:02:52,710 --> 00:02:55,470 well, over here, on this side, is where I'm getting blue, 67 00:02:55,470 --> 00:02:57,240 so add up all the counts from there, 68 00:02:57,240 --> 00:02:59,580 there, there, there, there, there, and there. 69 00:02:59,580 --> 00:03:01,530 And then I'll add up all the ones 70 00:03:01,530 --> 00:03:03,930 that are green on this strip. 71 00:03:03,930 --> 00:03:07,657 And then add up all the ones that are yellow on this strip. 72 00:03:07,657 --> 00:03:09,990 Then all the ones that are orange on this strip, and all 73 00:03:09,990 --> 00:03:12,870 the ones that are red on that strip. 74 00:03:12,870 --> 00:03:20,180 So if I had a detector there, I could make myself a histogram-- 75 00:03:20,180 --> 00:03:23,170 let me make sure I'm putting this on the right way-- 76 00:03:23,170 --> 00:03:25,260 I'm just going to go ahead and do it right here. 77 00:03:25,260 --> 00:03:26,010 I'm going to say-- 78 00:03:30,520 --> 00:03:33,336 move this down just a little bit. 79 00:03:33,336 --> 00:03:37,290 If I made a histogram, I'm going to measure-- 80 00:03:37,290 --> 00:03:47,970 I'm going to count up the number of photons 81 00:03:47,970 --> 00:03:54,380 of a certain color collected. 82 00:03:56,900 --> 00:03:59,600 And then over here, I'm going to represent the color. 83 00:03:59,600 --> 00:04:03,410 Or what is the word that we use to say color? 84 00:04:03,410 --> 00:04:05,622 What is color our experience of? 85 00:04:05,622 --> 00:04:06,651 AUDIENCE: Light. 86 00:04:06,651 --> 00:04:07,942 MARK HARTMAN: What about light? 87 00:04:07,942 --> 00:04:10,542 AUDIENCE: Uh-- [INAUDIBLE] flux? 88 00:04:10,542 --> 00:04:12,250 MARK HARTMAN: Flux, luminescence, color-- 89 00:04:12,250 --> 00:04:13,041 throw them all out. 90 00:04:13,041 --> 00:04:14,430 Maybe we'll get one right. 91 00:04:14,430 --> 00:04:14,930 David? 92 00:04:14,930 --> 00:04:16,070 AUDIENCE: Energy. 93 00:04:16,070 --> 00:04:17,899 MARK HARTMAN: Energy. 94 00:04:17,899 --> 00:04:21,589 So this is going to be the energy. 95 00:04:21,589 --> 00:04:22,490 And I could just-- 96 00:04:22,490 --> 00:04:26,150 I'm just going to start with this is say, blue down here. 97 00:04:26,150 --> 00:04:27,290 This is green. 98 00:04:27,290 --> 00:04:33,440 This is yellow, orange, and red. 99 00:04:33,440 --> 00:04:36,562 Except that's not the way I wanted to go, but that's OK. 100 00:04:36,562 --> 00:04:38,270 AUDIENCE: You can just make a bigger one. 101 00:04:38,270 --> 00:04:41,150 MARK HARTMAN: So what I can do is I can say, all right, 102 00:04:41,150 --> 00:04:43,790 let me count up the number of purple photons that I got. 103 00:04:43,790 --> 00:04:48,020 In this case, it kind of looks like they're all 104 00:04:48,020 --> 00:04:51,140 about the same amount. 105 00:04:51,140 --> 00:04:53,060 They all look about the same brightness. 106 00:04:58,460 --> 00:05:02,830 So I'm going to say for blue, I'm going to put a-- 107 00:05:02,830 --> 00:05:04,730 I'm going to use a better marker first. 108 00:05:12,370 --> 00:05:16,000 I'm going to say there's my blue and make it like that. 109 00:05:16,000 --> 00:05:18,730 Green looks about the same. 110 00:05:18,730 --> 00:05:21,040 Yellow-- there's my histogram. 111 00:05:21,040 --> 00:05:23,830 Orange and red. 112 00:05:23,830 --> 00:05:25,571 I'm just drawing a little bar there. 113 00:05:25,571 --> 00:05:27,070 Now, I can draw them so that they're 114 00:05:27,070 --> 00:05:29,980 kind of right next to each other if I wanted to, 115 00:05:29,980 --> 00:05:32,650 but then, I'd have to add in a few more colors. 116 00:05:32,650 --> 00:05:33,970 What about down here? 117 00:05:33,970 --> 00:05:37,690 If I have my blue filter and I spread that light out, 118 00:05:37,690 --> 00:05:41,380 how could I represent my histogram, again, 119 00:05:41,380 --> 00:05:46,570 of this is the energy and it goes blue-- 120 00:05:46,570 --> 00:05:52,690 again, blue, green, yellow, orange, and red. 121 00:05:52,690 --> 00:05:55,570 And I'm still going to record the number of photons 122 00:05:55,570 --> 00:05:56,639 collected. 123 00:06:00,950 --> 00:06:03,410 How would this one be different? 124 00:06:03,410 --> 00:06:06,284 AUDIENCE: It should only be blue. 125 00:06:06,284 --> 00:06:07,700 MARK HARTMAN: Well, let's actually 126 00:06:07,700 --> 00:06:09,920 look at what we've got here. 127 00:06:09,920 --> 00:06:14,309 How is it-- how is this purple part, or this blue part, here, 128 00:06:14,309 --> 00:06:16,100 how is it different from this blue up here? 129 00:06:18,764 --> 00:06:20,420 AUDIENCE: It's fainter. 130 00:06:20,420 --> 00:06:22,500 MARK HARTMAN: It's fainter, but what word would 131 00:06:22,500 --> 00:06:24,710 we use to describe that? 132 00:06:24,710 --> 00:06:27,320 AUDIENCE: The photons aren't as strong. 133 00:06:27,320 --> 00:06:30,390 MARK HARTMAN: The photons all have the same energy. 134 00:06:30,390 --> 00:06:32,940 Blue photons, regardless of whether they're up here or down 135 00:06:32,940 --> 00:06:36,004 there, have the same energy. 136 00:06:36,004 --> 00:06:37,170 What is it that's different? 137 00:06:37,170 --> 00:06:38,430 What am I-- 138 00:06:38,430 --> 00:06:42,690 What is my y-axis here? 139 00:06:42,690 --> 00:06:44,690 AUDIENCE: Flux. 140 00:06:44,690 --> 00:06:46,950 MARK HARTMAN: It's actually related to flux, 141 00:06:46,950 --> 00:06:48,741 and we're going to get to that in a second. 142 00:06:48,741 --> 00:06:51,860 But we're looking at the number of photons collected. 143 00:06:51,860 --> 00:06:57,140 If we put our detector up here in this same area, 144 00:06:57,140 --> 00:06:59,780 would we collect more or less photons 145 00:06:59,780 --> 00:07:01,662 than if we put our detector here? 146 00:07:01,662 --> 00:07:02,900 AUDIENCE: Less. 147 00:07:02,900 --> 00:07:05,210 MARK HARTMAN: We collect less because there's 148 00:07:05,210 --> 00:07:09,890 less flux of the color blue. 149 00:07:09,890 --> 00:07:13,250 So in comparison, we don't want to make our histogram 150 00:07:13,250 --> 00:07:14,290 bar that tall. 151 00:07:14,290 --> 00:07:16,940 We maybe want to make it blue. 152 00:07:16,940 --> 00:07:19,670 Let's maybe make it-- 153 00:07:19,670 --> 00:07:23,248 can I have another couple of markers please? 154 00:07:23,248 --> 00:07:24,739 AUDIENCE: There's one right-- 155 00:07:27,670 --> 00:07:30,870 MARK HARTMAN: This one seems to work a little bit better. 156 00:07:30,870 --> 00:07:33,160 And I'll throw that one out. 157 00:07:33,160 --> 00:07:36,040 What about green? 158 00:07:36,040 --> 00:07:39,700 Is there as many photons getting through here down here? 159 00:07:39,700 --> 00:07:42,670 No, so I want to make my green one a little bit shorter, 160 00:07:42,670 --> 00:07:44,035 still about the same as blue. 161 00:07:44,035 --> 00:07:44,785 What about yellow? 162 00:07:47,320 --> 00:07:50,300 Here, I've got yellow in this part. 163 00:07:50,300 --> 00:07:53,470 Here, I've still got some yellow. 164 00:07:53,470 --> 00:07:57,580 So maybe I'll make it still not very tall. 165 00:07:57,580 --> 00:08:00,690 What about orange and red? 166 00:08:00,690 --> 00:08:02,530 AUDIENCE: [INAUDIBLE] 167 00:08:02,530 --> 00:08:04,840 MARK HARTMAN: You don't have any orange and red. 168 00:08:04,840 --> 00:08:07,060 So my histogram would be down here at zero. 169 00:08:09,820 --> 00:08:11,830 So this is a way that I can represent 170 00:08:11,830 --> 00:08:18,280 the difference between this spectrum and this spectrum. 171 00:08:18,280 --> 00:08:22,030 So I'm going to give you a couple of definitions. 172 00:08:22,030 --> 00:08:23,920 Juan actually jumped right to the point 173 00:08:23,920 --> 00:08:26,650 when he said, well, we are collecting the number 174 00:08:26,650 --> 00:08:28,765 of photons of a certain color. 175 00:08:28,765 --> 00:08:31,390 But we're going to call-- we're going to review and we're going 176 00:08:31,390 --> 00:08:34,780 to say that this is-- 177 00:08:34,780 --> 00:08:36,010 so these are definitions. 178 00:08:41,190 --> 00:08:51,270 We said that flux is the number of photons collected. 179 00:08:54,305 --> 00:08:56,430 And again, I just want to make sure everybody knows 180 00:08:56,430 --> 00:08:59,400 when I write this little symbol, this pound sign, that 181 00:08:59,400 --> 00:08:59,942 means number. 182 00:08:59,942 --> 00:09:02,191 You can actually physically write out the order number 183 00:09:02,191 --> 00:09:02,940 if you want to. 184 00:09:02,940 --> 00:09:05,910 So the number of photons collected 185 00:09:05,910 --> 00:09:11,690 per second divided by the area of the collector. 186 00:09:16,740 --> 00:09:17,910 That's what we said before. 187 00:09:17,910 --> 00:09:19,451 It's just the total number of photons 188 00:09:19,451 --> 00:09:24,450 collected every second divided by the area of your collector. 189 00:09:24,450 --> 00:09:26,624 We're going to define-- 190 00:09:26,624 --> 00:09:28,290 what's the difference on this axis here? 191 00:09:28,290 --> 00:09:30,990 It's the number of photons collected, 192 00:09:30,990 --> 00:09:33,145 but it's the number of photons of a certain color. 193 00:09:37,990 --> 00:09:53,540 We are going to define intensity to be the number of photons 194 00:09:53,540 --> 00:10:09,410 of a certain color collected per second per area of collector. 195 00:10:16,110 --> 00:10:17,880 So what's the difference? 196 00:10:17,880 --> 00:10:19,350 Flux is just the total. 197 00:10:19,350 --> 00:10:21,600 We don't care about which color they are. 198 00:10:21,600 --> 00:10:24,120 That's what we had in our detector-- in our images, 199 00:10:24,120 --> 00:10:27,330 because we didn't always-- 200 00:10:27,330 --> 00:10:29,760 we just collected the numbers of photons. 201 00:10:29,760 --> 00:10:32,010 We couldn't tell what their energy was. 202 00:10:32,010 --> 00:10:34,040 Well now, if we know what their energies are, 203 00:10:34,040 --> 00:10:37,440 intensity is number of photons of a certain color collected 204 00:10:37,440 --> 00:10:40,830 per second divided by the area of the collector. 205 00:10:40,830 --> 00:10:43,710 Another way to write that, if we wanted 206 00:10:43,710 --> 00:10:46,320 to be a little more specific, we can also say it's 207 00:10:46,320 --> 00:11:09,570 the number of photons in a certain range of energy 208 00:11:09,570 --> 00:11:16,580 collected per second, per area of the collector. 209 00:11:19,580 --> 00:11:24,470 So these two phrases of a certain color 210 00:11:24,470 --> 00:11:29,060 and in a certain range of energy, those 211 00:11:29,060 --> 00:11:30,080 mean the same thing. 212 00:11:34,360 --> 00:11:38,382 Because remember, we said our experience of color or color 213 00:11:38,382 --> 00:11:40,090 to us, is just the way that we experience 214 00:11:40,090 --> 00:11:42,190 photons of different energy. 215 00:11:42,190 --> 00:11:46,210 And we just happen to say well, this range of energy 216 00:11:46,210 --> 00:11:51,010 right here, we're going to call this purple. 217 00:11:51,010 --> 00:11:55,870 This range of energy right here, we're going to call this blue. 218 00:11:55,870 --> 00:11:58,270 This range of energy we're going to call green. 219 00:11:58,270 --> 00:12:01,436 So it's kind of just based on the way that our bodies work. 220 00:12:01,436 --> 00:12:03,310 But what we really want to look is intensity. 221 00:12:03,310 --> 00:12:05,680 It's the number of photons in a certain range of energy. 222 00:12:10,160 --> 00:12:12,470 These two definitions are essentially the same thing. 223 00:12:16,460 --> 00:12:19,670 And then lastly, we're going to define what a spectrum is. 224 00:12:19,670 --> 00:12:22,840 We had talked yesterday about the electromagnetic spectrum. 225 00:12:22,840 --> 00:12:25,010 We're talking about these are spectrums. 226 00:12:25,010 --> 00:12:26,930 A little kid-- you can just say a spectrum 227 00:12:26,930 --> 00:12:29,690 is a rainbow, because this is what it looks like. 228 00:12:29,690 --> 00:12:36,620 For us though, a spectrum is going 229 00:12:36,620 --> 00:12:40,925 to be the composition of light from a source. 230 00:12:56,190 --> 00:12:58,920 We said, any time that we are collecting light, 231 00:12:58,920 --> 00:13:02,340 there must be a source that gave off that light, 232 00:13:02,340 --> 00:13:06,116 and we're going to figure out what is that light composed of? 233 00:13:06,116 --> 00:13:07,770 A simple way you can say is well it's 234 00:13:07,770 --> 00:13:10,080 composed of different colors. 235 00:13:10,080 --> 00:13:12,240 But colors are just the way that we experience, 236 00:13:12,240 --> 00:13:15,030 so we really want to say certain energies. 237 00:13:15,030 --> 00:13:17,370 So the spectrum, if you wanted to play Jeopardy, 238 00:13:17,370 --> 00:13:19,020 like and they said, blah, blah, blah, 239 00:13:19,020 --> 00:13:20,850 and you'd say what is a spectrum? 240 00:13:20,850 --> 00:13:26,580 The answer to the question, what is a spectrum or spectrum 241 00:13:26,580 --> 00:13:47,840 is the answer to the question, how many photons of each energy 242 00:13:47,840 --> 00:13:51,020 do we receive-- 243 00:13:51,020 --> 00:13:53,720 I'm sorry-- not do we receive, but do we collect. 244 00:14:00,240 --> 00:14:03,140 So if I were to ask you how many photons of each energy do 245 00:14:03,140 --> 00:14:09,122 we collect from a source, and you would say spectrum. 246 00:14:09,122 --> 00:14:10,580 We can-- we've already seen that we 247 00:14:10,580 --> 00:14:12,990 can represent the spectrum in two different ways. 248 00:14:12,990 --> 00:14:15,320 We can actually draw a picture of it 249 00:14:15,320 --> 00:14:19,750 or we can represent it as this histogram. 250 00:14:19,750 --> 00:14:22,130 And it's a histogram of the number 251 00:14:22,130 --> 00:14:24,950 of photons of a certain color, which we're 252 00:14:24,950 --> 00:14:30,080 going to call this intensity. 253 00:14:30,080 --> 00:14:36,423 Intensity versus energy is what a spectrum is.