1 00:00:00,000 --> 00:00:07,920 What is optics, and how is algebra used in optics? 2 00:00:07,920 --> 00:00:13,200 Optics is the study of light, what it is, how it moves through space, and how it interacts 3 00:00:13,200 --> 00:00:14,680 with objects. 4 00:00:14,680 --> 00:00:19,920 Light can be controlled with lenses and mirrors, and these elements can be combined into optical 5 00:00:19,920 --> 00:00:25,320 instruments like telescopes, lasers, and cameras, just like the one being used to take this 6 00:00:25,320 --> 00:00:26,320 picture now. 7 00:00:26,320 --> 00:00:28,760 There are two types of telescopes. 8 00:00:28,760 --> 00:00:32,360 This is a refractor telescope that has a lens in the front. 9 00:00:32,360 --> 00:00:37,560 This is a reflector telescope that has no lens, but a mirror in the bottom of it. 10 00:00:37,560 --> 00:00:42,360 The light from the object goes through the tube, is concentrated by the mirror, to form 11 00:00:42,360 --> 00:00:45,340 an image which I see with my eye. 12 00:00:45,340 --> 00:00:49,120 Reflector telescopes are better for looking at faint objects like distant stars, and are 13 00:00:49,120 --> 00:00:51,520 therefore better for astronomy. 14 00:00:51,520 --> 00:00:56,400 I've taken this mirror out of a telescope to show you how the light is focused down 15 00:00:56,400 --> 00:00:59,320 to a spot at the focal point. 16 00:00:59,320 --> 00:01:04,320 This distance from the spot to the mirror is called the focal length, and there's an 17 00:01:04,320 --> 00:01:10,280 algebraic expression that relates the distance of the focal length, the distance u, to an 18 00:01:10,280 --> 00:01:15,080 object, and the distance v to the image formed by the mirror. 19 00:01:15,080 --> 00:01:19,960 That expression is 1 over f is equal to 1 over v plus 1 over u. 20 00:01:19,960 --> 00:01:24,760 We use this equation to test telescopes here at the X-ray Calibration Facility. 21 00:01:24,760 --> 00:01:28,800 We want to have the object source as far away from the telescope as possible, so we 22 00:01:28,800 --> 00:01:33,320 put it at the end of this tunnel, which is a third of a mile, or 500 meters away. 23 00:01:33,320 --> 00:01:37,840 Then, with the telescope at the other end, we measure the image formed by the mirror 24 00:01:37,840 --> 00:01:42,440 very precisely, to make sure that the telescope is built properly, and will focus the stars 25 00:01:42,440 --> 00:01:43,440 correctly. 26 00:01:43,440 --> 00:01:47,320 And that's how we use algebra in optics. 27 00:01:47,320 --> 00:01:53,720 Ground-based telescopes have revealed much over their nearly 400-year history, but they're 28 00:01:53,720 --> 00:01:56,240 really limited in what they can show us. 29 00:01:56,240 --> 00:02:01,600 Things like light pollution, cloud cover, and the Earth's turbulent atmosphere interfere 30 00:02:01,600 --> 00:02:04,920 with ground-based telescope observations. 31 00:02:04,920 --> 00:02:10,120 So in 1990, NASA launched the Hubble Space Telescope, an automated reflecting telescope 32 00:02:10,120 --> 00:02:13,400 which orbits the Earth every 97 minutes. 33 00:02:13,400 --> 00:02:17,360 The Hubble Telescope was named after Edwin Hubble, who discovered that the universe is 34 00:02:17,360 --> 00:02:22,040 expanding, and the more distant a galaxy, the faster it appears to move away. 35 00:02:22,560 --> 00:02:25,400 Remember the graph we analyzed at the beginning of the show? 36 00:02:25,400 --> 00:02:29,640 Well, Hubble created a graph that's not too different from our pizza graph. 37 00:02:29,640 --> 00:02:31,280 Check it out. 38 00:02:31,280 --> 00:02:36,560 Hubble's graph shows a linear relationship between distance and velocity. 39 00:02:36,560 --> 00:02:41,640 Remember the linear equation we used for the pizza graph, n times 2 equals p? 40 00:02:41,640 --> 00:02:48,720 Well, the linear equation for Hubble's graph is h times d equals v. h is the Hubble constant. 41 00:02:48,960 --> 00:02:52,240 It is similar to the number 2 in our previous equation. 42 00:02:52,240 --> 00:02:54,760 Remember there were two servings and one pizza? 43 00:02:54,760 --> 00:03:00,760 Anyway, d is the distance of the object, and v is the velocity, or speed, of the object.