WEBVTT 00:00:00.080 --> 00:00:02.794 This is College Physics Answers with Shaun Dychko. 00:00:03.685 --> 00:00:09.314 The RAC Bow radio telescope has a diameter of 300 meters 00:00:09.668 --> 00:00:13.154 and it receives wavelengths of four centimetres. 00:00:13.154 --> 00:00:14.565 These are radio waves. 00:00:15.320 --> 00:00:18.531 And the question is what is the minimum resolvable angle 00:00:18.657 --> 00:00:22.628 between two objects for this type of telescope. 00:00:23.280 --> 00:00:27.925 So the really good criterion tells us that, that's 1.22 times lambda over d. 00:00:28.365 --> 00:00:31.537 So the 1.22 times four times ten to the minus two meters. 00:00:31.708 --> 00:00:33.577 That's the wavelength written in meters 00:00:34.542 --> 00:00:41.131 and divide that by the size of the mirror which is 300 meters. 00:00:41.845 --> 00:00:45.954 So this thing is as a mirror that reflects the radio waves up to a sensor 00:00:45.954 --> 00:00:48.405 that's not shown in the picture it would be somewhere up here. 00:00:49.640 --> 00:00:54.285 So that's 1.63 times ten to the minus four radians is the minimum angle 00:00:54.285 --> 00:00:56.565 between two objects in order to distinguish them. 00:00:57.685 --> 00:01:04.485 And now part b says consider these objects to be two million light years away, 00:01:06.245 --> 00:01:09.645 how far are they separated given this minimum angle. 00:01:11.285 --> 00:01:15.565 Well we can think of this as a triangle between the two objects here and here 00:01:16.257 --> 00:01:19.697 and this angle is theta that we just found in part a. 00:01:20.485 --> 00:01:24.697 And so tangent of theta is gonna be this delta Y distance between the objects 00:01:24.988 --> 00:01:27.320 divided by the adjacent 00:01:27.320 --> 00:01:32.862 which is the distance from the earth here to one of the objects. 00:01:34.291 --> 00:01:37.811 So solving for delta Y by multiplying both sides by x 00:01:37.897 --> 00:01:39.954 we get the delta Y is x Tan theta. 00:01:40.794 --> 00:01:45.782 So that's two times ten to the six light years times tangent of 1.6267 00:01:45.782 --> 00:01:48.657 times ten to the minus four radians that we figured out up here. 00:01:49.805 --> 00:01:54.977 And that gives a 345 light years is the smallest separation 00:01:55.165 --> 00:01:58.754 that we can discern with this radio telescope.