WEBVTT 00:00:00.111 --> 00:00:02.400 This is College Physics Answers with Shaun Dychko. 00:00:02.933 --> 00:00:06.088 Structures on a bird feather act like a diffraction grating that reflects 00:00:06.488 --> 00:00:08.177 with 8,000 lines per centimeter. 00:00:08.577 --> 00:00:12.800 And the first order maximum is what we want to find. 00:00:12.800 --> 00:00:14.488 What is the angle to the first order of maximum 00:00:14.733 --> 00:00:17.866 given a wavelength that's incident to 600 nanometers. 00:00:19.355 --> 00:00:23.000 So the separation between the, 00:00:25.288 --> 00:00:29.000 we wouldn't call them slits because the light is not transmitting through 00:00:29.266 --> 00:00:31.400 the diffraction grating in this case it's reflecting off. 00:00:31.400 --> 00:00:34.755 So you might see these scratches in the structure 00:00:36.000 --> 00:00:38.533 and the separation between each scratch 00:00:38.777 --> 00:00:41.888 is gonna be one time state of the minus two meters that's one centimeter 00:00:42.355 --> 00:00:43.666 for every 8,000 lines. 00:00:44.066 --> 00:00:46.688 And this means there is one in a quarter micrometers 00:00:46.844 --> 00:00:51.088 between each line that's 1.25 times ten to the minus six meters between each line. 00:00:51.911 --> 00:00:54.533 We want to know the first order of maximum, so m is one 00:00:54.777 --> 00:00:56.422 and the wavelength is 600 nanometers 00:00:56.777 --> 00:00:58.577 and this formula, we can solve for theta 00:00:58.977 --> 00:01:00.933 by dividing both sides by d 00:01:01.888 --> 00:01:03.377 and then take the inverse sine of both sides. 00:01:03.955 --> 00:01:06.822 So the angle is going to be the inverse sine of the order times the wavelength 00:01:06.820 --> 00:01:10.533 divided by the separation between the cuts. 00:01:11.266 --> 00:01:13.444 So that's inverse sine of the order of one 00:01:13.622 --> 00:01:15.622 times 600 times ten to the minus nine meters 00:01:15.733 --> 00:01:18.377 divided by 1.25 times ten to the minus six meters 00:01:18.755 --> 00:01:21.288 giving an angle of 28.7 degrees 00:01:21.577 --> 00:01:22.711 to the first order of maximum 00:01:23.066 --> 00:01:25.177 with 600 nanometer wavelength light.