WEBVTT 00:00:00.091 --> 00:00:02.742 This is College Physics Answers with Shaun Dychko. 00:00:03.188 --> 00:00:06.291 We're going to show that when a light ray travels from air into water, 00:00:06.531 --> 00:00:09.017 its wavelength changes such that it becomes 00:00:09.148 --> 00:00:12.445 0.75 times in the water when it was in the air. 00:00:13.411 --> 00:00:16.634 So, the speed of wave in a medium 00:00:17.011 --> 00:00:19.388 is its frequency times its wavelength in that medium 00:00:19.725 --> 00:00:23.794 and this is the speed in a vacuum divided by the index of refraction. 00:00:24.171 --> 00:00:28.902 And basically, index of refraction is defined this way, and that it's C over V. 00:00:29.594 --> 00:00:32.880 And, you can see that by showing how these are related. 00:00:34.565 --> 00:00:37.160 In which case, V equals C over N. 00:00:38.314 --> 00:00:40.000 And, this is the wave equation 00:00:40.000 --> 00:00:42.622 that the speed of a wave equals its frequency times its wavelength. 00:00:42.931 --> 00:00:47.582 So, we can solve this for the wavelength in a medium of some index of refraction N, 00:00:47.582 --> 00:00:51.554 that's why the subscript N is there by dividing both sides by frequency. 00:00:52.645 --> 00:00:56.308 And, we get the wavelength in a medium is the speed of light in a vacuum 00:00:56.640 --> 00:00:59.851 divided by frequency times the index of refraction of the medium. 00:01:00.931 --> 00:01:05.891 So, to answer this question, we take the wavelength in water 00:01:06.091 --> 00:01:07.954 and divide it by the wavelength in air. 00:01:08.737 --> 00:01:12.817 And then, we substitute this formula in place of each Lambda. 00:01:13.194 --> 00:01:15.742 So, we have speed of light divided by frequency 00:01:15.742 --> 00:01:18.040 times index of refraction of the water. 00:01:18.165 --> 00:01:20.937 This replaces Lambda and W. 00:01:21.685 --> 00:01:26.228 And then, we're going to divide by the wavelength in air, 00:01:26.377 --> 00:01:28.908 but I'm going to instead multiply by the reciprocal of this, 00:01:28.908 --> 00:01:31.354 because it gets messy when you divide a fraction by a fraction. 00:01:31.525 --> 00:01:35.217 So, we're going to multiply by the reciprocal of the wavelength in air. 00:01:35.474 --> 00:01:37.908 So, that's frequency times index of refraction of air 00:01:37.908 --> 00:01:39.914 divided by speed on light in a vacuum. 00:01:41.308 --> 00:01:44.885 Notice that the frequency does not get a subscript water and air 00:01:45.182 --> 00:01:46.914 because the frequency doesn't change. 00:01:47.005 --> 00:01:48.462 It's only the wavelength that changes. 00:01:49.891 --> 00:01:53.971 So, the C's and the F's cancel, and the ratio of wavelengths 00:01:53.971 --> 00:01:58.731 is the reciprocal of the ratio of the indexes of refraction. 00:01:59.302 --> 00:02:03.897 So, the wavelength in water divided by the wavelength in air 00:02:04.234 --> 00:02:07.634 is the index of refraction of air divided by the index of refraction of water. 00:02:07.800 --> 00:02:11.320 So, that's one divided by 1.33, which is 0.75.