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It seems that some insects even use the sky’s polarization for navigation! Although the hairy ball theorem isn’t essential here, it still quietly shows up — and makes everything just a bit more beautiful. Literature: Heinze, Stanley and Steven M. Reppert. "Sun Compass Integration of Skylight Cues in Migratory Monarch Butterflies." Neuron, vol. 69, no. 2, 27 Jan. 2011, pp. 345-58, doi:10.1016/j.neuron.2010.12.025. Crawford, Frank S. Waves (The Berkeley Physics Course, Vol. 3). Education Development Center, Inc., Newton, Massachusetts, 1968. Library of Congress Catalog Card Number: 64-66016. Similar: • PHYS 201 | Polarized Scattering 2 - The Bl... Concepts of modern mathematics by Ian Nicholas Stewart [1981] (page 156) dipole • Electric Dipole Propagation Pattern [Dipol... Visualizing dipole radiation. Girwidz, R. V. (2016). Visualizing dipole radiation. European Journal of Physics, 37(6), 065206, pp 1-13. http://iopscience.iop.org/article/10.... 00:00:00 Intro and who this video is for 00:00:40 What is light? Plane wave 00:01:24 Polarization 00:01:47 Wavelengths 00:01:58 Wave packets 00:02:27 Polarized glasses — polarizer 00:03:07 A tricky question 00:03:18 Scatterers 00:03:40 The hairy ball theorem 00:04:14 Dipole source 00:05:05 The Sun is not a dipole 00:05:27 Molecules in the atmosphere 00:05:46 The main idea 00:06:29 How the Sun excites dipoles 00:06:49 What we see 00:07:27 Experiment 00:07:48 ADDITION–CORRECTION! This is the simplest Rayleigh model — but reality is more complex (as always!). There are often four neutral points (zero polarization): Babinet, Arago, Brewster, and a fourth one that appears under specific conditions. These points arise due to multiple scattering and other effects. For detailed analysis, see, for example, Kattawar, George W., et al. "Multiple scattered radiation emerging from Rayleigh and continental haze layers. 1: Radiance, polarization, and neutral points." Appl. Opt., vol. 15, no. 3, 1 Mar. 1976, pp. 632-47, doi:10.1364/AO.15.000632. or Horváth, Gábor, et al. "First observation of the fourth neutral polarization point in the atmosphere." J. Opt. Soc. Am. A, JOSAA, vol. 19, no. 10, 1 Oct. 2002, pp. 2085-099, doi:10.1364/JOSAA.19.002085. 00:08:16 Why the sky is blue 00:08:48 Why the sunset is red 00:09:10 Tyndall effect at home 00:10:11 Why the sky is not violet or black? I thank ChatGPT for creating some of the images (not all) and / @anpoddubny for bringing my attention to Tyndall effect #SoME4