By Emily Zhou “You’ll never find a rainbow if you’re looking down,” quotes Charlie Chaplin, the famous silent film comic actor. Indeed, the rainbow has developed over the centuries as a symbol of happiness, beauty, and magical blessings. However, many are unaware of the involvement of physics with the creation of these displays of light; by understanding the workings of science behind them, you may be able to see one every single day. Why are rainbows colorful?Rainbows usually result from refraction of light through suspended water droplets. In the 1660s, Isaac Newton conducted his prism experiments, which isolated a single beam of sunlight to shine through a glass prism and create a visible color spectrum as a multi-colored band of light. When Newton placed a second prism in front of the first, he was capable of combining the colors back into the beam of white light. His findings proved that the sunlight, which usually appears white to our eyes, is actually a combination of a range of all colors that are detectable to the human eye. Thus, when light travels across mediums of different density, (in this case from air to water), beams of light at different wavelengths are deflected at slightly different angles, bending to separate into individual colors. For example, red light, which has the longest wavelength on the spectrum of visible light, will be refracted at a steeper angle than blue light, which has a shorter wavelength. Difference in angle after refraction allows the human eye to distinguish the bands of light by color. Why are rainbows curved?The misnomer of rainbows based on their signature curved shapes invokes surprise in many who don’t realize that these optical illusions always form as full circles. In 1637, Rene Descartes noted the interaction between a single spherical droplet of water and the light that shines upon it; as the sun shone, light entered the droplet, struck the interior wall of the droplet, and was deflected out of the droplet. The light is also refracted slightly at the points where it entered and exited the droplet, forming an angle of deviation about 40 to 42 degrees. As sunlight departs in scattered directions, the human eye can pick up the different photons deflected directly towards them. Since the proportion of the rainbow seen is dictated by the position of the sun in the sky, it is usually cut off by the horizon line, creating an arc. How are double rainbows formed?Rainbows are generally categorized into primary, secondary, and supernumerary rainbows. Secondary rainbows are usually a more indistinct inverted band of color separated by a short distance from the outer ring of the primary rainbow, caused by double reflection of light inside a raindrop. As light is bounced off the interior of the droplet a second time, it acts as a mirror, reversing the colors to be seen in the opposite order. According to the principle of linear superposition, the displacement between waves of the same frequency allow constructive and destructive interference, changing the amplitude of the light and canceling some parts of the curve while brightening other parts. This phenomenon forms supernumerary rainbows are faint pastel bands bordering the primary or secondary rims formed by rays varying in length and path in phase. Other variations include cloud rainbows, fogbows, twinned rainbows, and lunar rainbows. How do I see a rainbow?Diversification in the time of day, the presence of water droplets, and your position influence the probability of viewing a rainbow. If you wish to view one after a natural shower outdoors, optimal conditions are having the sun to your back and looking 40 degrees above the horizon line at the anti-solar point directly above the shadow of your head in the afternoon, when the light from the water can reflect directly towards you. There may not be a pot of gold waiting to be found, but you can still admire “the product of physics working for your appreciation of beauty”, as stated by Kyle Hill. Citations“About Rainbows.” The National Center for Atmospheric Research | UCAR | UOP, eo.ucar.edu/rainbows/. Nave, R. “Rainbows.” Primary and Secondary Rainbows, HyperPhysics, hyperphysics.phy-astr.gsu.edu/hbase/atmos/rbowpri.html. Slowik, Edward. “Descartes' Physics.” Stanford Encyclopedia of Philosophy, Stanford University, 22 Aug. 2017, plato.stanford.edu/entries/descartes-physics/#StraCartPhys. “Interference.” PY106 - Elementary Physics II , Boston University, physics.bu.edu/~duffy/PY106/Interference.html. Society, National Geographic. “Rainbow.” National Geographic Society, 9 Oct. 2012, www.nationalgeographic.org/encyclopedia/rainbow/. Davidson, Michael W, and Kirill I Tchourioukanov. “Newton's Prism Experiments.” Molecular Expressions: Science, Optics and You, The Florida State University, 9 May 2016, 9:30 A.M., micro.magnet.fsu.edu/primer/java/scienceopticsu/newton/. Suggested Readings"Global rainbow thermometry for droplet-temperature measurement":
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-24-23-1696 "Much like white light, spacetime is also composed of a certain rainbow": https://www.sciencedaily.com/releases/2016/01/160114113514.htm
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