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When sunlight shines through a raindrop, the water droplet acts like a tiny prism. As light enters the droplet, it bends, a process called refraction. It then reflects off the inside back of the droplet before exiting and bending again. Because white sunlight is actually a mixture of many different colors, each with its own unique wavelength, each color bends at a slightly different angle. The color with the longest wavelength bends the least, and this causes it to appear highest in the sky from our perspective.
This is why the familiar arc always follows the same color pattern, often remembered by the mnemonic ROY G. BIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet). The long wavelength of red light causes it to refract at an angle of about 42 degrees relative to the observer, placing it on the outer edge of the bow. Violet, with the shortest wavelength, bends the most and therefore appears on the inner edge at about 40 degrees.
Interestingly, if you ever spot a fainter secondary rainbow outside the first one, you'll notice its colors are reversed. This happens because the light reflects twice inside the raindrops before exiting. This second reflection flips the order, putting violet on the outside and red on the inside of the secondary arc.
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