A rainbow displays the colors red, orange, yellow, green, blue, and violet due to the phenomenon of dispersion, which occurs when sunlight passes through water droplets in the atmosphere. As light enters and exits the droplets, it bends (refracts) and separates into its constituent colors based on their wavelengths, with red having the longest wavelength and violet the shortest. This separation creates the distinct color bands we observe in a rainbow. The arrangement of these colors follows the order of the visible spectrum, often remembered by the acronym ROYGBIV.
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