The secondary rainbow is a rainbow of radius 51 degrees, occasionally visible outside the primary rainbow. It is produced when the light entering a cloud droplet is reflected twice internally and then exiting the droplet. The color spectrum is reversed in respect to the primary rainbow, with red appearing on its inner edge. A tertiary rainbow has, to my knowledge, never been observed. It should be in the direction of the sun, but since it will be very faint (due to three internal reflections in a water droplet), and also in the brightness of the sky near the sun, it gets lost in the glare. However, try to look for it - not necessarily when a bright primary and/or secondary rainbow is visible, since it will be in a totally different part of the sky!
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