When sunlight interacts with water droplets, it creates a rainbow. This arc of colors appears when light is refracted, reflected, and dispersed by water droplets. While a single rainbow is common, a double rainbow presents a rarer and more complex variation, with an additional, fainter arc.
The Secondary Rainbow
The second, fainter arc in a double rainbow is called a secondary rainbow. It typically appears outside the brighter primary rainbow, forming a larger and broader band. This secondary arc is less intense than its primary counterpart. Its presence is a result of a distinct light path within the water droplets.
The Physics of Double Reflection
A primary rainbow forms when sunlight enters a water droplet, undergoes one internal reflection, and then exits the droplet, refracting as it leaves. This process causes the light to emerge at an angle of approximately 40 to 42 degrees, with red light appearing at about 42 degrees and violet light at about 40 degrees. A secondary rainbow involves two internal reflections inside the raindrop. This additional reflection causes the light to emerge at a different angle, typically between 50 and 53 degrees. Red light exits around 50.4 degrees, and violet light exits around 53.4 degrees, positioning the secondary rainbow further out from the observer’s anti-solar point.
Distinguishing the Two Arcs
Several visual cues help differentiate the primary and secondary rainbows. A key difference is the reversal of color order in the secondary arc. While the primary rainbow displays red on its outermost edge and violet on its innermost edge, the secondary rainbow exhibits the opposite arrangement, with red on the inside and violet on the outside. The secondary rainbow is also fainter than the primary, largely because light is lost with each additional internal reflection. This additional light loss means the secondary rainbow possesses only a fraction of the primary’s brightness, sometimes as little as one-tenth the intensity or 43% of its total brightness.
Moreover, the secondary rainbow appears broader than the primary. A distinct dark band, known as Alexander’s Dark Band, often appears between the primary and secondary rainbows. This region of the sky is noticeably darker because raindrops in this specific area do not direct light towards the observer, creating a visual void between the two arcs.