Sunlight interacting with water droplets creates the familiar rainbow through refraction and internal reflection. This optical phenomenon projects a spectrum of color when light enters the drop, reflects off the back, and exits toward the observer. A double rainbow occurs when a second, fainter arc appears just outside the primary one. Though the physical mechanism for this secondary arc is always present, its clear visibility is not guaranteed, raising the question of how frequently this dual phenomenon occurs.
The Physics Behind the Second Arc
The formation of the primary rainbow requires sunlight to enter a water droplet, refract, reflect once off the inner back surface, and then refract again as it exits the drop. This sequence causes the light to emerge at a maximum angle of approximately 42 degrees relative to the incoming sunlight. The secondary rainbow is generated by a slightly different, more complex light path within the droplet.
For the second arc to form, the light must undergo a double reflection inside the water droplet before exiting. After the initial refraction, the light reflects off the back surface, travels across the drop, and reflects a second time off the front surface. This double reflection fundamentally differentiates the two arcs.
The double reflection causes the light to emerge from the drop at a different, wider angle, ranging from about 50 to 53 degrees. This larger angle places the secondary rainbow arc outside the primary one in the sky. The light path for the secondary bow involves an extra reflection, which is a factor in its reduced intensity compared to the main arc.
Determining Rarity: Factors Influencing Visibility
Seeing a distinct double arc is considerably less common than seeing a primary rainbow. The secondary bow is technically always present, but it is often too dim for the human eye to perceive clearly. Therefore, the rarity lies not in the formation, but in the visibility.
Sun Angle and Intensity
A primary requirement for a highly visible double rainbow is a low angle of the sun, preferably below 42 degrees (early morning or late afternoon). The lower the sun, the higher the arcs appear above the horizon, allowing more of the circular structure to be seen. Since the double reflection causes a significant loss of light energy, the secondary arc requires maximum solar intensity to be noticeable.
Raindrop Size
The size of the raindrops also plays a substantial role in the clarity and color separation of both bows. Larger, more uniform raindrops, typically greater than one millimeter in diameter, produce a much more vivid and well-defined primary rainbow. These conditions are necessary to provide the brightness and strong color separation needed for the fainter secondary arc to rise above the background sky color.
Atmospheric Clarity
Atmospheric clarity is another significant factor in determining the visibility of the second arc. The air between the observer and the water droplets must have minimal haze or dust, which would otherwise scatter the already weakened light from the secondary reflection. The area of darker sky between the two bows is known as Alexander’s Dark Band. This dark region is a tell-tale sign of the atmospheric clarity required for a clear double rainbow sighting because light cannot exit the water droplets at the angles that fall between the primary and secondary arcs.
Key Visual Differences Between Primary and Secondary Bows
Once a secondary arc is sighted, two distinct visual characteristics set it apart from the primary rainbow. The most apparent difference is the intensity, as the secondary bow is noticeably fainter. The light forming the second arc loses considerable energy during its extra internal reflection, resulting in a brightness that can be as low as one-tenth that of the primary bow.
The second defining characteristic is the reversed order of the colors in the secondary arc. In the primary rainbow, the sequence places red on the outside edge and violet on the inside. The extra reflection within the water droplet causes a complete inversion of this color order. Consequently, the secondary rainbow displays violet on its outer edge and red on its inner edge, facing the primary arc.