Santa Fe Supernumerary Rainbow

Alternating dark and light rays converge to the horizon opposite the sun. How could that be? If I turned around and looked at the setting sun, I would see sunrays emanating from the sun, diverging out into space, and yet when I look away from the sun, I see rays converging on the horizon. Did the rays bend as they traveled from west to east? What we are seeing is one of nature’s most surprising optical illusions.

The apparent bending of the sun’s rays is a matter of linear perspective. The sun is very far away. Light rays from the sun are parallel by the time they reach the earth. When we look towards the sun, the rays appear to diverge upwards into the sky, and when we look away from the sun, toward the opposite horizon, they seem to converge to a vanishing point. In reality, the sun rays are perfectly parallel.

Consider what you would see standing on railroad tracks. When you look down the tracks in one direction, the parallel rails appear to converge. Look in the other direction, and they also seem to converge. This phenomenon is known as “linear perspective” and is fundamental to how we perceive parallel lines, vanishing points, and the horizon.

What causes these sun rays to form in the first place? Clouds do! Shadows form when sunlight is blocked by clouds. Air molecules, dust, and aerosols in the atmosphere scatter sunlight towards our eye. Cloud shadows reduce the amount of light incident on these small particles and therefore appear dark.

The bright and dark rays are known as crepuscular rays since they are more apparent during the crepuscular parts of the day (just after sunrise and just before sunset). The Latin word “crepuscular” means twilight.

Crepuscular rays are seen looking towards the setting sun over the Jemez Mountains, New Mexico.

The contrast of crepuscular rays increases when we look along the rays, towards the horizons, and look through a longer path length of shadowed air.  An increase in scatterers in the air will increase the contrast.  This is evident with forest fire smoke.

The contrast of the anti-crepuscular rays is high in front of the rainbow.  Raindrops scatter light back to our eye, cloud shadows reduce the amount of sunlight on the rain and therefore show up as a dark ray contrasting the bright rainbow.

Anti-crepuscular rays at sunrise, looking west these parallel rays appear to converge on the horizon, away from the sun.

It is easier to see crepuscular rays, those on the same horizon as the sun, either at sunrise or sunset, then it is to see anti-crepuscular rays on the horizon away from the sun. When you do notice crepuscular rays, turn around and look for anti-crepuscular rays on the opposite horizon.

Light rays that undergo the same deviation angle when refracting and reflecting from a raindrop reach the observer’s eye after traveling different path lengths inside the raindrop.   Although the path length can be defined by suing the concept of a light ray (“geometrical optics“) the wave nature of light now comes into play.

Light waves that travel different distances to our eye can be in phase, meaning the crests and troughs of the light wave are aligned. Other pairs of light  waves will be out of phase, with the crest of one wave arriving at our eye the same time a trough of another wave arrives.  The resulting light we see is the sum over all the rays in a given direction and over all phases.  The different waves interfere with each other.  Interference is a phenomena associated with waves, including electromagnetic waves (light), sound and water waves.

When multiple light waves arrive in phase, the light is brighter (“constructive interference“)  than when the incident light waves are out of phase (“destructive interference“).

Inside the primary arc of the rainbow we can see alternating bright and dark bands, of different colors (usually greens and purples).  These color bands are where the light waves that traveled different path lengths in the raindrop interfere in a way that reinforces (“constructive interference“)  the brightness (i.e. light waves that are in phase with each other), the dark areas between the bright areas are where “destructive interference” occurs (i.e. the light waves that reach our eye are out of phase with each other).

The size of the raindrops affects supernumerary bows.  Smaller raindrops result in wider spacing between the supernumeraries, making them easier to see.  The uniformity in the size of the raindrops also affects how well supernumeraries can be seen.  The more uniform the size of the raindrops, the stronger the supernumeraries will stand out.