Science of rainbows explains much, steals the magic not at all

Dec 5, 2016 by Scott McDowell

Rainbows require sunlight and moisture in the air but it’s the magic angle of 42 degrees that causes rainbows to exist.

Light rays from the sun appear to the naked eye as white light, but each ray contains a broad range of wavelengths. As a ray passes through water droplets in the atmosphere, the different wavelengths of light separate into a spectrum of colors that are nicely displayed in rainbows. For a single (primary) rainbow, the colors transition inward from red to orange, yellow, green, blue, indigo and violet.

The position of a rainbow is specific to each observer but always occurs with the sun at the observer’s back as he/she faces the “anti-solar point” — the geometric center of the rainbow. A rainbow’s appearance is dependent upon the size of the water droplets reflecting the sun’s rays. Large drops generate narrow rainbows with intense colors while small droplets produce broader bows with less color saturation.

Light rays that enter a water droplet are reflected outward at an angle of 42 degrees from the incoming angle for red light, which we observe at the top of the rainbow. Other colors that have smaller reflection angles are situated slightly lower in the primary rainbow as we look downward from its highest point.

The top of a rainbow can only reach 42 degrees above an observer’s land or sea horizon. This maximum height occurs at sunrise or sunset when the anti-solar point sits exactly on the horizon. At this time, the rainbow is fullest and is a perfect semi-circle with ends that are perpendicular to the horizon.

As the sun rises in a morning sky, a rainbow continually descends. Eventually, only the top arc is visible before it sets below the horizon with a rising sun. Rainbows cannot appear when the sun is high in the sky because the anti-solar point has descended well below the horizon.

Interestingly, the probability of seeing a rainbow is greatest at high latitudes where the sun is lower in the sky for more hours per day than at tropical latitudes.

If we view a rainbow while aloft, it forms a complete circle from the observer’s perspective because water droplets can exist beneath the aircraft, not just above. From a technical standpoint, we see a circular bow because we can see more than 42 degrees below the anti-solar point.

A ray of sunlight can be reflected more than once within a single water droplet. Upon escape, it can create a secondary rainbow above and concentric with the primary bow. The secondary has a radius of 51 degrees and is always situated 9 degrees outside the primary bow. The secondary’s color pattern is nearly twice the width of the primary, resulting in half the brightness. Most noticeable is that the colors of the secondary are reversed above the primary such that reds face each other in the adjacent bows.

When the sun is low in the sky, light rays pass horizontally through more of the lower atmosphere to reach the earth’s surface or an observer’s eye. Consequently, the rays are scattered by more air molecules and dust particles than when sun rays approach from overhead. Because short-wavelength blue and green light are scattered more than red and yellow light, rainbows at times of sunrise and sunset often display the brightest reds. This also explains our bright red sunrises and sunsets, independent of rainbows.

If you are at sea and view a bright rain-produced rainbow touching the horizon, you might notice the bow continuing downward, below the horizon near the vessel as you look over the side toward the water. Careful viewing will reveal that the two segments of rainbow do not exactly connect. The segment of bow created by sea spray has a slightly smaller radius than the upper bow because salt water in spray reflects light more sharply than fresh water droplets. Physicists have an answer for almost everything.

When a full moon exists opposite a rainy sky, a moonbow can develop according to the same physics that govern rainbows. Moonbows are rare because the sky must be very dark and the bright moon close to the horizon and unobstructed. Typically, colors are not observed in moon bows because the light intensity is insufficient for our eyes’ color receptors to distinguish the separate wavelengths. Still, keep an eye out for this rare, evening phenomenon.

Scott E. McDowell has a doctorate in ocean physics, is a licensed captain and author of Marinas: a Complete Guide, available at Comment at