Scott McDowell, Ph.D.
Sea Science Articles written for The Triton magazine
Rainbows – The Magic of 42°
Rainbows require sunlight and moisture in the air but it’s
the magic angle of 42° 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° 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° 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° 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° and
is always situated 9° 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.
Scott McDowell, Ph.D.
Sea Science Articles written for The Triton magazine
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.
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