Let there be light
Most people understand that a rainbow is light spread into various colors by airborne water drops. Though a rainbow can seem like a random, unpredictable phenomenon, the natural laws governing rainbow are actually quite specific and predictable, and understanding these laws can help photographers anticipate a rainbow and enhance its capture.
The sun’s visible wavelengths are captured by our eyes and interpreted by our brain. When our eyes take in light comprised of the full range of visible wavelengths, we perceive it as white (colorless) light. Color registers when some wavelengths are more prevalent than others. For example, when light strikes an opaque (solid) object such as a tree or rock, some of its wavelengths are absorbed; the wavelengths not absorbed are scattered (reflected). Our eyes capture this scattered light, send the information to our brains, which interprets it as a color. When light strikes water, some is absorbed, some passes through to reveal the submerged world, and some light is reflected by the surface as a reflection.
To understand the interaction of water and light that creates a rainbow, it’s simplest to visualize what happens when sunlight strikes a single drop. Light entering a water drop refracts (bends), with different wavelengths refracting different amounts, which separates the originally homogeneous white light into the myriad colors of the spectrum.
But simply separating the light into its component colors isn’t enough to create a rainbow—if it were, we’d see a rainbow whenever light strikes water. Seeing the rainbow spectrum caused by refracted light requires that the refracted light be returned to our eyes somehow.
A raindrop isn’t flat like a sheet of paper, it’s spherical, like a ball. Light that was refracted (and separated into multiple colors) as it entered the front of the raindrop, continues through to the back of the raindrop, where some is reflected. Red light reflects back at about 42 degrees, violet light reflects back at about 40 degrees, and the other spectral colors reflect back between 42 and 40 degrees. What we perceive as a rainbow is this reflection of the refracted light—notice how the top color of the primary rainbow is always red, the longest visible wavelength; the bottom color is always violet, the shortest visible wavelength.
Follow your shadow
Every raindrop struck by sunlight creates a rainbow. But just as the reflection of a mountain peak on the surface of a lake is visible only when viewed from the angle the reflection bounces off the lake’s surface, a rainbow is visible only when you’re aligned with the 40-42 degree angle at which the raindrop reflects the spectrum of rainbow colors.
Fortunately, viewing a rainbow requires no knowledge of advanced geometry. To locate or anticipate a rainbow, picture an imaginary straight line originating at the sun, entering the back of your head, exiting between your eyes, and continuing down into the landscape in front of you—this line points to the “anti-solar point,” an imaginary point exactly opposite the sun. With no interference, a rainbow would form a complete circle, skewed 42 degrees from the line connecting the sun and the anti-solar point—with you at the center. (We don’t see the entire circle because the horizon usually gets in the way.)
Because the anti-solar point is always at the center of the rainbow’s arc, a rainbow will always appear exactly opposite the sun (the sun will always be at your back). It helps to remember that your shadow always points toward the anti-solar point. So when you find yourself in direct sunlight and rain, locating a rainbow is as simple as following your shadow and looking skyward—if there’s no rainbow, the sun’s probably too high.
High or low
Sometimes a rainbow appears as a majestic half-circle, arcing high above the distant terrain; other times it’s merely a small circle segment hugging the horizon. As with the direction of the rainbow, there’s nothing mysterious about its varying height. Remember, every rainbow would form a full circle if the horizon didn’t get in the way, so the amount of the rainbow’s circle you see (and therefore its height) depends on where the rainbow’s arc intersects the horizon.
While the center of the rainbow is always in the direction of the anti-solar point, the height of the rainbow is determined by the height of the anti-solar point, which will always be exactly the same number of degrees below the horizon as the sun is above the horizon. It helps to imagine the line connecting the sun and the anti-solar point as a fulcrum, with you as the pivot—picture yourself in the center of a teeter-totter: as one seat rises above you, the other drops below you. That means the lower the sun, the more of its circle you see and the higher it appears above the horizon; conversely, the higher the sun, the less of its circle is above the horizon and the flatter (and lower) the rainbow will appear.
Assuming a flat, unobstructed scene (such as the ocean), when the sun is on the horizon, so is the anti-solar point (in the opposite direction), and half of the rainbow’s 360 degree circumference will be visible. But as the sun rises, the anti-solar point drops—when the sun is more than 42 degrees above the horizon, the anti-solar point is more than 42 degrees below the horizon, and the only way you’ll see a rainbow is from a perspective above the surrounding landscape (such as on a mountaintop or on a canyon rim).
Of course landscapes are rarely flat. Viewing a scene from above, such as from atop Mauna Kea or from the rim of the Grand Canyon, can reveal more than half of the rainbow’s circle. From an airplane, with the sun directly overhead, all of the rainbow’s circle can be seen, with the plane’s shadow in the middle.
Double Your pleasure
Not all of the light careening about a raindrop goes into forming the primary rainbow. Some of the light slips out the back of the raindrop to illuminate the sky, and some is reflected inside the raindrop a second time. The refracted light that reflects a second time before exiting creates a secondary, fainter rainbow skewed 50 degrees from the anti-solar point. Since this is a reflection, the colors of the secondary rainbow are reversed from the primary rainbow.
And if the sky between the primary and secondary rainbows appears darker than the surrounding sky, you’ve found “Alexander’s band.” It’s caused by all the light machinations I just described—instead of all the sunlight simply passing through the raindrops to illuminate the sky, some of the light was intercepted, refracted, and reflected by the raindrops to form our two rainbows, leaving less light for the sky between the rainbows.
Waterfalls are easy
Understanding the optics of a rainbow has practical applications for photographers. Not only does it help you anticipate a rainbow before it happens, it also enables you to find rainbows in waterfalls.
Unlike a rainbow caused by rain, which requires you to be in exactly the right position to capture the incongruous convergence of rainfall and sunshine, a waterfall rainbow can be predicted with clock-like precision—just add sunshine.
Yosemite is my location of choice, but there’s probably a waterfall or two near you that will deliver. Just figure out when the waterfall gets direct sunlight early or late in the day, then put yourself somewhere on the line connecting the sun and the waterfall. And if you have an elevated vantage point, you’ll find that the sun doesn’t even need to be that low in the sky.
Understanding rainbow optics can even help you locate rainbows that aren’t even visible to the naked eye. A “moonbow” (lunar rainbow) is a rarely witnessed and wonderful phenomenon that follows all the natural rules of a daylight rainbow. But instead of resulting from direct sunlight, a moonbow is caused by sunlight reflected by the moon.
Moonlight isn’t bright enough to fully engage the cones in your eyes that reveal color, though in bright moonlight you can see the moonbow as an arcing monochrome band. But a camera on a sturdy tripod can use its virtually unlimited shutter duration to accumulate enough light to bring out a moonbow in full living color. Armed with this knowledge, all you need to do is put yourself in the right location at the right time.
A Gallery of Rainbows
Click an image for a closer look and to view slide show.