Rainbows are one of nature’s most spectacular optical phenomena. They take ordinary sunlight and rain and transform it into a colorful arc that is truly magnificent. But how does this magic happen exactly? It’s not magic at all; it’s just the beautiful interplay between light, water Droplets and physics. To understand how we can see these beautiful arcs, we need to learn about Refraction, reflection, and dispersion of light.
The Ingredients for a rainbow
There are two Ingredients that we need to create a rainbow: sunlight and water drops in the air. That is why rainbows are generally observed during periods of heavy rain. The angle of the water drops and the sun are important as well. There will be a rainbow whenever the sun is directly behind you and the rain is in front of you.
White sunlight
White sunlight is composed of many Colors. Think of the Colors of the rainbow: red, orange, yellow, green, blue, indigo, and violet. Each of these Colors has a different length. The length of red light is the greatest while the length of violet light is the least.
Water drops as prisms
Small spherical water drops in rain, mist or a garden hose spray function as miniatures of prisms. When sunlight enters a small sphere-shaped water drop it creates Refraction and splits the sunlight into the various Colors of light.
How rainbows form
three optical principles are used to generate a rainbow. Those are Refraction, reflection, and dispersion.
Refraction – bending light
When light goes from one medium to another (from air to water), it changes both its velocity and its path. When sunlight goes from air into water it begins to refract. Because each color of light has a slightly different speed in water, they bend differently. Violet light bends sharper than red light due to its smaller wave-length.
Internal reflection – bouncing back
As soon as sunlight enters a water droplet and is refracted it continues on to the back interior surface of the water droplet. Once at the rear surface of the droplet it is internally reflected. The majority of the light reaches the rear surface at an angle such that it bounces off the inside of the droplet like a mirror and heads toward the front of the droplet. At no time does this light exit the droplet.
second Refraction – exiting the droplet
As soon as the light has bounced off the rear surface of the droplet, it continues on to the front surface. Upon exiting the water droplet and re-entering air it is refracted for a second time. This second Refraction spreads out the Colors further. Finally, the light proceeds to your eyes, displaying the Colors of the rainbow.
Dispersion – spreading Colors
In combination, the first and second refractions along with one internal reflection separate white sunlight into its component Colors (similarly to how a glass prism separates white light into its component Colors). In this manner each individual water drop functions independently as a prism, separating white sunlight into its component spectrum of Colors.
Why an arc shaped rainbow?
Because of geometry and the particular angles at which light returns to your eye after being reflected by water Droplets, you see an arc shaped rainbow. To see a rainbow you must be positioned so that light from water Droplets is reflected back to your eyes by sunlight.
Since every observer views rainbows from a somewhat different location and therefore observes rainbows that include slightly different sets of water Droplets which reflect light to their respective locations, each observer will observe a somewhat different rainbow.
Primary vs Secondary Rainbows
Occasionally observers report seeing two separate rainbows in addition to the normal arc-shaped rainbow. The more prominent and bright of these two rainbows is referred to as a Primary rainbow. A Primary rainbow occurs when light is internally reflected once in a set of water Droplets. The Colors occur in sequence from red on the outside to violet on the inside of the Primary rainbow.
The less prominent and larger arc-shaped rainbow appearing on the outside of a Primary rainbow is referred to as a secondary rainbow. A secondary rainbow occurs when light is internally reflected twice within water Droplets, reversing the sequence of Colors (violet on the outside and red on the inside) compared to that of a Primary rainbow and reducing brightness. Angles associated with Secondary Rainbows are approximately 50° for red light and 53° for violet light.
Factors affecting rainbow visibleness
The following factors affect how easily or frequently you can see a rainbow:
- Angle of sunlight
The sun must be close to being overhead. Typically, this requires that the sun be no higher than 42° above the horizon. During periods when the sun is too far above the horizon, the central portion of a rainbow (opposite the sun) would likely be under your feet and therefore invisible. - Droplet Size
Larger raindrops produce brighter, more vivid rainbows with greater separation between Colors. Smaller Droplets (such as those in mist or fog) can produce fainter, less distinct rainbows and can even produce ‘fogbows’ which are either white or contain subtle coloration. - Atmospheric Conditions
Clear space between yourself and a rainbow produces better visibility for that rainbow. Dust or haze present in space between yourself and a rainbow can scatter sunlight producing duller rainbows. - Your Position
You must be located so that sunlight is behind you and rain is in front of you. Due to differences in location for observing rainbows, each observer will observe a somewhat different rainbow since each observer views rainbows based upon a somewhat different set of water drops that are reflecting light onto their respective locations.
Rainbows demonstrate how fundamental physical properties of light and water interact to produce visually stunning effects. Individual spherical water drops function as small prisms creating separated spectra. Specific angles of Refraction and reflection allow us to see these beautiful effects. Next time you observe a rainbow, remember there was science involved in producing that beautiful display!
Frequently asked questions
Can a rainbow ever really touch down?
No. Rainbows exist solely as an optical phenomenon and therefore never physically contact anything including earth. Since visibility depends upon light reaching your eyes at specific angles, what you perceive as touching down is merely an illusion caused by your Position relative to the light source.
Do i sometimes see double rainbows?
Yes, you could say this! The brighter rainbow nearest to you (the Primary) is produced when light reflects once from inside raindrops. The weaker arc-shaped rainbow on the outside of your Primary (the secondary) is generated when light reflects twice inside raindrops causing it to reverse color order and reduce brightness.
Are all rainbows complete circles?
Yes! Rainbows are always complete circles. Since we almost always view them from below and half of each circle lies beneath our feet we normally only see half of each circle as a semi-circle.
Can i see rainbows at night?
Yes, occasionally you may be able to see rare ‘moonbow’ or lunar rainbow. Moonbows occur when moonlight interacts with water drops. Since moonlight contains significantly less energy than direct sunlight moonbows are greatly diminished compared to solar rainbows and appear white or grey unless photographed using extended exposure techniques.
Rainbows are truly magical displays but their beauty comes from understanding basic optics!
Sources
- What Is a Rainbow? — NASA
- How Do Rainbows Form? — Scientific American
- Rainbows — National Weather Service (NOAA)
- Rainbow | Meteorology — Britannica
- Rainbows & Arc Optics — Atmospheric Optics
