Rainbow: Nature's Colorful Arc
The Physics of Light and Color
To understand a rainbow, we must first understand light. What we see as white light from the sun is actually a mixture of different colors. This was famously demonstrated by Sir Isaac Newton[1] in the 17th century when he used a triangular piece of glass called a prism to split a beam of sunlight into a band of colors. This band is called a spectrum.
Light travels as a wave, and each color of light has a different wavelength. Red light has the longest wavelength, and violet light has the shortest. When all these wavelengths mix together, our eyes perceive the combination as white light. The sequence of colors in a rainbow is always the same because it is determined by their wavelengths: Red, Orange, Yellow, Green, Blue, Indigo, Violet. A simple way to remember this order is the acronym ROY G. BIV.
How a Rainbow is Formed: Step by Step
The formation of a rainbow is a precise dance of light and water. It involves three key optical processes happening inside countless raindrops. Let's follow the path of a single sunbeam as it enters a single spherical raindrop.
Step 1: Refraction. When a ray of sunlight enters a water droplet, it slows down and bends. This bending is called refraction. Because the different colors that make up white light have different wavelengths, they bend by different amounts. Violet light (shorter wavelength) bends the most, while red light (longer wavelength) bends the least. This begins the separation of colors.
Step 2: Reflection. After being refracted, the light ray travels through the droplet until it hits the inner back surface. Here, most of the light is reflected (it bounces off the inside wall of the droplet).
Step 3: Second Refraction. The reflected light ray now travels back toward the front of the droplet. As it exits the water and re-enters the air, it speeds up and is refracted again. This second refraction further spreads out the colors.
The combined effect of these steps is that sunlight is separated into its full spectrum. But we only see one specific color from each raindrop. Millions of raindrops are needed to create the full arc we see: raindrops higher in the sky send red light to our eyes, while those lower send violet light, with the other colors in between.
The Geometry of the Rainbow Arc
Why is a rainbow a bow, or an arc? The answer lies in geometry. The light that reaches your eye from each raindrop is concentrated at a specific angle. This angle is measured from the direction opposite the sun (the antisolar point) to the raindrop and then to your eye.
For the primary rainbow, the most common type, the angle for red light is about 42°, and for violet light, it's about 40°. All the raindrops that lie on a circle at a 40°-42° angle from the antisolar point will contribute to the rainbow you see. Since a set of points at a fixed angle from a point forms a cone, and the ground cuts this cone, what you see is a circular arc. If you were in an airplane high above the ground, you might see a full circular rainbow!
The relationship between the angle of observation ($\theta$), the angle of incidence ($i$), and the angle of refraction ($r$) inside the droplet can be described by geometry. The angle of deviation ($D$), which is the total angle the light ray is bent, for a primary rainbow is given by: $D = 180° + 2i - 4r$ The minimum deviation for red light occurs near 138°, which means the supplementary angle seen by the observer is 42° (180° - 138° = 42°).
Types of Rainbows and Related Phenomena
Not all rainbows look the same. Depending on the conditions, you might see different and sometimes rare types of rainbows.
| Type | How It's Formed | Key Characteristic |
|---|---|---|
| Primary Rainbow | One internal reflection inside water droplets. | Brightest, red on the outer edge, violet on the inner edge. |
| Secondary Rainbow | Two internal reflections inside water droplets. | Fainter, appears above the primary, colors reversed (violet on outer edge). |
| Double Rainbow | A primary and secondary rainbow visible together. | The area between the two bows (Alexander's band[2]) is noticeably darker. |
| Supernumerary Rainbow | Caused by interference[3] of light waves, not just geometry. | Faint, pastel-colored bands appear just inside the primary rainbow. |
| Fogbow | Formed by much smaller water droplets in fog or mist. | Very broad, almost white with faint red on the outside and blue on the inside. |
Rainbows in the Real World: From Sprinklers to Waterfalls
You don't need a rainstorm to see a rainbow. Any time there are water droplets in the air and sunlight comes from behind you, a rainbow can form. A classic example is using a garden hose or sprinkler on a sunny day. By standing with the sun at your back and spraying a fine mist of water into the air, you can create your own personal rainbow. The physics is identical to a rain-induced rainbow.
Waterfalls and fountains are also excellent places to spot rainbows. The constant spray of water creates a permanent mist in the air. As sunlight hits this mist, the conditions for refraction, reflection, and dispersion are perfectly met. This application shows how the principles of optics are constantly at work in our environment. Even the spray from a wave crashing on the shore can create a fleeting rainbow.
Common Mistakes and Important Questions
The rainbow is a perfect demonstration of how simple physical laws can create breathtaking natural beauty. From the refraction that bends light to the dispersion that splits it into a vibrant spectrum, each step in the rainbow's formation is a lesson in optics. The next time you see a rainbow arching across the sky, you can appreciate it not just for its beauty, but for the elegant science that makes it possible. It serves as a reminder that the world around us, even in its most magical moments, can be understood through curiosity and scientific inquiry.
Footnote
[1] Sir Isaac Newton: An English mathematician, physicist, and astronomer (1643-1727) who made groundbreaking contributions to science, including the laws of motion and universal gravitation, and the study of light and color.
[2] Alexander's band: The dark region of sky between the primary and secondary rainbows. It appears darker because light is being scattered away from this area towards the rainbows.
[3] Interference: A wave phenomenon where two or more waves combine to form a new wave pattern. Constructive interference makes bright bands, while destructive interference makes dark bands.