What is a Rainbow?

Introduction: What is a Rainbow?

A rainbow is one of nature's most splendid optical and meteorological phenomena. It appears as a multicolored arc in the sky, a direct result of sunlight interacting with water droplets. While often associated with rain showers followed by sunshine, rainbows can also be seen near waterfalls, mist, or even the spray from a garden hose.

Beyond their beauty, rainbows are a perfect illustration of fundamental physics principles, primarily involving the behavior of light. Understanding how a rainbow forms means delving into concepts like dispersionThe splitting of white light into its constituent colors (spectrum)., refractionThe bending of light as it passes from one medium to another., and reflectionThe bouncing of light off a surface.. This article will guide you through these concepts to unravel the science behind this captivating spectacle.

Key Insight

Rainbows are not physical objects located at a specific distance. They are optical illusions whose apparent position depends entirely on the observer's location relative to the sun and water droplets.

The Key Ingredients

Three essential components must be present and correctly aligned for a rainbow to appear:

1. Sunlight (White Light)

Sunlight, which appears white or yellowish to us, is actually a mixture of all visible colors of the spectrum. This composite nature is crucial for the separation of colors that forms a rainbow.

2. Water Droplets

Millions of tiny, near-spherical water droplets suspended in the air (like rain, mist, or fog) act as miniature prisms. Each droplet refracts, reflects, and disperses the sunlight passing through it.

3. Observer's Position

The observer must be positioned between the sun and the water droplets. The sun needs to be behind the observer, and the water droplets in front. The lower the sun in the sky, the more of the rainbow arc is visible.

Visualizing the Setup:

The sun must be behind the observer, shining towards the water droplets. The rainbow appears in the part of the sky opposite the sun, centered on the antisolar pointThe point in the sky directly opposite the sun from the observer's perspective..

The Science of Light

To understand rainbows, we need to grasp three key ways light interacts with matter: dispersion, refraction, and reflection.

Dispersion: Splitting White Light

Dispersion is the phenomenon where white light splits into its constituent spectral colors (red, orange, yellow, green, blue, indigo, violet - ROYGBIV) when it passes through a medium like a prism or a water droplet. This happens because the refractive indexA measure of how much light bends when entering a material. of the material varies slightly with the wavelength (color) of light.

Shorter wavelengths (like violet and blue light) bend more than longer wavelengths (like red light). This difference in bending angles causes the colors to separate.

Refraction: Bending Light

Refraction is the bending of light as it passes from one transparent medium to another (e.g., from air into water, or water back into air). This bending occurs because light travels at different speeds in different media.

When light enters a denser medium (like water from air) at an angle, it slows down and bends towards the normalAn imaginary line perpendicular to the surface at the point where light enters.. When it exits into a less dense medium (like air from water), it speeds up and bends away from the normal. The amount of bending depends on the angle of incidence and the refractive indices of the two media, described by Snell's LawA formula (n1*sin(θ1) = n2*sin(θ2)) that describes the relationship between angles of incidence and refraction, and refractive indices..

Reflection: Bouncing Light

Reflection occurs when light bounces off a surface. For rainbows, a specific type of reflection called Total Internal Reflection (TIR)When light traveling in a denser medium strikes the boundary of a less dense medium at an angle greater than the critical angle, it is completely reflected back into the denser medium. is crucial.

Inside a water droplet, if light traveling from water towards the air boundary strikes this boundary at an angle greater than the "critical angle" (about 48 degrees for water-air interface), it doesn't exit the droplet but is instead reflected back into it. This internal reflection is key to redirecting sunlight back towards the observer.

How a Rainbow Forms: Step-by-Step

The formation of a primary rainbow involves a precise sequence of events within countless individual water droplets:

Step 1: Entry & First Refraction/Dispersion

Sunlight enters a water droplet. As it passes from air to water, it refracts (bends) and disperses, splitting into its component colors. Violet light bends more than red light.

Step 2: Internal Reflection

The dispersed light rays travel to the back of the droplet. Here, a portion of the light undergoes total internal reflection, bouncing off the inner surface of the droplet.

Step 3: Exit & Second Refraction/Dispersion

The reflected light travels to the other side of the droplet. As it exits from water back into air, it refracts and disperses again, further separating the colors.

Step 4: The Critical Angles

Each color emerges from the droplet at a slightly different angle relative to the incoming sunlight. For a primary rainbow, red light exits at an angle of approximately 42°, while violet light exits at about 40°. Other colors exit at angles in between.

Step 5: Collective Effect

An observer sees red light from droplets that are at an angle of 42° from the antisolar point, and violet light from droplets at 40°. Millions of droplets, each contributing a specific color based on their angle to the observer, form the complete arc of the rainbow.

Why is a Rainbow Curved?

The curved shape of a rainbow is a consequence of how we perceive the light scattered by water droplets. Each color of the rainbow is seen from droplets that lie on the surface of a cone, with the observer's eye at the apex of this cone.

Imagine the antisolar pointThe point in the sky directly opposite the sun from your perspective. It's the center of the rainbow's circle. – this is the point in the sky directly opposite the sun, relative to you. A rainbow forms a circle (or part of a circle) centered on this antisolar point.

All the water droplets that reflect red light back to your eyes at the specific angle of ~42° lie on a circle. Similarly, all droplets reflecting violet light at ~40° form another, slightly smaller, concentric circle. This collection of circles for each color creates the arc.

We usually see only an arc because the ground obstructs the lower part of the circle. If you were high up, like in an airplane, and conditions were right, you might see a full 360° circular rainbow!

The Order of Colors (ROYGBIV)

The familiar order of colors in a primary rainbow – Red, Orange, Yellow, Green, Blue, Indigo, Violet (often remembered by the acronym ROYGBIV) – is a direct result of how different wavelengths of light are dispersed.

As sunlight enters and exits a water droplet, its constituent colors are separated because each color (wavelength) is refracted by a slightly different amount:

Red light, having the longest wavelength, is bent the least. It emerges from the droplets at an angle of approximately 42° relative to the incoming sunlight.
Violet light, with the shortest wavelength, is bent the most. It emerges at an angle of approximately 40°.

Since red light exits at a larger angle, it appears on the outer (upper) edge of the rainbow arc. Violet light, exiting at a smaller angle, forms the inner (lower) edge. The other colors (orange, yellow, green, blue, indigo) appear in between, according to their wavelengths and corresponding exit angles.

Interactive Rainbow Simulator

Experiment with the conditions needed to see a rainbow. Adjust the sun's altitude and toggle the presence of rain to see how the rainbow appears. Remember, rainbows are best seen when the sun is low in the sky.

Controls

Sun Altitude: 20°

Horizon (0°) Overhead (90°)

Rain Present

Note: A primary rainbow's top is visible when the sun's altitude is below ~42°. The lower the sun, the higher the rainbow arc.

Types of Rainbows

While the primary rainbow is the most common, other fascinating variations can occur:

This is the brightest and most commonly seen rainbow. It's formed by light undergoing one internal reflection inside water droplets. Red appears on the outer edge (approx. 42° from antisolar point) and violet on the inner edge (approx. 40°).

Light Path: Refraction -> Reflection (1) -> Refraction
Colors: Red (outer) to Violet (inner)
Angular Radius: ~40-42°

A fainter, larger arc seen outside the primary rainbow. It's caused by light undergoing two internal reflections within droplets. The order of colors is reversed: violet is on the outer edge (approx. 53°) and red on the inner edge (approx. 50°). The sky between the primary and secondary bows, known as Alexander's dark bandA darker region between primary and secondary rainbows where light from single or double reflections doesn't reach the observer., appears darker because less light is scattered from this region.

Light Path: Refraction -> Reflection (2) -> Refraction
Colors: Violet (outer) to Red (inner) - REVERSED
Angular Radius: ~50-53°

Formed by very small water droplets in fog (typically less than 0.05 mm in diameter). Due to diffractionThe bending of light waves around the corners of an obstacle or through an aperture. effects caused by these tiny droplets, the colors are very faint and often overlap, making the fogbow appear mostly white or very pale. They are also sometimes called white rainbows.

A rainbow produced by moonlight instead of sunlight. Moonbows are much fainter than solar rainbows because the moon reflects far less light. To the human eye, they often appear white because the light is too dim to stimulate the eye's cone color receptors. However, long-exposure photography can reveal their colors. Best seen during a full or near-full moon when the moon is low in the sky.

Common Misconceptions

Rainbows are beautiful and somewhat mysterious, leading to several common misunderstandings:

Myth: You can reach the end of a rainbow.

Reality: A rainbow is an optical phenomenon, not a physical object. Its position is relative to the observer. As you move, the rainbow appears to move too, so you can never reach its "end" or get any closer to it.

Myth: Rainbows only appear after rain.

Reality: While commonly seen after rain showers, rainbows can form wherever there are water droplets in the air and sunlight shining from behind the observer at a low enough angle. This includes mist, fog, spray from waterfalls, or even a garden sprinkler.

Myth: Everyone sees the same rainbow.

Reality: Each person sees their own unique rainbow. Because a rainbow's position depends on the observer's specific location relative to the sun and water droplets, no two people (even standing side-by-side) see exactly the same set of droplets forming their rainbow.

Myth: The sun must be shining brightly.

Reality: While direct sunlight is needed, it doesn't have to be an intensely bright, cloudless day (except for the sun's position relative to the observer). Rainbows can appear even when parts of the sky are cloudy, as long as the sun can illuminate the water droplets and the observer is in the right spot.

Conclusion

Rainbows, with their ethereal beauty, are a stunning demonstration of light physics at play in nature. They arise from a delicate interplay of sunlight, water droplets, and the observer's unique perspective. The processes of refraction, dispersion, and reflection within millions of tiny water spheres work in concert to separate white sunlight into its vibrant spectrum, painting an arc of color across the sky.

From the specific 40-42 degree angles that define the primary bow to the reversed colors of a secondary bow, each aspect of a rainbow tells a story about how light behaves. Understanding this science doesn't diminish the magic of seeing a rainbow; rather, it adds a layer of appreciation for the elegant natural laws that govern our world.

The Enduring Wonder

The next time you witness a rainbow, take a moment to marvel not just at its colors, but at the incredible journey of light that creates it – a personal spectacle crafted just for your eyes by the sun and the rain.