Rainbows: Formation, Optics, and Viewing Conditions

How is a 🌈 formed?

A rainbow is a meteorological phenomenon caused by the reflection, refraction, and dispersion of light in water droplets, resulting in a spectrum of light appearing in the sky.

The Essential Ingredients: Sunlight and Water Droplets

The formation of a rainbow hinges on two fundamental components: sunlight and suspended water droplets, typically from rain, mist, or spray.

• Sunlight: What we perceive as white sunlight is, in fact, a composite of various colors, each corresponding to a different wavelength within the electromagnetic spectrum. When these wavelengths are separated, they reveal the familiar colors of the rainbow: red, orange, yellow, green, blue, indigo, and violet.
• Water Droplets: These tiny spheres of water act as miniature prisms. As sunlight encounters these droplets, its path is altered, leading to the spectacular display we observe.

The Process of Light Refraction and Reflection

The journey of light through a water droplet involves a precise sequence of optical events:

• Entering the Droplet (First Refraction): When a ray of sunlight enters a water droplet, it transitions from air (a less dense medium) to water (a more dense medium). This change in medium causes the light ray to bend, or refract. Crucially, different wavelengths (colors) of light refract at slightly different angles; violet light bends the most, and red light bends the least. This separation of colors is known as dispersion.
• Internal Reflection: After entering and refracting, the dispersed light rays travel to the back interior surface of the water droplet. Here, most of the light undergoes total internal reflection, bouncing off the back of the droplet much like a mirror.
• Exiting the Droplet (Second Refraction): The reflected light then travels back through the droplet to the front surface, where it exits and re-enters the air. As it exits, it undergoes a second refraction, further separating the colors and directing them towards the observer.

Why We See an Arc

The arc shape of a rainbow is a consequence of the specific geometry required for the dispersed and reflected light to reach the observer's eye.

• Specific Angle of Observation: For the light to be visible as a rainbow, it must be reflected and refracted at a precise angle relative to the incoming sunlight. The most intense light from the primary rainbow is observed at an angle of approximately 42 degrees from the anti-solar point (the point directly opposite the sun from the observer's perspective). Because this angle is constant for all water droplets, and the sun's rays are essentially parallel, the collection of droplets that send light to the observer's eye forms a circular arc.
• Millions of Droplets: It's not one single droplet creating the rainbow. Instead, millions of droplets are involved, each contributing a tiny bit of colored light. The specific droplets that contribute to your rainbow are those positioned at the correct angle relative to your eye and the sun.
• Observer-Specific: This means that every individual sees a slightly different rainbow, composed of light from a unique set of water droplets. Your rainbow is unique to your position.

Understanding Primary and Secondary Rainbows

While the primary rainbow is the most common, sometimes a fainter, larger secondary rainbow can be seen.

• Primary Rainbow: This is the brighter rainbow with the color sequence of red on the outside and violet on the inside. It results from one internal reflection within the water droplet.
• Secondary Rainbow: This fainter rainbow appears outside the primary arc, with the colors reversed (violet on the outside, red on the inside). It is formed by light undergoing two internal reflections within the water droplet. Each additional reflection diminishes the light's intensity, which is why the secondary rainbow is less vibrant.

Conditions for Viewing a Rainbow

For a rainbow to be visible, specific environmental conditions must align:

• Sun Behind You: The sun must be behind the observer, casting light onto the rain in front.
• Rain In Front: There must be water droplets (rain, mist, or spray) in the air opposite the sun.
• Low Sun Angle: Rainbows are best seen when the sun is low in the sky, typically less than 42 degrees above the horizon. This allows the anti-solar point to be above the horizon, making the full arc visible.

Conclusion: A Scientific Spectacle

The formation of a rainbow is a stunning demonstration of the principles of optics—refraction, dispersion, and reflection—all working in concert. Far from being merely a beautiful sight, it is a testament to the predictable and elegant laws that govern light and its interaction with our natural world. Understanding its scientific basis only enhances the appreciation of this ephemeral yet enduring natural spectacle.