Rainbow: formation, colors and types of arcs explained

Rainbow with its secondary arc — The **rainbow** appears as a circular arc in the sky, typically opposite the Sun. Colors are ordered by wavelength, with red on the outside and violet on the inside of the arc. The light reaching the observer's eye comes from numerous water droplets dispersed in the air, each contributing to the formation of the rainbow. A much fainter secondary arc, with reversed colors, can be seen on this personal photo from 2013.
Image source: Astronoo

Scientific summary

Astronoo's article presents the rainbow, an optical and meteorological phenomenon resulting from the decomposition of white light by suspended water droplets. It details the fundamental physical processes: refraction, which bends light upon entering droplets; dispersion, which separates wavelengths into distinct colors; total internal reflection, which reflects light inside the droplet; and a second refraction upon exit, which intensifies the visible spectrum. The article also explores observation conditions, different types of arcs (primary, secondary, monochrome) and variations according to wavelengths.

What is a rainbow and how is it formed?

This article is dedicated to the rainbow, one of nature's most fascinating and studied phenomena. But how does this colored arc form in the sky? The answer lies in the combination of three fundamental optical processes: refraction, dispersion and internal reflection of light within water droplets. When white sunlight enters a water droplet, it is refracted, meaning it is bent and split into its different colors (the visible spectrum). These colors, ranging from red to violet, are then reflected on the inner wall of the droplet before being refracted again upon exit, forming the colored arc we observe. The 42-degree angle between the incident light and the arc is constant, which explains why the rainbow always appears at the same angular distance from the antisolar point.

Optical phenomenon of rainbow colors

The rainbow is an optical and meteorological phenomenon that manifests as a series of colors visible in the form of an arc in the sky. This phenomenon occurs mainly when white sunlight splits into seven colors (red, orange, yellow, green, blue, indigo, violet) as it passes through water droplets in the atmosphere.

The nature of white light and its wavelengths

The nature of white light emitted by the Sun is actually a mixture of all wavelengths of visible light. Each color corresponds to a specific wavelength:

Red: approximately 620-750 nm
Orange: approximately 590-620 nm
Yellow: approximately 570-590 nm
Green: approximately 495-570 nm
Blue: approximately 450-495 nm
Indigo: approximately 425-450 nm
Violet: approximately 380-425 nm

Origin of the seven colors according to Newton

The seven colors of the rainbow were popularized by Isaac Newton (1643-1727) in the 17th century. In his experiments with a prism, he observed that white light split into a spectrum of colors. Although this spectrum is continuous and the transitions between colors are smooth, Newton decided to divide it into seven distinct parts, drawing inspiration from cultural and musical concepts, such as the seven notes of the musical scale.

Physical processes involved in rainbow formation

Initial refraction

Refraction: When white light (such as sunlight) enters a water droplet, it changes direction — a phenomenon called refraction. Light travels slower in water than in air, causing a change in speed and direction within the droplet.

Dispersion of colors

Dispersion: White light consists of multiple wavelengths, each corresponding to a different color (red, orange, yellow, green, blue, indigo, violet). Upon entering the water droplet, the different wavelengths are refracted at different angles due to their different propagation speeds in water. This causes the separation of colors, a process called dispersion.

Total internal reflection

Total internal reflection: Once the light has been refracted and dispersed, it reaches the opposite surface of the water droplet. If the angle of incidence of the light is greater than the critical angle, the light will be completely reflected inside the droplet (total internal reflection).

Second refraction and spectrum intensification

Second refraction: After being reflected, the light heads again toward the exit of the water droplet, where it undergoes a second refraction. This causes further separation of colors, intensifying the dispersion effect.

Conditions required to observe a rainbow

For a rainbow to appear, water droplets suspended in the atmosphere are required, whether in the form of rain, fog or mist. The Sun must also be low on the horizon, typically early in the morning or late in the afternoon, and the observer must be positioned between the Sun and the water droplets, with the Sun at their back.

For a primary rainbow, the typical viewing angle is approximately 42 degrees from the direction opposite the Sun. In other words, if you imagine a line running from the Sun to the observer, the rainbow forms at 42 degrees above this line.

N.B. : The 42-degree angle is an average value that varies according to the refractive index of water and the wavelength of light. Red light, with its longer wavelength, is slightly more deviated than violet light, which explains why red is located on the outside of the arc.

Luminous arcs

Monochromatic lunar rainbow — The **monochromatic rainbow**, like "lunar rainbows", often fainter than colored rainbows.
Image source: astronoo.com (new window) — AI-generated image, public domain.

Types of luminous arcs

The primary rainbow is the best known and brightest. It displays a spectrum of seven distinct colors — red, orange, yellow, green, blue, indigo and violet — with red on the outside and violet on the inside of the arc. It is formed by a single internal reflection of light within the water droplets.
The secondary rainbow, rarer and fainter, appears above the primary arc. It is produced by two internal reflections, which reverses the order of colors: violet is on the outside and red on the inside. Its intensity is approximately half that of the primary rainbow.
The dewbow, less common, forms at ground level when sunlight reflects off dew droplets deposited on grass or spider webs. It is generally very pale, even white. The lunar rainbow is produced by moonlight passing through water droplets; it is so faint that it often appears white to the naked eye, although long-exposure photographs can reveal its colors.
The supernumerary arc is a more subtle phenomenon, manifesting as additional pastel-colored layers located just inside the primary arc. It results from interference effects between light waves and requires water droplets of very uniform size. The fogbow forms in dense fog composed of very small droplets; it appears as a white arc or very faintly colored, often wide and diffuse.
The red arc or monochrome arc is a rare phenomenon that occurs when the Sun is very low on the horizon (at sunrise or sunset). The light then passes through a thick layer of atmosphere that scatters short wavelengths (blue, green), leaving only the red color. The arc then appears entirely red, offering a striking spectacle.
The monochromatic rainbow forms with only a single color, often in specific conditions such as the luminous arcs observed around the Moon, called lunar rainbows.

N.B. :
The visibility and intensity of these different arcs depend on multiple factors: droplet size, Sun angle relative to the horizon, atmospheric purity and observer sensitivity. Secondary, supernumerary and monochrome arcs are rarer and require particularly favorable optical conditions.

Table of different types of luminous arcs

Comparison between different types of rainbows
Type of rainbow	Internal reflections	Color order	Brightness	Position	Specific conditions
Primary arc	1 reflection	Red outside, violet inside	High (vivid)	—	Sun behind, rain ahead
Secondary arc	2 reflections	Reversed: violet outside, red inside	Fainter (2× less bright)	Above primary arc	Larger water droplets
Dewbow	1 reflection	Similar to primary arc	Very pale, often white	Near ground	Dew on grass or spider webs
Lunar rainbow	1 reflection	Similar to primary, attenuated colors	Very faint (often white)	—	Full moon, dark night
Supernumerary arc	1 reflection	Additional layers (pastel)	Very pale, sometimes iridescent	Inside primary arc	Uniform-sized droplets (interference)
Fogbow	1 reflection	White or almost white	Very faint	—	Very small fog droplets
Red arc (monochrome)	1 reflection	Red only	Faint	—	Sunrise or sunset (grazing light)

N.B. :
The intensity and visibility of rainbows depend on droplet size, Sun angle and atmospheric purity. Secondary and supernumerary arcs are rarer and require specific optical conditions.

References

FAQ: Everything you need to know about rainbows

Why is the rainbow curved?

The rainbow is curved because it is formed by the reflection and refraction of sunlight in water droplets. The circular shape is an optical illusion: each water droplet reflects light at a fixed angle (approximately 42° for the primary arc). The set of droplets that reflect light toward the observer's eye forms a cone with the eye at its tip. The intersection of this cone with the rain curtain gives an arc. If the Sun is low on the horizon, the arc is larger; if it is higher, the arc is smaller.

Why are the colors of the secondary rainbow reversed?

The secondary rainbow is formed by two internal reflections instead of one within the water droplets. This double reflection reverses the order of colors: red is on the inside of the secondary arc and violet is on the outside. Additionally, the secondary arc is less bright because each internal reflection loses some of the light intensity.

Can we see a rainbow at night?

Yes, this is called a lunar rainbow or lunar rainbow. It is produced by moonlight (which is only a reflection of sunlight) passing through water droplets. However, moonlight is much weaker, so lunar rainbows are generally pale and appear monochrome or with very attenuated colors to the naked eye. Long-exposure photographs can reveal their colors.

Can a rainbow be complete?

A rainbow is actually a complete circle, but the horizon hides the lower part. From the ground, we therefore see only an arc. However, from an airplane or a high point, it is sometimes possible to observe a complete circular rainbow, provided that the light and water droplet conditions are met all around.

Why is the rainbow associated with seven colors?

This association dates back to Isaac Newton, who artificially divided the continuous spectrum of white light into seven distinct colors (red, orange, yellow, green, blue, indigo, violet). He chose this number in reference to the seven musical notes and the seven days of the week, a common practice in his time. In reality, the spectrum is continuous and contains an infinite number of shades.