Rainbows: Formation, Seven Spectral Colours and Science Behind the Perfect Arc

A rainbow is one of the few natural occurrences that captivates people's imaginations. The rainbow, which arcs across the sky in a brilliant span of colour following a downpour, has influenced mythology, poetry and scientific research for millennia. Beneath its beauty, however, is a tale of incredible optical precision, a tale of light splitting, bending and bouncing inside millions of tiny water droplets hovering in the atmosphere.

Table of Contents:

• The Physics of Formation
• The Arc: Why Always a Bow
• The Colours: VIBGYOR and its Logic
• Secondary Rainbows and Supernumerary Arcs
• Rainbows Across Culture and Science

The Physics of Formation

When sunlight interacts with spherical water droplets in the sky, a rainbow is created. A source of white light (the sun), water droplets (from rain, mist or spray) and an observer properly positioned between the two are the basic components.

A sunlight beam that enters a droplet of water experiences refraction, which causes it to bend as it moves from a less dense medium (air) to a denser one (water). The wavelength, or colour, of the light determines how much it bends. Longer wavelengths (orange, red) bend less than shorter wavelengths (violet, blue).

The light enters the droplet, hits its inner surface and is internally reflected before returning to the droplet's front. It refracts once more as it leaves, bending once more. This double refraction, with internal reflection in between, is what separates white sunlight into its component colours, fanning them out into the familiar spectral sequence.

The Arc: Why Always a Bow

A rainbow's geometry is specified mathematically; it is not coincidental. Each colour emits water droplets at a specific angle relative to the incoming sunlight. Red light exits at approximately 42 degrees; violet at approximately 40 degrees. These angles are fixed by the laws of optics, regardless of droplet size.

Because you are always at the centre of the rainbow's geometry, with the sun behind you and the arc in front, the bow traces a circle of constant angular radius around the point directly opposite the sun (called the antisolar point). You never see a full circle from the ground because the horizon cuts it off. From an aircraft above a rain shower, a complete circular rainbow is, in principle, visible.

The centre of every rainbow is the antisolar point, which lies exactly opposite the sun from the observer’s perspective. This is why you can never approach a rainbow, as you move, the antisolar point moves with you, keeping the bow perpetually at the same angular distance.

The Colours: VIBGYOR and its Logic

The rainbow’s canonical sequence, red, orange, yellow, green, blue, indigo, violet (often remembered in India as VIBGYOR, read from inner to outer arc), is not arbitrary. It follows directly from the physics of refraction.

Red emerges near the top of the arc (outermost), has the longest visible wavelength (~700 nanometers) and is least refracted. Violet is the most refracted colour and appears at the bottom (innermost) since it has the shortest visible wavelength (~400 nanometers). The other colours arrange themselves between these extremes in order of wavelength.

In a primary rainbow, red is always on the outside and violet on the inside. The region inside the bow often appears noticeably brighter than the sky outside. This is called Alexander’s band and it results from the angular geometry of reflection, meaning less light is scattered into that sky region.

Secondary Rainbows and Supernumerary Arcs

A secondary rainbow, when visible, appears outside the primary bow at an angle of about 51 degrees. It is produced by light undergoing two internal reflections inside each droplet rather than one. This reverses the colour order, in the secondary rainbow, red is on the inside and violet on the outside. Secondary rainbows are always fainter than primary ones because each additional reflection scatters and absorbs more light.

Supernumerary rainbows are faint, pastel-coloured arcs occasionally visible just inside the primary rainbow. They arise from wave interference, a quantum optical effect that occurs when droplets are unusually uniform in size. Their existence was, historically, one of the first clues that light behaved as a wave.

Rainbows Across Culture and Science

Across cultures, the rainbow has been a symbol of divine covenant, hope and transformation. In Indian tradition, the rainbow (Indradhanush, or Indra’s bow) is associated with the deity Indra. Newton’s famous prism experiments in 1666 first demonstrated that white light contained all colours, laying the foundation for understanding the rainbow scientifically. The rainbow remains a perfect emblem of the moment nature and physics conspire to produce something that seems, impossibly, too beautiful to explain.