The Physics of Rainbows: How Light and Water Create Colorful Arcs

Rainbows evoke wonder in people of all ages, whether you spot them after a spring thunderstorm, over a waterfall, or in the spray from a garden hose. While they may seem magical, rainbows are the consequence of predictable physical processes that govern how light interacts with water droplets. Understanding these principles reveals why rainbows always appear opposite the Sun, why their colors are arranged in a specific order, and what creates rarer phenomena like secondary bows and supernumerary arcs.

White light and the spectrum

Sunlight appears white, but it is actually made of many different colors. Each color corresponds to electromagnetic waves of a different wavelength: red light has longer wavelengths, while violet light has shorter wavelengths. When white light passes through a transparent medium like glass or water, the individual colors slow down by different amounts. This difference in speed causes the light to change direction, a process known as refraction. Because each color refracts by a slightly different angle, the beam splits into a spectrum.

You can observe this dispersion with a glass prism. Shine a beam of sunlight through the prism, and a fan of colors spreads out on the opposite side. A raindrop acts like a miniature spherical prism. Instead of being flat with sharp edges, the droplet’s curved surface causes incoming sunlight to undergo multiple interactions before it emerges.

Refraction, reflection and dispersion inside a drop

When a ray of sunlight enters the top of a water droplet, it slows down and bends. Some of the light reflects off the back interior surface of the droplet, then bends again as it exits into the air. Each color is refracted by a unique angle. For a typical primary rainbow, red light leaves the drop at an angle around 42 degrees from the incoming sunlight, while violet light exits around 40 degrees. To an observer, each droplet sends out a single color toward their eye. The combined effect of countless droplets, each sending a different color at the required angle, produces the bright multicolored arc we call a rainbow.

Because the angles are fixed, you see a rainbow only when you stand between the Sun and falling water droplets with your back to the Sun. The bow forms a circle centered on the point directly opposite the Sun, known as the antisolar point. On the ground, you typically see only the upper half of the circle. From an airplane or mountaintop when the Sun is high, you may see a full circular rainbow encircling the shadow of the aircraft.

Color order and brightness

The order of colors in a primary bow always runs from red on the outer edge through orange, yellow, green and blue to violet on the inner edge. The brightness peaks in the middle of the bow. Above the primary arc, the sky appears darker because rays refracted at larger angles do not reach the observer. Below the bow, the sky looks lighter because rays that bend less create a continuum of light outside the color bands.

A secondary rainbow sometimes appears outside the primary. It arises from rays that undergo two internal reflections inside each droplet before emerging. These rays exit at larger angles, around 50–54 degrees. Because they reflect twice, the colors appear in reversed order with violet on the outside and red on the inside, and the bow looks fainter. Between the primary and secondary arcs lies a darker region called Alexander’s band, where few rays emerge.

Under the right conditions, you may see fainter, closely spaced fringes on the inside of the primary bow. These supernumerary bows result from interference between light waves traveling slightly different paths through the droplet. They appear as pastel bands that blend the main spectrum and reveal the wave nature of light.

What controls visibility

Rainbows are most common when the Sun is low in the sky—mornings and late afternoons—because the required angles place the bow higher above the horizon. The Sun must be behind you, so you are facing the rain. If the Sun is too high, the bow will be below the horizon and hidden from view. The diameter of the droplets also affects the bow’s appearance; larger droplets produce brighter, more distinct colors and sharper edges, while tiny droplets in mist or fog create faint, washed-out arcs called fogbows. Fogbows lack strong colors because the droplets are so small that diffraction dominates and the spectrum blends.

You can create artificial rainbows by standing with your back to the Sun and spraying water from a hose or sprinkler. Tilt your head to change the angle until you see the arc. This is a great way to experiment with the effect of droplet size: a gentle mist yields a large, pale bow, while a coarse spray gives you a bright, vivid arc with supernumerary fringes.

Beyond the visible spectrum

Just as white light splits into the colors you can see, it also splits into invisible wavelengths. Infrared light, with wavelengths longer than red, and ultraviolet light, shorter than violet, are refracted by the droplets too. However, your eyes cannot detect these rays, so they do not contribute to the visible rainbow. Instruments like spectrometers exploit the same dispersion effect to analyse the composition of light sources, from stars to streetlamps.

Cultural significance and symbolism

Rainbows have inspired myths and folklore across cultures. They are often seen as symbols of hope, peace and transformation. In science, they represent the unity of the spectrum and the wave nature of light. Understanding the physics behind rainbows does not diminish their beauty—it enhances it by revealing the subtle interactions at play and highlights the remarkable fact that something as simple as sunlight and water can produce such a striking pattern.

Next time you catch a glimpse of a rainbow, take a moment to consider the journey of each ray of light as it enters and exits countless droplets. Whether you are watching a storm recede or creating your own arc with a garden hose, you will be witnessing a spectacular demonstration of refraction, reflection and dispersion at work.