How does a rainbow form?

Rainbows form when sunlight interacts with many tiny spherical water droplets and the geometry between those droplets and an observer. In each droplet sunlight slows and bends (refraction), splits into colors (dispersion), reflects once inside the drop, then bends again as it leaves. Because each wavelength exits at a slightly different angle, an observer sees a circular arc of separated colors; the bright primary arc appears near 42 degrees from the line directly opposite the sun.

Basic physical processes: refraction, dispersion and internal reflection

The optical sequence inside a single spherical raindrop combines three effects. First, refraction changes the light's direction and speed as it enters water from air. Second, dispersion makes different wavelengths travel at different speeds in water, so colors separate. Third, internal reflection redirects light back toward the observer before the light refracts a second time leaving the drop.

For a short primer on how bending and color separation differ in principle, see Refraction and Dispersion in Light. Those two ideas together explain why white sunlight becomes a spectrum inside a drop.

Step-by-step: what happens inside a single raindrop

Entrance refraction: sunlight hits the curved surface and partly enters the water. The beam bends toward the normal because water is optically denser than air.
Dispersion: shorter wavelengths (blue, violet) slow slightly more than longer ones (red), so the beam fans into its component colors inside the droplet.
Internal reflection: some of that light reflects off the rear inner surface of the droplet. For the primary rainbow a single internal reflection is the dominant contribution.
Exit refraction: the internally reflected rays exit the droplet and refract again. Because the exiting directions differ by wavelength, each color leaves at a characteristic angle relative to the incoming sunlight.

Geometry and the observer viewing angle

The rainbow you see is not at the sky location of the physical droplets themselves but determined by angle. The essential point: an observer sees colors where outgoing rays from many different drops converge at the eye at roughly the same angle. For the primary rainbow that angle is approximately 42 degrees measured from the line pointing directly away from the sun (the antisolar point).

Put another way: if you draw a cone with its tip at your eye and its axis pointing toward the antisolar point, the cone's half-angle is about 42 degrees for red light; blue and violet exit at slightly smaller angles, so colors sort along the cone's rim. The visible arc is where that cone intersects the cloud or raindrop field.

Worked geometry example

To locate the top of a primary rainbow: take the sun's altitude above the horizon, call it a degrees. The antisolar point is a degrees below the horizon, so the rainbow's apex will be at elevation approximately 42 - a degrees above the horizon. Example: if the sun is 10 degrees above the horizon, the primary rainbow's apex will appear roughly 32 degrees above the horizon.

Why color order and variations occur

The familiar red-on-outside, violet-on-inside ordering follows from dispersion: red exits at a larger angle than violet after one internal reflection. Droplet size and uniformity also affect the rainbow's sharpness and the presence of extra features.

Large drops (millimeter-sized) produce vivid, well-separated colors and a thin arc.
Small drops (tens to hundreds of micrometers) blur the colors and can create additional faint bands called supernumerary rainbows.
Multiple internal reflections produce secondary rainbows; these are fainter, reversed in color order, and centered at a larger angle (roughly 50 to 53 degrees). For more detail on these forms see Secondary and Supernumerary Rainbows.

Practical guide: how to find and observe a rainbow

Finding a rainbow is a simple exercise in geometry and timing: you need sunlight and water droplets with the observer between them and the sun behind you. Use this checklist before stepping outside.

Sun location: keep the sun at your back. Low sun angles (near sunrise or sunset) make taller arcs.
Water source: rain showers, mist from waterfalls, sprinklers or post-storm drizzle provide droplets.
Clear background: darker clouds opposite the sun increase contrast and make colors easier to see.
Viewer position: move so the antisolar direction (opposite the sun) points across the droplet field; the arc will trace around that point at about 42 degrees.

Step-by-step to observe a rainbow

Stand with your back to the sun and identify the opposite direction.
Scan the sky around the antisolar point at a radius of about 42 degrees for the primary arc.
If the sun is low, expect a larger, higher arc; if the sun is high, the arc may be small or below the horizon.
For a secondary bow look slightly farther from the antisolar point (larger angle) and expect fainter, reversed colors.

Tips for photographing and measuring rainbows

Photographing a rainbow requires framing a wide field and letting the camera capture the angular relationships. For technique and camera settings that work for weather optics, consult Photographing Rainbows and Sunlight Phenomena. A wide-angle lens and tripod help when the arc is large or the light is dim.

Common mistakes and misconceptions

Thinking a rainbow is at a fixed place: it depends on your eye position. Two observers standing apart see different raindrops producing their own rainbows.
Believing the rainbow is a physical object you can reach: the arc has no single location in space; it is an angular effect of light reaching your eye.
Assuming only rain makes rainbows: any ensemble of nearly spherical droplets can create them, including mist and sea spray.
Confusing refraction with dispersion: refraction changes direction, dispersion separates colors; both occur together inside the drop and are explained in more detail in Refraction and Dispersion in Light.

When things look different: supernumerary and secondary bows

Supernumerary bows are faint, closely spaced pastel bands just inside the main arc. They arise from interference between waves emerging from droplets of similar size and are most visible when drops are small and uniform. Secondary bows form when light undergoes two internal reflections inside each drop; they are dimmer and have color order reversed. For a technical discussion see Secondary and Supernumerary Rainbows.

Closing: what you can confidently expect to see

In ordinary circumstances a primary rainbow requires sunlight behind you and a field of droplets ahead; its colors appear because light is refracted, dispersed, internally reflected, and refracted again. The characteristic viewing geometry—about 42 degrees from the antisolar point—lets you predict where the arc will appear. Use the practical checklist and step-by-step instructions above the next time you encounter a post-shower sky to find and photograph the phenomenon with confidence.