What Causes Rainbows: Light Bent Twice Inside a Raindrop

A rainbow is not a physical object sitting at some fixed location in the sky the way a cloud is. It is an optical effect built fresh, moment to moment, from millions of individual raindrops, each acting as a tiny prism, and no two observers standing even a meter apart are looking at exactly the same set of drops. Understanding why requires following a single ray of sunlight into one raindrop and back out again.

Refraction: light bends entering the drop

Sunlight looks white but is actually a mixture of every visible wavelength, from red at the long-wavelength end to violet at the short-wavelength end. When that light passes from air into a denser medium like water, it slows down and bends, a phenomenon called refraction. Critically, different wavelengths bend by slightly different amounts — violet light bends more than red light, a property called dispersion, the same effect a glass prism uses to spread white light into a visible spectrum. Sunlight entering the curved surface of a raindrop refracts, and dispersion begins separating the colors from that very first surface.

Internal reflection: light bounces off the back of the drop

Having entered the raindrop and started separating by color, the light travels to the inside of the drop's far surface, where instead of exiting, most of it reflects back into the drop, similar to how light bounces around inside a glass of water under the right angle. This isn't a perfect mirror-like reflection the way a silvered mirror works; it happens because of the angle at which the light strikes the water-air boundary from inside, a phenomenon related to what makes total internal reflection possible in fiber optic cables, though a raindrop's geometry is curved rather than a straight channel.

Refraction again: light bends exiting the drop

The reflected light travels back across the drop and exits through its surface a second time, refracting and dispersing further as it crosses back from water into air. By the time light emerges from the raindrop, having refracted twice and reflected once, the different wavelengths have separated enough to be visible as distinct colors rather than blending back into white. Red light emerges from each raindrop at an angle of about 42 degrees relative to the original direction of the sunlight; violet emerges at about 40 degrees. This roughly 2-degree spread between red and violet is what gives a rainbow its visible width and color banding.

Why every rainbow is at exactly 42 degrees

Because the refraction and reflection angles inside a spherical raindrop are governed by the same optical physics regardless of which particular drop the light passes through, every raindrop capable of producing red light for a given observer does so at the same 42-degree angle, measured from the antisolar point — the point directly opposite the sun as seen from that observer's own eyes, typically marked by the shadow of their own head. This is why a rainbow always appears as an arc centered on that antisolar point, why you can never walk toward a rainbow and reach it, since a different set of raindrops satisfies the correct angle as you move, and why an airplane passenger can occasionally see a rainbow as a complete circle, since there's no ground to cut off the lower half of the arc from that vantage point.

The secondary rainbow: reversed and fainter

Under the right conditions, a fainter second rainbow is visible outside the primary one, at an angle of roughly 51 degrees rather than 42. This secondary bow forms from light that reflects twice inside each raindrop instead of once, which flips the order the colors emerge in, so a secondary rainbow always shows red on the inside and violet on the outside, the reverse of the primary bow's red-outside, violet-inside pattern. Each additional internal reflection loses more light to the exit refraction that does eventually happen at each bounce, which is why the secondary bow is noticeably dimmer, and why a third-order rainbow, while physically possible from three internal reflections, is essentially never visible to the naked eye against ordinary sky brightness.

Why rainbows need the sun behind you and rain ahead

Because the antisolar point sits directly opposite the sun, a rainbow can only appear in the part of the sky opposite the sun from where you're standing, which is why rainbows are visible in the direction away from the sun, typically when the sun is relatively low in the sky behind an observer and rain, or airborne water droplets from a sprinkler or waterfall, is present ahead of them in that opposite direction. Optical phenomena of this kind, along with the related physics of how droplets and ice crystals scatter light to produce halos and glories, are documented extensively by atmospheric optics researchers and agencies such as the National Oceanic and Atmospheric Administration.