How Do Rainbows Form?

What happens to sunlight inside a raindrop?

A rainbow is sunlight that water droplets have spread into its colors and sent back toward the eye of an observer.^[1] Inside each drop, the light is bent, reflected and bent again.^[4][5] As sunlight enters a drop, it slows down and changes direction, a bending called refraction.^[2][7] Part of that light then reflects off the inside of the back of the drop, and it bends a second time as it leaves.^[3][5]

Sunlight looks white, but it contains a whole spectrum of colors.^[3] How much light bends depends partly on its color: violet, the shortest visible wavelength, bends the most, and red, the longest, bends the least.^[2][7] By the time the light leaves the drop, the colors have fanned apart.^[2][7]

Light does not leave a drop in just one direction.^[5] Rays taking many different paths bunch together near one angle of minimum deviation, and that concentrated light produces the bright bow.^[1][5] The National Weather Service calls this path the rainbow ray, and the physics reference HyperPhysics notes that it is often called the Descartes ray, because Descartes is credited with first working out these paths.^[1][5]

Where does the 42-degree angle come from?

The National Weather Service gives the angle of the rainbow ray as 42 degrees.^[1] HyperPhysics gives a range, placing the primary bow between about 40 and 42 degrees from the antisolar point.^[4]

The antisolar point is the imaginary point exactly opposite the Sun, and it sits at the shadow of your head.^[4][8] A rainbow is really a full circle around that point, and the bow people usually see is only part of the circle.^[1][8] The ground normally blocks the lower half, but from a high place such as an aircraft, the whole circle can sometimes be seen.^[2][3]

Why must the Sun be behind you and low in the sky?

The light bounces off the back of each drop and heads back roughly the way it came.^[2] So to see a rainbow, you need to stand with the Sun at your back and the rain in front of you.^[1][3] HyperPhysics adds a handy check: if you can see the shadow of your own head during a rain shower, you are in position to see a rainbow when conditions are right.^[4]

The lower the Sun, the more of the circle shows, and at sunset the bow is a full half-circle whose top stands 42 degrees above the horizon.^[1] If the Sun is more than 42 degrees above the horizon, no rainbow is visible.^[1] That is why, at most latitudes, rainbows are not seen around midday.^[4] They are most common in the later afternoon, when a shower has passed and the Sun in the west lights up rain moving away to the east.^[4][7]

Why are the colors always in the same order?

Because each color leaves the drop at a slightly different angle, the colors always land in the same bands.^[1] In a primary rainbow, red is on the outside of the arc and violet is on the inside.^[7] The Met Office lists the classic order as red, orange, yellow, green, blue, indigo and violet, with red having the longest wavelength and violet the shortest.^[3] It adds that Isaac Newton popularized the idea of seven separate colors, although a rainbow really holds a continuous range of shades, far more than the human eye can tell apart.^[3] National Geographic notes that many scientists think indigo is too close to blue to be truly distinguishable.^[8]

The sky just inside a rainbow often looks brighter.^[4][6] Other rays leave the drops at different angles and reach the eye from drops below the bow.^[5] Those rays include some of every color, so they add a nearly colorless glow rather than more bands.^[6]

What causes a double rainbow?

Not all of the light escapes after one reflection: part of it reflects a second time inside the drop and comes out at a different angle.^[1] The primary rainbow comes from one internal reflection, and the secondary rainbow comes from two.^[1] The National Weather Service puts the secondary bow at around 50 degrees instead of 42, and HyperPhysics places it about 10 degrees farther from the antisolar point than the primary bow.^[1][4] It is about twice as wide, and its colors are reversed, with violet on the outside and red on the inside.^[4][7] It is also fainter: HyperPhysics, citing Schaaf, puts its light at one-tenth the intensity of the primary bow under the same conditions.^[4]

Between the two bows lies a darker strip of sky known as Alexander's band.^[3][6] The primary bow is formed by rays that reach the eye from the highest angle for once-reflected light, while the secondary bow is formed by rays from the lowest angle for twice-reflected light.^[6] As a result, drops in between send no internally reflected light to the observer's eye.^[6] The band is named after the Greek sage Alexander of Aphrodisias, who described it in about 200 AD.^[6]

Why does everyone see their own rainbow?

A rainbow is not an object in a fixed place.^[2][8] It appears only when the sunlight, the water droplets and the viewer's position are all just right.^[2] Every person has a different antisolar point and a different horizon, so no two people see the same rainbow.^[8] When you move, the rainbow moves with you, and a friend standing beside you sees theirs in a slightly different spot.^[7] Someone who seems to be standing at the "end" of your rainbow sees another rainbow, rising from their own horizon.^[8] Because rainbows are circles that shift with each viewer, there is no end to reach.^[8] In 17th-century Ireland, people said that finding a pot of gold was about as likely as finding the end of the rainbow.^[1]