Optics & Atmosphere

Why Do Rainbows Curve?

A rainbow is not shaped like an arch in the sky. It is part of a full circle, with the horizon hiding the rest from view.

The short answer

A rainbow is actually a full circle. You see an arc only because the horizon blocks the lower half from view. From an airplane above the rain, you can sometimes see a complete circular rainbow below you. The curve exists because the optics that create a rainbow operate at a specific fixed angle from the antisolar point, the point directly opposite the sun from your perspective. Each raindrop in the air acts as a tiny prism and mirror. Light enters the front of the drop, refracts (bends) as it passes into the water, reflects off the back interior surface, and refracts again as it exits. Red light exits at about 42 degrees from the antisolar point and violet exits at about 40 degrees. Because these angles are fixed by the physics of water, the only raindrops that can direct red light to your eye are those that sit at exactly 42 degrees from your line of sight to the antisolar point. Every such drop forms a circle at that angle around the antisolar point, which is why the rainbow traces a circular arc in the sky.

Full rainbow arc over an open green field after rain

Rainbows are full circles

Geometrically, every rainbow is a complete circle centered on the antisolar point. The horizon blocks the lower half from view for observers on the ground. Pilots and skydive instructors regularly see circular rainbows.

The magic angle

Red light exits raindrops at 42 degrees from the antisolar point. Violet exits at 40 degrees. These angles are fixed by the refractive index of water. Every rainbow has these same angles.

Common myth

No two people see the same rainbow. Every observer sees light from different raindrops, because the drops forming your 42-degree red ring are different drops from those forming anyone else's. A rainbow is personal to each observer.

Secondary rainbows

The fainter rainbow sometimes visible outside the main arc is a secondary rainbow produced by light reflecting twice inside each raindrop. This reverses the color order (red on the inside) and appears at about 51 degrees.

Visual answer

Why Raindrops Only Return Specific Colors to Your Eyes at Specific Angles

The geometry that forces every rainbow to be a circular arc centered on the antisolar point.

1

Light enters the raindrop and refracts

White sunlight hits the curved front surface of a raindrop. Different wavelengths (colors) refract at slightly different angles because the refractive index of water varies with wavelength.

2

Light reflects off the back of the drop

The separated colors reflect off the inside back surface of the spherical drop, staying inside the water. About 4 to 5 percent of light exits the back as a transmitted beam; the rest reflects.

3

Light exits at a specific angle for each color

The refracted and reflected light exits through the front of the drop. Due to the spherical geometry and the refractive properties of water, red exits at about 42 degrees and violet at about 40 degrees from the incoming light direction.

4

Only drops at the exact angle reach your eye

For red to reach your eye, the raindrop must be at exactly 42 degrees from your line to the antisolar point. All such drops form a circle around that point at that angle, creating the circular arc.

The antisolar point

The Shape of Every Rainbow Is a Consequence of Spherical Geometry

The antisolar point is always directly opposite the sun from your perspective. To find it, draw an imaginary line from the sun, through your head, and out the other side. That endpoint is the center of every rainbow you will ever see. Rainbows are always centered on this point, which is why the antisolar point is always below the horizon when the sun is above it, meaning you can only see the upper portion of the circle.

The radius of the arc is fixed at 42 degrees for the primary rainbow. This never changes because it is determined by the refractive index of water, which is a physical constant. You cannot see a rainbow of a different size or at a different angle from a rain shower because those geometric conditions do not exist for water.

Moonbows, which are rainbows produced by moonlight rather than sunlight, exist and have been photographed. They follow identical geometry and the same 42-degree rule. They appear white or very pale to the human eye because moonlight is too dim to activate color vision effectively, but long-exposure photographs reveal full color.

Tiny note

You can never reach the end of a rainbow because it moves with you

A rainbow is not a fixed object in the sky. It is a visual phenomenon defined by the angle between your eye, the raindrops, and the sun. As you move toward where a rainbow appears to end, the antisolar point moves with you and the rainbow moves with it. The end of a rainbow always remains exactly the same angular distance away. You cannot walk to it any more than you can walk to the horizon.

Myth vs reality

Myth vs Reality

What people think

Rainbows exist in the sky like physical objects

Rainbows have no fixed location. They are an optical phenomenon that appears at a specific angle relative to each individual observer. The drops forming your rainbow are different drops from those forming anyone else's rainbow, even if you are standing next to each other.

What actually happens

A rainbow is a personal optical experience produced in your line of sight

The rainbow is generated specifically for your viewpoint by the geometry of sunlight, your eye position, and the position of the water drops. Change your viewpoint by even a few feet and you are seeing a slightly different set of drops arranged at the required angle.

Quick answers

Common questions

Why does the sky inside a rainbow look brighter?

Light that reflects once inside a raindrop exits in a range of angles below 42 degrees, not just at the rainbow angle. This scattered light fills the area inside the arc with diffuse illumination, making the interior look noticeably brighter than the sky outside the arc.

Why are the colors always in the same order?

The order is fixed by the refractive index of water for each wavelength of light. Red refracts least and exits at the widest angle (42 degrees). Violet refracts most and exits at the narrowest angle (40 degrees). This always places red on the outside and violet on the inside.

Can you see a rainbow at noon?

No. For a rainbow to be visible, the sun must be below 42 degrees above the horizon. If the sun is higher than 42 degrees, the 42-degree rainbow arc falls entirely below the horizon and is invisible from the ground. Rainbows are typically visible only in early morning or late afternoon.

What is a fogbow?

A fogbow is produced by tiny fog droplets instead of raindrops. Because fog droplets are much smaller than raindrops, diffraction effects dominate over refraction and the colors blur together, producing a white or faintly colored arc slightly wider than a standard rainbow.

Why does the secondary rainbow have reversed colors?

The secondary rainbow forms from light that reflects twice inside each raindrop before exiting. This second reflection reverses the geometry and the exit angles, placing red on the inside and violet on the outside, the opposite of the primary rainbow.

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