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Double rainbow over an Alaskan landscape

~42°

A primary rainbow is centered on the point opposite the Sun.

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Photo: Eric Rolph at English Wikipedia · CC BY-SA 2.5

The short answer

A primary rainbow is centered on the antisolar point, directly opposite the Sun from your viewpoint. Its outer red edge lies about 42 degrees from that direction.

Why it's true

A rainbow is a viewing geometry, not a colored object fixed above the landscape. The droplets that send light to your eyes occupy particular directions relative to you and the Sun. Another observer sees light from a different set of droplets, even when both people describe the same apparent arc.

Sunlight bends as it enters a water droplet, reflects once inside, and bends again on leaving. Different wavelengths bend by different amounts. This dispersion separates the colors, while the geometry concentrates emerging light near the angles that make the bright primary bow.

The reference direction is the line from the Sun through your position and onward away from it. The rainbow forms a circular pattern around this antisolar direction. Red appears on the outside of the primary bow, while violet lies closer to its center.

By the numbers

~42°

Angular radius of the primary red edge

1

Internal reflection in the primary light path

360°

Possible complete circular extent

The backstory

The familiar arch is only the visible portion of a possible circle. On level ground, the horizon and nearby terrain normally prevent you from seeing the droplets that would complete the lower section. There is no physical requirement for a rainbow to end at the ground, and its apparent feet do not mark reachable locations.

From an aircraft, or from a sufficiently elevated viewpoint with illuminated droplets below, a full circular rainbow can sometimes be visible. Height alone does not guarantee this view: the Sun, observer, and droplets still need the correct arrangement. The circle remains centered opposite the Sun rather than on a particular mountain or cloud.

This geometry also explains why a higher Sun makes a ground observer's rainbow appear lower. As the Sun climbs, the antisolar point moves farther below the horizon. Under ordinary level-ground conditions, a primary bow is generally not visible once the Sun is higher than roughly its angular radius.

The wider picture

The quoted 42 degrees describes an angle at the observer, not the size of a droplet or the distance to the rain. A nearby spray and a distant rain shower can produce bows with similar angular radii. Their physical distances may differ greatly, but the optical paths select approximately the same viewing directions.

A secondary rainbow follows a different path involving two internal reflections. It appears outside the primary bow and reverses the color order. It should not be confused with a second copy of the primary circle; the extra reflection changes both the emerging angle and the amount of light available.

Worth remembering

  • A primary rainbow belongs to an observer's viewing geometry, so it cannot be approached like a fixed object.
  • Its red outer edge is approximately 42 degrees from the direction opposite the Sun.
  • A complete circular bow is possible when the viewing position and droplets allow the lower portion to be seen.

In context

A rainbow is a direction-dependent pattern of light arriving at an observer, not a painted arch fixed to a location in the landscape. Different observers can see similar arcs while receiving light from different droplets. Moving toward an apparent end changes the geometry rather than reaching a physical object.

A closer look

Why a bow can form a circle

Droplets sending the relevant light toward the eye can occupy directions around the antisolar axis. The ground often hides the lower portion, producing the familiar arch. From a sufficiently unobstructed elevated viewpoint, more of the circle may become visible. Its center still depends on the Sun and observer rather than a fixed point marked on the ground.

Several optical steps work together

Sunlight refracts on entering a droplet, reflects internally and refracts again on leaving. Different wavelengths follow slightly different directions, separating the colors. The main bright arc arises from the concentration of outgoing rays near particular directions, not because each drop chooses a single permanent color. A secondary bow involves an additional internal reflection and reverses the color order.

Related facts

The blue sky involves scattering rather than the droplet geometry of a rainbow. Air scatters short wavelengths of visible light more strongly than long ones.

Orbital landmark visibility also requires specifying the observer and viewing conditions. The Great Wall is difficult to distinguish from orbit with the naked eye.

Cloud droplets supply a related example of liquid water interacting with sunlight. An ordinary puffy cloud can weigh more than a million pounds.

The light-based meter connects optical behavior with precise measurement. The meter is defined using the speed of light in a vacuum.

Key terms

Antisolar point
The direction exactly opposite the Sun from an observer’s position.
Dispersion
The separation of light by wavelength because different wavelengths propagate differently in a material.

People also ask

Can I walk to the rainbow’s end?

No. Its apparent position is set by the light reaching your viewpoint, so moving changes which droplets contribute.

Do two people see exactly the same drops?

Not generally. Each observer receives the relevant rays along directions determined by their own position.

Can a rainbow be a full circle?

Yes. An unobstructed viewpoint can reveal more of the circular geometry normally hidden by the ground.

Why are the colors separated?

Water refracts different wavelengths by different amounts, producing wavelength-dependent outgoing directions.

Why is the secondary bow reversed?

Its additional internal reflection changes the ray geometry and reverses the order of colors compared with the primary bow.

Sources

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