Honest Figures

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Science

Rainbows

A rainbow is a full circle about 42 degrees from the point opposite the Sun, and the ground usually hides the lower half.

17 facts

Rainbows
Picture: Tomas Guus, CC0

At a glance

40 to 42 degrees

Angle of the primary bow from the antisolar point

1 reflection

Inside each drop for the primary bow

2 reflections

Inside each drop for the secondary bow

Light bent twice and reflected once

  1. A rainbow comes from sunlight refracting in falling water droplets and reflecting from the back of each droplet.

  2. Sunlight slows as it enters a raindrop and bends, splitting into its colours. Some of it reflects off the inside surface of the drop, then bends again as it exits, sending a spectrum of colours toward the observer.

  3. The light path of a primary rainbow involves refraction and a single reflection inside the drop.

  4. For a rainbow to appear, the Sun must be behind you and water droplets in front of you.

  5. Red has the longest wavelength and violet the shortest. Newton popularised the idea of seven colours, but a rainbow is a continuous range of hues, far more than the eye can tell apart.

Where the 42 degrees comes from

  1. The primary rainbow forms between about 40 and 42 degrees from the antisolar point, the point directly opposite the Sun.

  2. The most vivid and nearly pure colours of the primary bow sit in a narrow band from about 41 to 42 degrees.

  3. The antisolar point lies at the shadow of your own head. If you can see that shadow during a shower, you are in position to see a rainbow if conditions allow.

  4. Rainbows are rarely seen at midday, because at most latitudes the whole 42 degree circle is then below the horizon. They are seen most in the late afternoon, after a shower has passed and the Sun is low in the west.

  5. When the Sun is high, only a small arc of the bow may be visible above the horizon.

A circle with its lower half hidden

  1. The rainbow forms a circular arc around the antisolar point.

  2. Rainbows are actually full circles. The ground usually blocks the lower half.

  3. From a tall building, a mountain or an aircraft you may see the whole circle, as long as water droplets and sunlight are both present below you.

  4. You can look for a rainbow in a waterfall by finding the shadow of your head.

The fainter second bow

  1. A double rainbow has two concentric arcs. The secondary bow is fainter, sits outside the primary and has its colours reversed, because sunlight is reflected twice inside each drop.

  2. The darker strip between the two bows is called Alexander's band, because no sunlight is scattered toward the observer there.

The white rainbow in fog

  1. A fogbow is pale or nearly colourless and broader than an ordinary rainbow, because the tiny droplets make the light diffract and smear out the colours.

Sources

  1. Met Office, Rainbows: optical wonders
  2. Georgia State University HyperPhysics, Primary Rainbow
  3. West Texas A&M University, Why does a rainbow exist only in a narrow band?