Alexander’s Band

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This is one of a set of almost 40 diagrams exploring Rainbows.

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Description

Alexander's Band

What is Alexander’s Band
When both primary and secondary rainbows are visible, Alexander's band is a dark area between the two.
Is Alexander’s band the area between a primary and secondary rainbow?
Yes! Alexander's band is the darker area of sky between a primary and secondary rainbow.
What is a primary rainbow?
Primary rainbows appear when sunlight is refracted as it enters raindrops, reflects once off the opposite interior surface, is refracted again as it escapes back into the air, and then travels towards an observer.
What is a secondary rainbow?
A secondary rainbow appears when sunlight is refracted as it enters raindrops, reflects twice off the inside surface, is refracted again as it escapes back into the air, and then travels towards an observer.
How many times is sunlight reflected inside one of the raindrops that form part of a secondary rainbow?
The formation of a secondary rainbow involves two reflections inside falling raindrops.

About the Diagram

Alexander’s band

Alexander’s band (Alexander’s dark band) is an optical effect associated with rainbows. The term refers to the area between primary and secondary bows that often appears to be noticeably darker to an observer than the rest of the sky.

  • The areas of sky around a rainbow may appear blue or grey depending on weather conditions and the amount of cloud in the sky. But these areas outside, inside and between primary and secondary rainbows tend to appear tonally different from one another:
    • The area inside the arcs of a primary rainbow always appears tonally lighter than the rest of the sky.
    • The area outside primary and secondary rainbows appears darker.
    • The area between primary and secondary rainbows appears the darkest – this is Alexander’s band.
  • Alexander’s band can be explained by the fact that fewer photons are directed from this area of the sky toward an observer.
  • The raindrops that form a primary rainbow all direct exiting light downwards towards an observer so away from Alexander’s band.
  • The raindrops that form a secondary bow all direct light upwards, so away from Alexander’s band, before a second internal reflection directs light downwards towards an observer.
  • Alexander’s band is named after Alexander of Aphrodisias, an ancient Greek philosopher who commented on the effect in his writing.
Primary rainbow

The most common atmospheric rainbow is a primary bow.

  •  Primary rainbows appear when sunlight is refracted as it enters raindrops, reflects once off the opposite interior surface, is refracted again as it escapes back into the air, and then travels towards an observer.
  • The colours in a primary rainbow are always arranged with red on the outside of the bow and violet on the inside.
  • The outside (red) edge of a primary rainbow forms an angle of approx. 42.40 from its centre, as seen from the point of view of the observer. The inside (violet) edge forms at an angle of approx. 40.70.
  • To get a sense of where the centre of a rainbow might be, imagine extending the curve of a rainbow to form a circle.
  • If your shadow is visible as you look at a rainbow its centre is aligned with your head.
  • A primary rainbow is only visible when the altitude of the sun is less than 42.4°.
  • Primary bows appear much brighter than secondary bows and so are easier to see.
  • The curtain of rain on which sunlight falls is not always large enough or in the right place to produce both primary and secondary bows.
Secondary rainbow

A secondary rainbow appears when sunlight is refracted as it enters raindrops, reflects twice off the inside surface, is refracted again as it escapes back into the air, and then travels towards an observer.

  • A secondary rainbow always appears alongside a primary rainbow and forms a larger arc with the colours reversed.
  • A secondary rainbow has violet on the outside and red on the inside of the bow.
  • When both primary and secondary bows are visible they are often referred to as a double rainbow.
  • A secondary rainbow forms at an angle of between approx. 50.40 to 53.40 to its centre as seen from the point of view of the observer.
  • A secondary bow is never as bright as a primary bow because:
    • Light is lost during the second reflection as a proportion escapes through the surface back into the air.
    • A secondary bow is broader than a primary bow because the second reflection allows dispersing wavelengths to spread more widely.
Remember that:
  • The axis of a rainbow is an imaginary line passing through the light source, the eyes of an observer and the centre-point of the bow.
  • The space between a primary and secondary rainbow is called Alexander’s band.

Some Key Terms

Rainbow

A rainbow is an optical effect produced by illuminated droplets of water. Rainbows are caused by reflection, refraction (bending) and dispersion (spreading out) of light in individual droplets and result in the appearance of an arc of spectral colours.

  • Atmospheric rainbows only appear when weather conditions are ideal and an observer is in the right place at the right time.
  • Waterfalls, lawn sprinklers and other things that produce air-borne water droplets can produce a rainbow.
  • An atmospheric rainbow is formed from countless individual droplets each of which reflects and refracts a tiny coloured image of the Sun towards the observer.
  • As white light passes through water droplets, refraction causes the light to disperse and separate into the different colours seen by an observer.
  • If the sun is behind an observer then the rainbow will appear in front of them.
  • When a rainbow is produced by sunlight, the angles between the sun, each droplet and the observer determine which ones will form part of the rainbow, the colour each droplet will produce and the sequence in which they appear.
Spectral colour model

The spectral colour model represents the range of pure colours that correspond to specific wavelengths of visible light. These colours are called spectral colours because they are not created by mixing other colours but are produced by a single wavelength of light. This model is important because it directly reflects how human vision perceives light that comes from natural sources, like sunlight, which contains a range of wavelengths.

  • The spectral colour model is typically represented as a continuous strip, with red at one end (longest wavelength) and violet at the other (shortest wavelength).
  • Wavelengths and Colour Perception: In the spectral colour model, each wavelength corresponds to a distinct colour, ranging from red (with the longest wavelength, around 700 nanometres) to violet (with the shortest wavelength, around 400 nanometres). The human eye perceives these colours as pure because they are not the result of mixing other wavelengths.
  • Pure Colours: Spectral colours are considered “pure” because they are made up of only one wavelength. This is in contrast to colours produced by mixing light (like in the RGB colour model) or pigments (in the CMY model), where a combination of wavelengths leads to different colours.
  • Applications: The spectral colour model is useful in understanding natural light phenomena like rainbows, where each visible colour represents a different part of the light spectrum. It is also applied in fields like optics to describe how the eye responds to light in a precise, measurable way.

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