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🌈 Why the second bow in a double rainbow is reversed

The faint outer arc is not a second shower or a reflection off a cloud. It comes out of the same raindrops as the bright one, from light that bounced twice instead of once — and that single extra bounce costs it more than half its brightnes

5
lessons
~18 min
to learn
Adults
level
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What you’ll learn

  1. One drop, two reflectionsTrace how a single raindrop can send out both a primary and a secondary bow.Two refractions with one internal reflection make the primary; a second reflection makes the secondary, at the cost of most of its light.
  2. The geometry of a bowConnect a rainbow's size, position and colour order to the angles at which light reaches you.Both bows are circles centred on the antisolar point — about 42 degrees for the primary, 51 for the secondary, with the spectrum reversed in the outer one.
  3. The dark space betweenExplain why the sky between the two bows is genuinely darker, not merely apparently so.Neither reflection path can deliver light between about 42 and 50 degrees, and a bow is a lit disc rather than a ring, so the band is squeezed dark from both sides.
  4. How people worked it outFollow the people who took a raindrop apart, from a glass sphere of water to Newton's spectrum.Al-Fārisī around 1300 and Theodoric of Freiberg in 1304 each modelled a drop with a water-filled sphere; Descartes supplied the angles and Newton the colours.
  5. What else can a drop do?Place the double rainbow among the other bows a raindrop can make, and learn what it is not.Higher orders exist but are faint and mostly sunward; the fifth hides in Alexander's dark band, and a twinned bow is a separate, still-unexplained phenomenon.

Questions this course answers

How many internal reflections make the secondary rainbow?

The secondary bow is made by light that reflects twice inside a raindrop before leaving it.

What happens to a light ray at the moment it enters a raindrop?

Refraction at the curved surface bends short wavelengths more than long ones, which is what starts the colours separating.

How bright is the secondary bow compared with the primary?

Atmospheric Optics gives the secondary 43 per cent of the primary's total light, spread over a band 1.8 times wider — so any patch of it is dimmer still.

Where is the centre of a rainbow?

Every drop that sends you rainbow light sits at a fixed angle from the antisolar point, which is usually below the horizon — so the ground cuts the circle into an arch.

Roughly what angular radius does the secondary bow have?

The secondary sits at about 51 degrees, some nine degrees outside the primary's 42.

How is the secondary bow's colour order different?

Secondary rays are deviated through more than 180 degrees, so the least-deviated colour — red — emerges on the inner edge instead of the outer.

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