Rays** reflected once inside raindrops make the
primary. Its colours are produced by the two refractions as the
rays enter and leave. Rays are deviated back towards the incoming
sunlight to form a bow appearing opposite
The rays drawn in lighter tones form the "zero
order glow", the secondary
and higher order bows.
One internal reflection produces the primary bow.
over the slider to see the ray paths. Rays close to the drop centre
are deviated almost 180º back on themselves.
Rays further from the centre are deviated less and less until the
deviation reaches a minimum (about 137.5º for deep red light).
This is the "angle of minimum deviation" or "rainbow
angle". The deviation increases once more as the entrance
ray approaches the drop rim .
is deviated into a whole range of angles
cluster strongly around the rainbow angle, test it with the
mouse, and so the bow is at its brightest at that angle. Rays near
the rainbow angle form the bow's bright outer edge.
light is refracted less than blue and its minimum deviation angle
is less. Red is therefore on the outside of the primary bow.
deviated through larger angles make the sky brighter inside
the primary. The brighter sky is colourless because at those angles
the colours strongly overlap.
sky inside the bow
light is deviated through angles smaller than the minimum deviation
angle and the sky is therefore darker beyond the outer edge of the
the bow is dark
are never the tear shaped objects beloved of illustrators. Small
raindrops are kept strongly spherical by surface tension forces. Larger
drops are sometimes flattened by air resistance as they fall and they
may even oscillate or wobble. Even small departures from sphericity
destroy a rainbow or possibly cause some odd
paths are something of a fiction and geometric optics is incapable
of explaining many aspects of rainbows. However, when raindrops are
a millimetre or so in diameter the straight line rays are a reasonable
approximation to some aspects of how light behaves.
take ray paths too seriously
are traditionally measured from the direction of the incoming sunlight.
The deviation angle for red rays forming the edge of the primary bow
is about 137.5º. The centre of a rainbow is directly opposite
the sun (a deflection angle of 180º). The radius of the red edge
of the primary is therefore 180-137.5 = 42.5º
ray paths are accurately computed for wavelengths of 400 and 750 nm
passing through a water drop at 0 Celsius.