One of our planet’s most spectacular natural phenomena, rainbows, result from a
combination of light scattering processes in water droplets: reflection, refraction and diffraction
(and subsequent ‘interference’).
Although I have not studied the subject of ‘optics’ for 40 years, the recent unearthing of the photograph below,
taken by colleague, David Briggs, whilst on a two-year sabatical to the Antipodes, stimulated me to investigate the phenomenon of
rainbows a bit further.
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© David Briggs
17:41, 1 October 2004. Blue Mountains, New South Wales, Australia
Kodak DX 6490 (4Mp), no polarising filter or post-processing |
The three main features of a rainbow.
From the left: the secondary rainbow, then the primary rainbow.
‘Alexander’s dark band’ spans the ’bows. |
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A colour-enhanced (92% saturation, blue subtracted - using Adobe’s Photoshop Elements) magnification of the above image exagerates the diminishing series of supernumerary arcs associated with the primary rainbow. Three supernumerary arcs are just
discernible, but all the red ones overlap the violets of the previous arcs, resulting in turquoise and purple striations.
Even with this level of enhancement, no supernumerary arcs of the secondary ’bow are apparent. The brightest ones should be present just outside it.
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Tertiary Rainbow - enhanced
This brief spectacle, a rainbow around the sun - rather than opposite
it, lasted for several minutes. It resulted from three internal reflections of sunlight in the water droplets in a
patch of 'milky' cloud that had formed.
The colour-order (red inside) is reversed relative to that of a primary bow.
Given the maximum field-of-view of the camera (about 65° with no optical zoom),
I estimate that the corona/bow is offset by about 30° from incident sunlight - having nearly completed a 'lap' around the inside of the droplets.
Wife Patricia's hat was pressed into service as an improvised sun-mask.
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© Colin Poyton
12:30 GMT August 16, 2009. Canal bank at Kintbury, Berkshire, UK.
Sony DSC H20
(positioned 40cm above ground-level), no polarising filter, post-processed with Adobe Photoshop for 90% colour saturation.
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Links to articles that explain
how the features in the photographs are produced
- An overview of a rainbow’s formation
- The primary rainbow
- The secondary rainbow
- The formation of supernumerary arcs
- The physics of rainbow formation
- Mathematicical analysis of light ‘scattering’ in a water sphere predict the formation
of primary and secondary ’bows, the dark band, and supernumerary arcs
- Analyses closely match observations. Reference to
a Lee diagram suggests that, where the supernumeraries are brightest in the
photograph above, the diameter of water droplets was about 0.8mm
- A suggested, but nevertheless compelling, resolution of (and associated comments on) the ‘Violet Conundrum’.
This article explores the eye’s perception of the colours blue and violet and the limitations of conventional methods of representing violet.
Supernumeraries - my interpretation
An understanding of the manifestation of supernumary arcs is
not particularly intuitive. I offer the text below as my interpretation
of the explanations gleaned from the articles above.
If I have understood the above articles correctly, a shaft of sunlight (comprising
a large number of parallel light rays - except not absolutely parallel, as the solar disc subtends/occupies
about 0.5º) enters the top of a droplet of rain (which, as its size approaches
miniscule, can be considered to be spherical) where it is
first refracted (bent downwards to a degree that depends on its wavelength - colour).
Some of the numerous rays then, from the rear of
the droplet, undergo total internal reflection and then, for the simple case, emerge from the bottom of the droplet
where they are refracted (bent upward to a degree that depends on their colour) and,
as they emerge, they are also diffracted (spead-out).
For any given angle, close to 40º from the anti-solar point (the point below horizontal that is opposite the sun),
an observer will see a multitude of light rays returned from water droplets
in his/her line-of sight. From any individual droplet the observer will see two light rays, both of the virtually the same, single colour - because,
there are only two unique paths from his/her eye back to the sun via that droplet.
At angles of between 36º ish and 39º i.e. closer to
the ground, an observer will not be able to see rays from the sun directly through any
droplet (as the 'unique' rays will now be 'landing' towards the observer's feet) but can, from droplets
at a slightly lower angle than the previous droplet, observe pairs of monochromatic rays
that were diffracted as they emerged from the droplets. However
this pair of diffracted rays have each traversed different paths (and therefore spent
different times travelling at different speeds) so, when they combine at the eye, although
they will have a similar amplitude, they will not maintain a constant phase relationship for
differing diffraction angles. This pair of rays will therefore
interfere with each other either constructively (bright) or destructively (cancel
- dark) depending on the wavelength of the light and the difference in path
lengths that the rays experienced as they traversed the droplet.
Hence an observer, as he/she scans towards the anti-solar point, will see, alternately, the presence
or absence (cancelled-out) of narrow bands of relatively monochromatic (single colour) light (arcs of colour)
which rapidly diminish in intensity as the angle reduces.
There are no paths from sun-to-eye through the droplet, involving a single
reflection, for angles of greater than 40º from the anti-solar point.
On reflection, this explanation provides a clear corollary of the adage that a
picture (4th bullet above) is better than a thousand words! Also see:
http://www.philiplaven.com/p8f.html
Aren’t rainbows much more fascinating than you ever imagined?
page-visits since March 2007
