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   3rd & 4th Order Rainbows 


3rd & 4th order rainbows.

This BowSim simulation, made by tracing several hundred million rays through a raindrop, looks towards the sun.

On the left is an unfiltered view. All that can be seen is the white glare of the zero order glow surrounding the sun.

The filtered view at right shows only the rays making the 3rd order (inner) and 4th order (outer) rainbows.


Updated - Scroll down..       Rays leaving raindrops after three reflections produce a tertiary rainbow. Unlike the primary and secondary bows which are opposite the sun and centered on the antisolar point, the tertiary appears sunwards and is centered on the sun. With a nominal radius of 42.5º it is similar in size to, but broader than, the primary bow.

The tertiary bow's total brightness is 24% of the primary bow. We might therefore think that it ought to be easily visible. There are severe difficulties: (1) its light is swamped by that of rays that pass through raindrops without any internal reflection. These generate an intense glare around the sun, the zero order glow, (2) the tertiary is broader than the primary and secondary, thus its luminosity per unit solid angle of sky is correspondingly less, (3) glare and scattered light from the nearby sun interferes.

First ever image of a natural 3rd order bow

There were one or two early reports of visual sightings, the most significant by Pedgley*. But no photographs existed.

All that changed on the evening of May 15, 2011 when Michael Großmann at Kämpfelbach in SW Germany saw a rain shower approaching from the north. Primary and secondary bows were visible. The rain intensified at his camera position. It was also falling sunward and a dark cloud reduced the brightness of the near-sun sky. Michael blocked the sun with a tree and thought he could see a faint shimmering trace of a bow for 30 seconds. He took a picture and after processing it showed a definite rainbow!

Subsequent very critical and careful analysis confirmed the sighting (Photographic evidence for the third-order rainbow, M Grossmann, E Schmidt, & A Haussmann, Applied Optics, Vol. 50, Issue 28, pp. F134-F141 (2011)). Michael Großmann had made a special study of rainbows and his success came from painstaking observation, camera preparation and most important of all, knowing just where to look and what to look for.

Großmann's 3rd order rainbow - The first known image. Star field calibration and computation of the sun position and angular properties of the image verified that the coloured arc was indeed the long sought tertiary rainbow. Images ©Michael Großmann, shown with permission

4th order bow also seen

The 4th order bow (four internal reflections) is close to the 3rd order but with reversed colours. Its brightness is only 15% of that of the primary. That was photographed by Michael Theusner (Photographic observation of a natural fourth-order rainbow, M Theusner, Applied Optics, Vol. 50, Issue 28, pp. F129-F133 (2011)) only a month after Großmann's triumph.

Many more sightings

Somehow things are easier once they have been done once.   Previously unconquered mountains get thronged with climbers.   Now, the 3rd, 4th and even 5th order rainbows have been photographed several times.    Modern cameras and advanced post processing contribute – plus knowing that it is possible.

Click these thumbnails for sightings in roughly chronological order. Check OPOD for new ones.




And indoors..

Image them yourself

Perseverance, willingness to get wet and knowing where to look are needed more than anything else.   Even ‘ordinary’ primary and secondary rainbows are relatively infrequent and the right conditions to capture the elusive higher orders are more so. Do not search during a thunderstorm!

Bright primary and secondary bows are a good sign.   Then look sunwards.   Rain must be falling in that direction.   The 3rd order bow is two outstretched hand widths from the sun.   Uniform dark cloudy sky in that direction is best.   The sun itself should be shielded by a small cloud, a building or a special camera shield.

Use a relatively wide angle lens.   The lens must be clean with no raindrops – make a box for the camera or otherwise shield it.   Above all, no sun on the camera.    Take many shots.   Think maybe about stacking. Look how other observers have processed their images.   Avoid grotesque over saturation or contrast enhancement.  In general, if a feature does not show faintly on an original image, over 'enhancement' will not show it.

Good luck!


* D E Pedgley reported sighting the 3rd order bow in Nairobi and described it in Weather (Weather 41, 401 (1986)) "Whilst in Nairobi recently I had the good fortune to see a tertiary rainbow. On 21st May 1986 at 17.55 a new shower cloud had just started to rain out over my hotel in dense curtains of medium sized drops brilliantly lit by the low sun. From the balcony of my fourth floor room I could see not only a bright primary, accompanied by a moderate secondary, but also a weak bow in the direction of the sun, which was conveniently shielded by the side of the building. The bow was scintillating but distinct for two or three minutes. It was about the same size as the primary bow, with red on the outside and green on the inside."