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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 and 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.


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 centered on the sun. With a nominal radius of 42.5º it is similar in size to, but very much broader than, the primary bow.

The tertiary bow's total brightness is 24% of the primary bow and we might 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 that masks the tertiary, (2) the tertiary is much 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 natural higher order bow (3rd order)
There are one or two reports of visual sightings, the most significant by Pedgley* but no photographs had ever been reported. 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 already visible and the rain then intensified at his camera position. Rain was falling sunward and a dark cloud reduced the intensity of the near-sun sky. He blocked the sun with a tree and thought he could see a faint shimmering trace of a bow for 30s. His image after processing showed a definite rainbow and subsequent very critical and careful analysis have 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 has made a special study of rainbows and his success comes from painstaking observation and camera preparation and most important of all, knowing just where to look and what to look for.
Großmann's 3rd order rainbow. 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

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 too has now been photographed by Michael Theusner (Photographic observation of a natural fourth-order rainbow, M Theusner, Applied Optics, Vol. 50, Issue 28, pp. F129-F133 (2011)) a month after the first tertiary sighting.

* 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."