Rainbow Trails

Emma Mason captured this rainbow of many coloured trails at Bad Ragaz, Switzerland.    Water poured down from higher up within the gorge, its drops lit by sunlight at the perfect angles for a bow.    Individual drops left trails of colour during the 1/30sec that the camera’s shutter was open and they tell us much of how a rainbow is made.

©Emma Mason, shown with permission.

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High up at top left we see drops lighting a faint secondary rainbow. Then they become invisible to us. All but some oddballs talked about later. Then each drop flashes a succession of primary rainbow (not spectral!) hues starting with red through orange, yellows, greens, blues, indigos and violets. The colours get more subdued towards the violets. Their glints do not end there. They remain visible but only as ever fainter white and grey. Why?

Primary rainbow glints are all inside a cone extending from our eye and with its axis pointing towards the rainbow's centre, the anti-solar point opposite the sun. This is the ‘rainbow cone’. Drops outside the cone glint primary rainbow light just like those inside it but not to our eye. They cannot send their light towards the eye – they are dark.

As a drop plunges into the cone it first glints bright red. It is at the minimum deviation, MinDev, position where most red rays leaving it cluster forming a caustic. Then as the drop moves further, the MinDev conditions are reached in turn for other colours. The drop glints yellows through to violet.

That is the simple story of most textbooks.

Reality is richer. Let’s look at a drop (at lower left) when it has gone a little way into the cone - When it is glinting blue light towards us most intensely at the blue ray MinDev condition. Other rays than blue can still reach our eye. Two red rays can pass through the drop deviated through the same angle as the blue one. The red deviation angle is greater than the red MinDev angle but many red rays do that. Similarly for greens. Similarly for all colours of shorter wavelength than red. These are not bright MinDev ray clusters, they are fainter. But they are still there. They add their light to the glint making its colour less saturated.

Go far enough into the cone and all the individual colours emerging from each drop mix in the eye to make white. We see that in the top image. In a sky rainbow of millions of raindrops the white glow appears inside the bow as lighter sky. Here we are privileged to see how each drop makes that light.

In reality, a drop slightly inside the cone glints many colours. Here a drop glinting blue at the most intense minimum deviation condition also sends out at the same angle two red rays and two rays of all other longer wavelength colours. The extra colours are faint but collectively they dilute the blue's spectral purity.

Deeper inside the cone the colours glinted are all of similar intensity and we see white.
Rainbow Colours (part of the story)
The Rainbow Cone:
Only drops at the cone's surface or inside it can glint primary rainbow light to the eye.    Drops at the surface glint red. As they penetrate deeper they glint yellows through to violets.

Some trails flash on and off like strobes. Others have their colours displaced. The rainbow is ragged.

The flashing trails are probably from large wobbly oscillating drops. Rainbows need almost perfectly spherical drops. Lose that sphericity and the rainbow is blurred, distorted or destroyed.

Some of the strobed trails flash colours but not in a structured way. The constraining surface tension forces of large drops are relatively weak and they can oscillate in shape as they fall from oblate to prolate spheroids or through forms where one end is flattened. Light passing through these might sometimes glint towards the eye and not at other times.

Colour shifted trails probably result from a less severe distortion.  Drops departing from sphericity by no more than a few percent, flattened for example, can still produce a bow but it is no longer circular. The enigmatic twinned bows might arise in this way when there are two drop populations - small and spherical and large flattened. In the macro peep at a rainbow presented here we are seeing trails from drops of varying degrees of departure from sphericity.