[chris (OP)]

People walking on hillsides, travelling on boats and flying on aeroplanes often report seeing a shadow of themselves surrounded by a halo-shaped rainbow.

This is dubbed the Brocken Spectre effect: https://en.wikipedia.org/wiki/Brocken_spectre

But what actually causes the rainbow-effect, and why is it halo-shaped around the object's shadow?

Answers on a postcard... or just jot your explanations below!

[RD]

... what actually causes the rainbow-effect ...

Computer-generated models of diffraction are an accurate-fit (top left)...


http://www.atoptics.co.uk/droplets/gloab.htm

... and why is it halo-shaped around the object's shadow?

It's centered on the antisolar point of the viewer/camera, not necessarily the centered on the shadow which accompanies it, e.g. here the photographer is in the cheap-seats at the back of the plane.

[chris (OP)]

There's got to be refraction too, to split the white light into the constituent wavelengths.

So what's producing this?

[RD]

There's got to be refraction too, to split the white light into the constituent wavelengths.

If the array of spheres were opaque, (rather than transparent water), e.g. dust/powder,  the multi-colour pattern would still occur via diffraction & interference, so refraction is not necessary for the colours.

Figure 2: A Fraunhofer pattern from lycopodium powder in white light

http://optica.machorro.net/Optica/SciAm/DustInterference/1981-08-fs.html

[evan_au]

why is it halo-shaped around the object's shadow?

The directions in the sky illuminated in the Brocken spectre phenomenon (or in a rainbow) are the set of points which form a specific angle between your eye and the Sun. This defines a cone of directions in the sky that will look illuminated to you as the observer.

The light comes from the Sun and strikes rain (or dust) that is present in the air. But part of this light path is usually blocked by the ground or the road or mountain on which you stand. If you are not standing on any ground (you are in a plane, balloon, helicopter, etc), you can see the full cone illuminated - the halo effect.

[Colin2B]

There's got to be refraction too, to split the white light into the constituent wavelengths.

So what's producing this?

Diffraction.
With refraction, as in a rainbow, longer wavelengths are refracted more than shorter so the red is on the outside of the bow.
With diffraction it's the other way round, shorter wavelengths are diffracted more and so blue/Violet are on the outside of the rings.

[hamdani yusuf]

There's got to be refraction too, to split the white light into the constituent wavelengths.

So what's producing this?

Diffraction.
With refraction, as in a rainbow, longer wavelengths are refracted more than shorter so the red is on the outside of the bow.
With diffraction it's the other way round, shorter wavelengths are diffracted more and so blue/Violet are on the outside of the rings.

Correction:
longer wavelengths are refracted less than shorter so the red is on the outside of the bow.
shorter wavelengths are diffracted less and so blue/Violet are on the outside of the rings.


Comparison of the spectra obtained from a diffraction grating by diffraction (1), and a prism by refraction (2). Longer wavelengths (red) are diffracted more, but refracted less than shorter wavelengths (violet).

[Colin2B]

Correction

Thanks, I should have spent longer proof reading!

It is interesting that because most diffraction experiments are shown with monochromatic light the colour interference effect is often missed.

[chris (OP)]

Thank you everyone.

However, I still do not understand the origin of the rainbow "Glory" pattern manifest in the examples given above.

Why does the aeroplane / person appear to have a rainbow halo. Please can someone explain in more simple terms a logical argument I can follow for why this happens.

[Colin2B]

Why does the aeroplane / person appear to have a rainbow halo. Please can someone explain in more simple terms a logical argument I can follow for why this happens.

I'll try.
First of all the spectre is the shadow. That may seem obvious but it important because it means the sun is behind the head of the observer (shadow caster) so all the light reflected back from the mist will appear to that observer to be from a series of concentric circles centred on the shadow of their head. This is the same for a rainbow, although we only see part of the circle. There are differences between rainbow and Brocken Spectre. Firstly the observer is looking down on the mist and so sees more of the circle, secondly the droplet size is far smaller than raindrops so are not refracted, but are diffracted giving the characteristic inversion of the colour bands.

[chris (OP)]

Thank you! So you need mist or other fine particles in the air at the point where the shadow is cast to cause the diffraction?

[Colin2B]

Thank you! So you need mist or other fine particles in the air at the point where the shadow is cast to cause the diffraction?

Yes, the mist acts as the projection screen for the shadow and its small droplet size is essential for diffraction to occur.

Also, if you imagine the sun directly behind your head with parallel rays, any particular angle of diffraction - and hence colour - will lie on a circle as seen from your viewpoint, hence the halo.