What is a Glory?
A Glory is an optical effect, not unlike a rainbow, where an object appears to have a halo of light broken into individual colours. Usually, the object is a shadow of a person but, if flying, the object would be the aeroplane the person is flying in. Interestingly, you can tell where the person taking the photo is sat in the aeroplane by where the centre of the Glory intersects the aeroplane. In the photo, below the photographer is sat in the middle of the plane just ahead of the wings.
When the object is the distorted shadow of the person viewing the Glory, it is called a Brocken Spectre. The Brocken is a mountain in the Harz Mountains in Germany whose geometry and meteorological conditions lend themselves to the formation of these Glories.
How does it Work?
So the basics behind the Glory are that a light source, like the Sun, is directly behind the person seeing the Glory. In front of the person would be cloud or fog that reflects some of the light back to the person.
So, when out walking, you need a particular geometry to see this. You need the sun behind you and in front you need a cloud or fog bank. So you need to be on, for example, a ridge looking down, and the sun cannot be too high.
The spectre appears deformed because of the long shadow that is cast, but is really just you blocking out the sunlight.
The Glory Itself
The Glory itself is a set of concentric rings with blue at the centre and red further out. This is opposite to a rainbow where red is the lowest arc and blue the highest. It is also possible to see higher order rings following the same pattern as the innermost ring, but with reduced intensity.
Rainbows (more here) are an effect of refraction, “2” in the below diagram; whilst Glories have the characteristics of a diffraction phenomena, “1” in the below diagram.
The exact mathematics required to produce the Glory need a computer to calculate the light intensities based on Mie Scattering. The parameters are water droplet size, refractive index and angle on incidence. One thing that does seem to be required for a Glory is a fairly uniform droplet size.
Whilst Mie Scattering gives the right answer in terms of computer simulations it does not explain what is actually happening. Several theories have been tried:
Internal reflection of the light ray inside the water droplet. The issue with this is that water does not have a high enough refractive index to bend the light ray enough to return it to starting point. The best water can do comes up about 14º short.
Maybe there could be multiple internal reflections before the light ray returns to the observer. The issue here is that intensity is lost at each reflection so light reflected multiple times would be very faint; much fainter than is actually observed in Glories.
Next way an idea that light rays incident with the edge of the water droplet could propagate a short distance along the surface before being refracted and reflected off the back wall, thus making up the missing 14º. The issue with this is that the surface propagation, though possible, would result in a significant reduction in intensity of the light eventually reflected back.
The current theory is that the largest contribution to the formation of a Glory is from waves near (within 1 wavelength) of the surface of the water droplet. These waves are able to “tunnel” into the water droplet, and eventually after several shallow reflections (where energy is not lost) are able to tunnel out and return to the observer. This tunnelling effect has been observed in many areas of physics and quantum mechanical tunnelling is well known (for example in alpha particle radioactivity). However, it is a wave phenomenon and light is a wave.
So the conclusion is the Glory effect is a light tunnelling phenomena.