Glory formation, Debye theory & surface waves

Last updated on September 16, 2023

Glory Formation, Debye Theory & Surface Waves: A Detailed Exploration

Glory formation is a captivating atmospheric optics phenomenon that occurs directly opposite the sun. When observing a glory, one can notice a bright center with strongly polarized light. These observations suggest that droplets in the atmosphere somehow deflect light through angles of approximately 180º, involving at least one internal reflection.

While simple diffraction theory fails to fully explain the glory and the positions of its rings, rigorous Mie scattering theory, derived from Maxwell's equations of electromagnetism, accurately predicts the glory. However, Mie theory only describes what happens and not how it forms.

Fortunately, Peter Debye's reformulation of Mie theory sheds further light on the subject. According to Debye theory, the primary source of the glory's central illumination is light that undergoes a single internal reflection within the droplets. Additionally, there are lesser contributions from light reflected 10, 6, and 5 times.

Despite these insights, one aspect of the glory formation remains puzzling. An apparent contradiction arises when considering the ray path within the droplet. The dotted ray with one reflection, shown at the upper left in the accompanying image, appears impossible due to water's inability to refract strongly enough. The actual path, depicted as a solid line for red light, falls short of the expected 180º by 14.4º.

To resolve this contradiction, another optical phenomenon must be taken into account: surface waves. In addition to reflection, refraction, and diffraction, surface waves play a crucial role in explaining the glory formation. When an incoming ray grazes the surface of a droplet, it can travel along the rim as a "surface wave" before being refracted. The grazing incidence condition still holds during internal reflection, allowing for a delayed reflection. A third delay occurs as the light exits the droplet. These surface waves are represented schematically by red dotted lines in the image.

Surface waves are most pronounced when the incident light grazes the droplet's surface, causing the refracted ray to exit parallel to the surface. This creates an opportunity for a displaced and weaker internally reflected beam after a delay. Although surface waves decay rapidly, the total path length required for a 10µm diameter droplet is less than 1µm or 1-2 wavelengths.

While the explanation involving surface waves provides a compelling account of glory formation, alternative interpretations exist. It is important to acknowledge that our tendency to seek explanations based on everyday experiences may lead to misunderstandings. The physics described by Maxwell's equations, however, offers a comprehensive understanding of this captivating atmospheric phenomenon.

In conclusion, glory formation, Debye theory, and surface waves intertwine to unravel the mysteries of this captivating atmospheric optics phenomenon. By incorporating Debye theory and considering the influence of surface waves, we gain valuable insights into the mechanisms behind glory formation. Although some aspects may initially appear paradoxical, a deeper understanding of the underlying physics enables us to appreciate the beauty and complexity of the natural world.

A glory is directly opposite the sun and has a bright centre whose light is strongly polarised. These observations tell us that droplets somehow deflect light through angles of around 180º and that at least one internal reflection is involved.

Simple diffraction theory fails to explain the glory or the positions of its rings. Rigorous Mie scattering theory, as used in IRIS, predicts the glory perfectly. But gives gives no clues to how it forms. Mie theory - formulated at a fundamental level from Maxwell's equations of electromagnetism - says only what happens and not how.

Fortunately, a reformulation of Mie theory made by Peter Debye, reveals more. The major source of the glory's central illumination is light reflected once inside droplets. There are lesser contributions from light reflected 10, 6 and 5 times. Philip Laven provides an excellent account of the application of Debye theory to light scattering by water drops.

Impossible ray path? The dotted ray with one reflection shown at upper left is impossible! Water does not refract strongly enough. The actual path, drawn as a solid line for red light, leaves the droplet 14.4º short of the demanded 180º. Paths entering the sphere in other positions also fail to explain the glory. Diffraction in small droplets eliminates the sharp ray paths but does not solve the problem.

How do we explain the apparently impossible light path? We can do so by taking account of another optical phenomenon in addition to reflection, refraction and diffraction -- surface waves.

The incoming ray at left grazes the droplet surface. Under these conditions it can travel along the rim as a "surface wave" before being refracted. At the internal reflection the grazing incidence condition still holds and the reflection can be delayed. A third delay can take place as the light exits. The surface waves are shown schematically at left as red dotted lines.

Surface waves are strongest for light at grazing incidence, i.e.when the ray shown at right is refracted so that it would leave the denser medium parallel to the surface. The surface wave can, after a delay, form a displaced and weaker internally reflected beam. Surface waves decay very rapidly but for a 10µm dia. droplet the total path length required is less than 1µm or 1-2 wavelengths.

There are other interpretations. Any mystery is of our making in that we often seek explanations for the world in terms of our everyday or macro experience and these do not exist for the glory. Nonetheless, the physics of Maxwell is fully able to account for it.

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Reference Atmospheric Optics

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