What question did this study set out to answer?

To develop an improved theoretical description of high-frequency scalar plane wave scattering by a transparent sphere, resolving the mathematical mechanics of the rainbow and the glory.

January 1, 1969Journal of Mathematical Physics

High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory

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Authors

HNH. M. NussenzveigUniversidade Federal do Rio de Janeiro

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Implication

Theoretical analysis reveals uniform asymptotic expansions for wave scattering in transparent spheres, indicating surface waves and complex rays dictate rainbow and glory phenomena.

Key Points

To develop an improved theoretical description of high-frequency scalar plane wave scattering by a transparent sphere, resolving the mathematical mechanics of the rainbow and the glory.
Applied the modified Watson transformation to the third term of the Debye expansion for refractive indices between 1 and the square root of 2.
Employed the Chester-Friedman-Ursell extension of the method of steepest descents to derive uniform asymptotic expansions across six angular domains.
Evaluated surface-wave contributions, complex rays, and higher-order Debye terms in the near-backward scattering direction.
Derived a uniform asymptotic expansion for rainbow scattering that generalizes Airy's theory across significantly broader angular ranges and droplet size parameters.
Confirmed van de Hulst's conjecture that surface waves drive the glory, showing that Regge-pole dominance and higher-order Debye terms account for observed glory characteristics.
Identified that nearly closed paths of diffracted rays produce rapid quasiperiodic intensity fluctuations and cross-section ripples, reaching maximum amplitude in the backward direction.

Cite This Study

H. M. Nussenzveig (1969) studied this question.

synapsesocial.com/papers/6a774319576efb0ddaf73650 https://doi.org/10.1063/1.1664747

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Implication

Theoretical analysis reveals uniform asymptotic expansions for wave scattering in transparent spheres, indicating surface waves and complex rays dictate rainbow and glory phenomena.

High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory

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Implication

Key Points

Cite This Study

High-Frequency Scattering by a Transparent Sphere. II. Theory of the Rainbow and the Glory

Discussion

Member takes

Implication

Key Points

Cite This Study

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