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Rainbows: Mie computations and the Airy approximation.

R T Wang, H C van de Hulst

    Applied Optics
    |June 29, 2010
    PubMed
    Summary
    This summary is machine-generated.

    Mie theory accurately models light scattering from large water drops (up to 6 mm). The Airy approximation is validated for various internal reflections, revealing insights into rainbow phenomena and polarization.

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    Area of Science:

    • Atmospheric optics
    • Light scattering physics

    Background:

    • Mie theory provides accurate light scattering calculations.
    • The Airy approximation simplifies scattering analysis for large particles.

    Purpose of the Study:

    • To evaluate Mie coefficients using recursive relations.
    • To assess the Airy approximation's validity for diverse rainbow orders.
    • To analyze the dark band between primary and secondary rainbows.

    Main Methods:

    • Computation of Mie scattering intensity patterns for large size parameters (x up to 50,000).
    • Evaluation of Mie coefficients via ratios of successive-order Riccati-Bessel and Neumann functions.
    • Comparison of Mie and generalized Airy approximation intensity patterns.

    Main Results:

    • Accurate Mie computations are feasible for millimeter-sized water drops.
    • The Airy approximation closely matches Mie results for millimeter drops, including supernumerary maxima and polarization.
    • The dark band between rainbows contains contributions from higher-order rainbows (p=6, 7).
    • Agreement between Mie and Airy theories improves for smaller drops (0.02 mm) with higher refractive indices.

    Conclusions:

    • The generalized Airy approximation is a valid tool for analyzing light scattering from large water drops.
    • Higher-order rainbows significantly influence the dark band between primary and secondary rainbows.
    • The findings support experimental investigations in atmospheric optics and light scattering.