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    Area of Science:

    • Physics
    • Optics
    • Wave Propagation

    Background:

    • Geometric optics describes light ray behavior.
    • Refractive index gradients in media cause phenomena like mirages.
    • Understanding ray trajectories is crucial for wave propagation studies.

    Purpose of the Study:

    • To characterize light ray trajectories in random media with mean refractive index gradients.
    • To derive formulas for mean ray paths and displacements.
    • To provide insights into the mirage phenomenon.

    Main Methods:

    • Utilizing the framework of geometric optics.
    • Deriving formulas for mean ray path in isotropic and anisotropic stochastic fluctuation cases.
    • Calculating mean squared displacement for the isotropic model.

    Main Results:

    • Formulas for the mean ray path were derived for both isotropic and anisotropic random media.
    • A simple formula for mean squared displacement was obtained for the isotropic model.
    • The study characterizes ray trajectory deviations caused by refractive index gradients.

    Conclusions:

    • The derived formulas are applicable to random media with mean refractive index gradients.
    • Results are relevant for electromagnetic wave propagation in atmospheric conditions.
    • The findings aid in understanding and predicting mirages and wave behavior in complex media.