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應用數學報告

應用數學報告. B966C0023 王永年. Why is the sky blue ？ So how much more is violet light scattered than red ？ What causes variation in color of butterfly wings, bird plumage and oil slicks ？. I ＝ f （ V, r, λ , n 1 , n 2 , I 0 ）. V ： a particle of volume

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應用數學報告

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  1. 應用數學報告 B966C0023 王永年

  2. Why is the sky blue？ • So how much more is violet light scattered than red？ • What causes variation in color of butterfly wings, bird plumage and oil slicks？

  3. I＝f（V, r, λ, n1, n2, I0） • V：a particle of volume • r：the distance form the scatterer to the observation point • λ：the wavelength of the scattered radiation • n1：the refractive indices of the exterior media • n2：the refractive indices of the interior media • I0：the intensity of the incident radiation

  4. Dimensional analysis • I Vα rβλγ I0 • [L] 0＝ [L]3α [L]β[L]γ→3α+β+γ＝0 • 散射強度 散射量 微粒量 • 強度 振幅的平方→α＝2 • 強度隨距離的增加減少→ β＝-2 • 6-2+γ＝0 →γ＝-4 • Iscatt λ-4

  5. 結論

  6. 紅光波長 λr＝700nm（散射強度Sr） • 紫光波長 λv＝400nm（散射強度Sv）

  7. 結論 • 人眼直接感受不到紫外光 • 瑞利散射（Rayleigh scattering）→ 波長較短的藍光比波長較長的紅光更易散射

  8. 結論 • 具有厚度的薄膜造成光程差，形成了干涉現象 • 相長性干涉→不同波長的光 • 不同波長的反射光→不同的顏色 • 造成薄膜上有各種色彩。

  9. 資料來源 報告完畢 • 書籍：費曼物理學（費曼） 人人物理（基太哥羅得斯基） 物理傳奇-多彩的光（郭治） 物理入門Q＆A（都築卓司） 普通物理學（BENSON） • 網路：維基百科 blog.udn.com/linshyiming/2361591 www.tubaba.com/wallpaper/2007/0728/image_2270.html www.kekenet.com/read/200805/38719.shtml weatherblogger.mysinablog.com/index.php?op=ViewArticle&articleId=396792 www.phy.ntnu.edu.tw/demolab/optics/sky.html cn.made-in-china.com/image/2f0j01JMTtVSEBqUpQM/%E5%8D%B0%E5%88%B7%E5%85%89%E7%A2%9F%EF%BC%88A%2B%E7%BA%A7%EF%BC%89.jpg 感謝曾慶耀老師、王和盛老師的指導

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