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Strictly speaking, the first maximum of (2) is displaced by a small amount towards θ=0 as compared with (1), and for other maxima and minima this displacement becomes smaller and smaller. But the maxima of (2) may correspond to the minima of (1), and the minima to the maxima. (b) The value of (2), which corresponds to the maximum of (1), is smaller than that of (1), and the value of (2), which corresponds to the minimum of (1) is greater than that of (1). This difference between (1) and (2) increases with the value of Φ (i.e. with the increased diameter of the source). (c) As the value ofθ increases, the maximum value of (1) and (2) gradually decreases. While the minimum value of (1) always remains 0, the minimum value of (2) gradually increases until it becomes equal to the maximum value and assumes a stationary value, then the maxima and minima interchange, the difference of the maximum and minimum values at first increases and then decreases, then again assumes a stationary value, and so on. If in this interval between the two stationary values the maxima of 82) correspond to those of 81), then in the next interval the maxima of 82) correspond to the minima of 81). (d) For larger values of γ (radius of the drop) the intensity of (1) and (2) increase byγ7/3. But at the same time for (2), the difference between the maximum and minimum values is diminished by another factor F. (e) The above is more manifestly shown in the case of the laboratory experiment with a cylindrical glass rod and a straight slit as the source of light. The stationary points of (2) at which the maximum value coincides with the minimum are easily found by χΦ = m x interval of the maximum and minimum of (1),where m represents an integer. (f) According to Airy\u0027s theory, the low of the distribution of the colours of the rainbow is independent of the magnitude of the drop. But in the case of the finite source, the colour distributions are changed by the magnitude of the drop, especially in the supernumerary bows. (g) The supernumerary bows almost lose their colour as the consequence of the finiteness of the source. 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Theory of the Rainbow due to a Circular Source of Light
https://doi.org/10.15083/00037853
https://doi.org/10.15083/000378534c61abf1-3176-4bb5-a50a-2f0d573007f1
名前 / ファイル | ライセンス | アクション |
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jcs021003.pdf (1.3 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2010-02-05 | |||||
タイトル | ||||||
タイトル | Theory of the Rainbow due to a Circular Source of Light | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
ID登録 | ||||||
ID登録 | 10.15083/00037853 | |||||
ID登録タイプ | JaLC | |||||
著者 |
Aichi, K.
× Aichi, K.× Tanakadate, T. |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | From the above discussion, we obtain the following result, where (1) represents the case of a point source, (2) a circular source: - (a) The positions of the maxima and minima of (2) approximately coincide with those of (1). Strictly speaking, the first maximum of (2) is displaced by a small amount towards θ=0 as compared with (1), and for other maxima and minima this displacement becomes smaller and smaller. But the maxima of (2) may correspond to the minima of (1), and the minima to the maxima. (b) The value of (2), which corresponds to the maximum of (1), is smaller than that of (1), and the value of (2), which corresponds to the minimum of (1) is greater than that of (1). This difference between (1) and (2) increases with the value of Φ (i.e. with the increased diameter of the source). (c) As the value ofθ increases, the maximum value of (1) and (2) gradually decreases. While the minimum value of (1) always remains 0, the minimum value of (2) gradually increases until it becomes equal to the maximum value and assumes a stationary value, then the maxima and minima interchange, the difference of the maximum and minimum values at first increases and then decreases, then again assumes a stationary value, and so on. If in this interval between the two stationary values the maxima of 82) correspond to those of 81), then in the next interval the maxima of 82) correspond to the minima of 81). (d) For larger values of γ (radius of the drop) the intensity of (1) and (2) increase byγ7/3. But at the same time for (2), the difference between the maximum and minimum values is diminished by another factor F. (e) The above is more manifestly shown in the case of the laboratory experiment with a cylindrical glass rod and a straight slit as the source of light. The stationary points of (2) at which the maximum value coincides with the minimum are easily found by χΦ = m x interval of the maximum and minimum of (1),where m represents an integer. (f) According to Airy's theory, the low of the distribution of the colours of the rainbow is independent of the magnitude of the drop. But in the case of the finite source, the colour distributions are changed by the magnitude of the drop, especially in the supernumerary bows. (g) The supernumerary bows almost lose their colour as the consequence of the finiteness of the source. This effect is more remarkable when the drop becomes larger. | |||||
書誌情報 |
The journal of the College of Science, Imperial University of Tokyo, Japan = 東京帝國大學紀要. 理科 巻 21, p. 1-29, 発行日 1906-05-22 |
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書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA00695779 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
日本十進分類法 | ||||||
主題 | 451.75 | |||||
主題Scheme | NDC | |||||
出版者 | ||||||
出版者 | College of Science, Imperial University | |||||
出版者別名 | ||||||
東京帝國大學理學部 |