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In this report we want to find out the effect of the distance l between the slit and the screen on the measurement of the slit width. An expression I (s, i0, l, d) of the intensity of the diffraction patterns are introduced by the autheors. Here s, i and d are the slit width, the largest angle of incident beam on the plane of the slit and the distance from the optical axis to the observing point on the screen, respectively. The comparision of the theoretical expression with the measured values concludes as follows : 1. In this experiment, when l is smaller than about 10 cm it is impossible to regard the diffraction as Fraunhofer\u0027s diffraction, but when l is larger than about 20 cm it can be regarded as Fraunhofer\u0027s diffraction. And though l is about 10 cm, if s is smaller than about 0.002 cm, it may be regarded as Fraunhofer\u0027s diffraction approximately. 2. When l is small and it is impossible to regard it as Fraunhofer\u0027s diffraction, the theoretical errors originated from approximation must be corrected, and the slit width is measured by using the approximate expression of Fraunho fer\u0027s diffraction. Especially when i is large, the slit width may be measured more exactly by using Fresnel\u0027s diffraction. 3. The size i0 of the light-source gives negative errors but Fresnel\u0027s diffraction effect (when l is small) positive errors. Both the errors offset each other, but the errors originating in the size io are more remarkable than those originating in l. The results obtained for several values of io are as follows (a) In i0 = 0.0005 rad., the errors of the measured values are about 0.5% when they are corrected by calculation from the expression. In other words, in this case, the theoretical calculation gives the approximatly correct values. 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Fraunhofer の回折による細隙の幅の測定における Fresnel の回折の影響について
http://hdl.handle.net/10091/11737
http://hdl.handle.net/10091/11737581afe33-d7b5-4f80-bced-0aaebd1ca9e0
名前 / ファイル | ライセンス | アクション |
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2011-02-15 | |||||
タイトル | ||||||
言語 | ja | |||||
タイトル | Fraunhofer の回折による細隙の幅の測定における Fresnel の回折の影響について | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Effect of Fresnel's Diffraction on Measurement of Slit Width with Fraunhofer's Diffraction | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
高野, 昭
× 高野, 昭× 森本, 彌三八 |
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出版者 | ||||||
出版者 | 信州大学工学部 | |||||
引用 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 信州大学工学部紀要 26: 33-50 (1969) | |||||
書誌情報 |
信州大学工学部紀要 巻 26, p. 33-50, 発行日 1969-07-25 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Previously we have investigted the effect of the size of the light-source (that is the size of the slit width of the collimator i ) on the measurement of the slit width by using the approximate expression of Fraunhofer's diffraction. In this report we want to find out the effect of the distance l between the slit and the screen on the measurement of the slit width. An expression I (s, i0, l, d) of the intensity of the diffraction patterns are introduced by the autheors. Here s, i and d are the slit width, the largest angle of incident beam on the plane of the slit and the distance from the optical axis to the observing point on the screen, respectively. The comparision of the theoretical expression with the measured values concludes as follows : 1. In this experiment, when l is smaller than about 10 cm it is impossible to regard the diffraction as Fraunhofer's diffraction, but when l is larger than about 20 cm it can be regarded as Fraunhofer's diffraction. And though l is about 10 cm, if s is smaller than about 0.002 cm, it may be regarded as Fraunhofer's diffraction approximately. 2. When l is small and it is impossible to regard it as Fraunhofer's diffraction, the theoretical errors originated from approximation must be corrected, and the slit width is measured by using the approximate expression of Fraunho fer's diffraction. Especially when i is large, the slit width may be measured more exactly by using Fresnel's diffraction. 3. The size i0 of the light-source gives negative errors but Fresnel's diffraction effect (when l is small) positive errors. Both the errors offset each other, but the errors originating in the size io are more remarkable than those originating in l. The results obtained for several values of io are as follows (a) In i0 = 0.0005 rad., the errors of the measured values are about 0.5% when they are corrected by calculation from the expression. In other words, in this case, the theoretical calculation gives the approximatly correct values. (b) In i0 = 0.0010 rad. , when s is smaller than about 0.015 cm, the errors of the measured values corrected by the expression are within 1 %. But s is enlarged about 0.015 cm, the results calculated from the expression are remarkably different from those of the measured values. (c) In i = 0.0015 rad. , within about, 1= 2.5~5.0 cm (Fresnel's diffraction), as large as s = 0.010 cm, the errors of the measured values corrected by the expression are within 1 %. Over these bounds, the calculated values are remarkably different from those of the measurement. (d) In i0 = 0.0020 rad. , except about l = 2.5 cm, the calculated values are remarkably different from those of the measurement, and it seems impossible to measure the slit width with the diffraction phenomenon. | |||||
資源タイプ(コンテンツの種類) | ||||||
内容記述タイプ | Other | |||||
内容記述 | Article | |||||
ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0037-3818 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00121228 | |||||
出版タイプ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 |