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
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概要
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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.
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