Newton's and Fresnel's Diffraction Experiments The Continuation of Newton's Diffraction
Experiments Diffraction of Light at Slit and Hindrance InterferenceAngle Condition, Diffraction and
Imagery Diffraction One After Another and with
Intermediate Imagery Diminishing of Frequency of Light after
Diffraction Inner and Outer DiffractionFringes at
Circular Openings Superposition of Interference and Diffraction Diffraction Experiments with Inhomogeneous
Illumination Experiments with Polarized Light at Slit and
DoubleSlit The Background of DiffractionFigures Trial for Interpretation of Newton's Diffraction
Experiments Consequences for Photons out of Newton's
Diffraction Experiments Consequences for Structure of Electrons out of
that of Photons The Thermally Conditioned Electromagnetic Field Diffraction and LightEmission of Electrons EnergySteps of Electrons in Magnetic EigenField Faraday's Electrotonic States NearField Optics with Regard to Newton's
DiffractionExperiments Consideration of Magnetic Moment of Electron
in Quantum Theories 

Inner and Outer DiffractionFringes at Circular Openings
In a schlierenapparatus is shown that also at circularopenings bent light comes only from a small (<0.1 mm) surroundings of edges. It is important, also for circularopening, to distinguish between inner and outer diffractionrings, only in this way it is possible to comprehend the nature of diffraction. The differences of Fresnel's and Fraunhofer's manner of observation are demonstrated. Figure, 1. Photos of circularopenings in a schlierenapparatus. The circularopenings of the diameters of 1, 2 and 4 mm were drilled in an aluminium sheet and bevelled that only an edge about 0.1 mm was remaining which was blacken. Scale ratio 1 : 1 and optically enlarged. Figure 2. Experimental arrangement to examine the diffractionfigures of circularopenings in dependence of distance and of their diameter. L lightsource, a highpressure mercury lamp HBO 100; C  condenser; F  green filter; M  microscope objective; ID  illumination diaphragm, a spinningnozzle Ø 0.1 mm; Le 1 lens f' = 1 m; DD circular diffraction diaphragm with diameters of 4, 2 and 1 mm; Le 2  fallen off in Fresnel's observation manner, used with f'_{2} = e in Fraunhofer's observation manner; P  miniature reflex camera without optics Figure 3. Diffractionfigures at circularopenings in the arrangement of figure 2. The upper halves of all photos show the rings in Fresnel's manner of observation with parallel incident light. Left above the drawing line for comparison are arranged the diffraction figures from the halfplane in the same distance. They are so below arranged that equivalent rings and fringes border together. Right and below this line as lower halves of halfphotos are arranged the photos in Fraunhofer's manner of observation, thus is with the lens Le 2 with f'_{2} = e. The distance e in m is given left outside and the diameter of the used circularopening DD in mm on the top./em> Figure 4. Diffraction with and without imagery at circuitopenings in the arrangement of figure 2. Below rank: diameter of the used circular aperture in mm; left column: distance in m. The upper half of all photos are taken in Fresnel's manner of observation without the lens Le 2. The lower halves of the photos are taken with the lens Le 2 with a focallength f' = 0.5 m. The first rank of photos shows the results in 0.5 m resp. in the focallength. The second rank shows the results in 1 m distance resp. in the double focallength, the third rank in 1.5 m resp. in the threefold focallength. General remarks to diffractionrings at circularopeningsBy Fresnel's manner of observation in short distances and large circularopenings originate inner diffractionrings that correspond to inner diffractionfringes of slit or diffractionfringes of halfplane. The (unequal) intervals of diffractionrings are non noticeable dependent in diameter of opening but only of distance, where by parallel illumination the intervals grow only with the root of distance as already Fresnel [6] found experimentally for halfplanes. As Nieke [3] has proved, this dependence is valid first in distances greater than 10^{5} λ (at visible light about 50 mm.), before the diffractionfigure of halfplane is erected. However, in sufficient large distances or smaller openings outer rings instead of inner rings appear. Their intervals of rings harmonize with the intervals of rings, finding in Fraunhofer's manner of observation in the same distance, but with different intensities. They are proportional to the reciprocal diameter of opening. The transition from inner to outer in Fresnel's manner of observation (upper half in figure 3) takes place at f 4 mm between 1 and 2 m, at 2 mm f between 1/4 and 1/2 m and at 1 mm f between 1/16 and 1/8 m. Whereas the intervals of outer diffractionfringes at the slit are constant, so is that not the case at outer rings of circular openings, even if this is not so evident than in the intervals of fringes in halfplane or inner diffractionfringes of slit. According Huygen's principle and integration over the circular plane with the radius R or outer diffractionrings were calculated formally with the presupposition of large distances and not too great and not too small radii. With that (and only then) these outer rings were calculated by means of Besselfunctions sin α = χ λ / R (1) for minima χ = 0,61, 1,116, 1,619 ... and for the maxima χ = 0,819, 1,346, 1,850 ... . The derivation from constancy is small but notable. Deviations from all calculations by wavehypothesis appear at size of slit or diameter of circularopenings at smaller than 0.1 mm. Hönl, Maue and Westphal [8] quoted many formal or approximate estimations for this case. By Nieke [2] and [3] at slit width of 0.1 mm touch the two spheres from which bent light is coming. So a physical argument can be given because here at small slitwidths or circularopenings must rule other conditions. Here the presupposition of (inadmissible and wrong) extrapolation (cf. Nieke [9]) of formula for diffraction at slit with outer fringes in the slitplane was fulfilled, that bent light has to come from the whole slit, but just here the calculation does not agree. Fresnel's zoneconstruction describes a system of rings in the plane of diaphragm where the way of light from lightsource to testpoint grows respectively for λ / 2. Sommerfeld [10] wrote to that (translated): "A very descriptive, if only qualitative understanding, of these results yields the construction of Fresnel'szones". This theory constructs a system of rings that yield only in special cases the right radius of diffractionrings. References[1] I. Newton, Opticks, or a Treatise of the Reflexions, Refractions Inflexions and Colours of Light. London 1704; Opera quae exstant omnis, Tom IV, London 1782; Optics, Reprint, Bruxelles 1966; Optik II + III, Übers. W. Abendroth, Ostwald's Klassiker Nr. 97, Engelmannn, Leipzig 1898; Neuauflage Bd. 96/97, Vieweg, Braunschweig 1983; Optique, Trad. J. P. Macat 1787; Bourgois, Paris 1989. [2] H. Nieke, Newtons Beugungsexperimente und ihre Weiterführung. Halle 1997, Comp. Print 1 Arbeit 2; (Vorhanden in vielen deutschen Universitätsbibliotheken); Newton's Diffraction Experiments and their Continuation. Halle 1997, Comp. Print 3, paper 2. (Available in some university libraries. [3] As [2], paper 3. [4] W. Arkadiew, Phys. Z. 14 (1913) 832. [5] As [2], paper 4. [6] A. J. Fresnel, Oeuvre Complétes I. Paris 1866; Abhandlungen über die Beugung des Lichtes. Ostwalds Klassiker Nr. 215, Engelmann, Leipzig 1926. [7] J. v. Fraunhofer, Gesammelte Schrift en. Verlag bayr. Akad. München 1888 [8] H. Hönl, A. W. Maue u. K. Westphal, in: Handbuch der Physik Bd. XXV/1 Springer, Göttingen. Heidelberg, Berlin 1961. [9] As [2], paper 1. [10] A. Sommerfeld, Vorlesungen über theoretische Physik, Bd. IV Optik. Dietrich, Wiesbaden 1950 S. 222.


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