Original scientific paper
Correlation between diffraction of light by circular aperture and close-range interaction energy of two charged spheres
Vladimir Paar
; Department of Physics, University of Zagreb, Bijenička 32, HR-10000 Zagreb
Nenad Pavin
; Department of Physics, University of Zagreb, Bijenička 32, HR-10000 Zagreb
Krešimir Pavlovski
; Department of Physics, University of Zagreb, Bijenička 32, HR-10000 Zagreb
Antun Rubčić
; Department of Physics, University of Zagreb, Bijenička 32, HR-10000 Zagreb
Jasna Rubčić
; Department of Physics, University of Zagreb, Bijenička 32, HR-10000 Zagreb
Abstract
It is shown that the coefficients Ak of angles θk, corresponding to the minima of light intensity in the diffraction by a circular aperture, can successfully be described by a function which appears in the electrostatic interaction energy between two uniform surface-charged spheres. The coefficient Ak defines the angle θk by sin θk = Akλ/d, k = 1, 2, 3, . . . , where λ is the wavelength of light and d is the diameter of the aperture. These coefficients may be correlated with a dimensionless function fb/R, encountered in the relation of the interaction energy terms of two spheres of equal radii R, with uniformly-distributed surface charges q and q0 and at a mutual distance b. The total interaction energy, i.e. the Coulomb potential energy, is W = qq0 /(4π²0b), where ²0 is the permitivity of vacuum. This energy contains two terms, a positive one W(+) = W fb/R and negative one W(−) = W(1 − fb/R). The correlation between Ak and the function fb/R is given by Ak −k = u+vfb/R,k, where u and v are constants. Coefficients Ak obtained by this correlation agree with those defined by the diffraction method within an error of 10−3% at k = 1, and gradually diminishing to 10−4% at k = 10.
Keywords
circular aperture; diffraction minima; two uniformly charged spheres; electrostatic interaction energy; positive and negative part of Coulomb potential energy; correlation
Hrčak ID:
301560
URI
Publication date:
1.10.2001.
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