Correlation between diffraction of light by circular aperture and close-range interaction energy of two charged spheres

Scientific paper - Original scientific paper

• Author: Vladimir Paar
• Author: Nenad Pavin
• Author: Krešimir Pavlovski
• Author: Antun Rubčić
• Author: Jasna Rubčić; MBZ: 2533
• Author's institution: University of Zagreb; Faculty of Science; (Department of Physics)
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract (english)

It is shown that the coefficients A_k of angles θ_k, 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 A_k defines the angle θ_k by sinθ_k = A_kλ/d, k = 1,2,3, ¼ , where λ is the wavelength of light and d is the diameter of the aperture. These coefficients may be correlated with a dimensionless function f_b/R, encountered in the relation of the interaction energy terms of two spheres of equal radii R, with uniformly-distributed surface charges q and q¢ and at a mutual distance b. The total interaction energy, i.e. the Coulomb potential energy, is W = qq¢/(4πε_0b), where ε_0 is the permitivity of vacuum. This energy contains two terms, a positive one W(^+) = W f_b/R and negative one W(^-) = W (1-f_b/R). The correlation between A_k and the function f_b/R is given by A_k - k = u + v f_b/R,k, where u and v are constants. Coefficients A_k 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 (english): circular aperture; diffraction minima; two uniformly charged spheres; electrostatic interaction energy; positive and negative part of Coulomb potential energy; correlation
• Language: english
• Publication type: Scientific paper - Original scientific paper
• Publication status: Published
• Peer review: Peer review
• Publication version: Published version
• Journal title: Fizika A
• Numbering: vol. 10, no. 4, pp. 141-154
• p-ISSN: 1330-0008
• URN:NBN: urn:nbn:hr:217:534757
• Publication: 2001
• Document URL: http://fizika.hfd.hr/fizika_a/av01/a10p141.htm
• Type of resource: Text
• Access conditions: Open access
• Created on: 2019-10-11 14:35:51