 
FIZIKA A 10 (2001) 4 , 141154
CORRELATION BETWEEN DIFFRACTION OF LIGHT BY CIRCULAR APERTURE AND
CLOSERANGE INTERACTION ENERGY OF TWO CHARGED SPHERES
VLADIMIR PAAR, NENAD PAVIN, KREŠIMIR PAVLOVSKI, ANTUN RUBČIĆ and
JASNA RUBČIĆ
Department of Physics, University of Zagreb, Bijenička 32, HR10000
Zagreb
Dedicated to Professor Kseno Ilakovac on the occasion of his 70^{th}
birthday
Received 22 June 2001; revised manuscript received 9 January 2002
Accepted 21 January 2002 Online 6 April 2002
It is shown that the coefficients A_{k} of angles q_{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 surfacecharged spheres. The coefficient A_{k} defines
the angle q_{k} by sinq_{k}
= A_{k}l/d, k = 1,2,3, Ľ ,
where l 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 uniformlydistributed surface charges q and q˘ and at
a mutual distance b. The total interaction energy, i.e. the Coulomb potential energy, is W
= qq˘/(4pe_{0}b), where e_{0} is the permitivity of vacuum. This energy contains two
terms, a positive one W^{(+)} = W f_{b/R} and negative one W^{()} = W (1f_{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.
PACS numbers: 42.25.Fx, 41.20.Cv
UDC 535.42
Keywords: circular aperture, diffraction minima, two uniformly charged spheres,
electrostatic interaction energy, positive and negative part of Coulomb potential energy,
correlation
