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FIZIKA A 10 (2001) 4 , 141-154
 
CORRELATION BETWEEN DIFFRACTION OF LIGHT BY CIRCULAR APERTURE AND
CLOSE-RANGE 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, HR-10000
Zagreb
Dedicated to Professor Kseno Ilakovac on the occasion of his 70th
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 Ak of angles qk,
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 qk by sinqk
= Akl/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 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 q˘ and at
a mutual distance b. The total interaction energy, i.e. the Coulomb potential energy, is W
= qq˘/(4pe0b), where e0 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 + v fb/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.
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
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