= Solution
The <Arago spot> is a bright axial point inside the geometrical shadow of a circular opaque object. Under coherent illumination, contributions from points around its circular edge have equal optical path to an axial observation point and interfere constructively. It is a <Fresnel diffraction> effect, so geometrical rays alone miss it. In the ideal paraxial plane-wave model, <Babinet's principle> gives $U_{\rm disk}=U_0-U_{\rm aperture}=U_0e^{ika^2/(2z)}$ on axis for disk radius $a$; thus \b[the axial intensity equals the unobstructed intensity] in that model. The whole shadow is not bright: off-axis phases differ and form a localized central feature. Finite source size, poor coherence or an imperfect edge reduce its visibility.
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