Fluctuations of the interface between coexisting colloidal fluid phases have been measured with confocal microscopy. Due to a very low surface tension, the thermal motions of the interface are so slow that a record can be made of the positions of the interface. The theory of the interfacial height fluctuations is developed. For a host of correlation functions, the experimental data are compared with the theoretical expressions. The agreement between theory and experiment is remarkably good
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