Submicrometer size droplets of sulfuric acid on mica have been imaged using scanning polarization force microscopy (SPFM). Our study shows that, contrary to the macroscopic case, the drop profile depends on the size of the drops, with a decrease of the contact angle with decreasing size droplets in the present case. This dependence can be explained by taking into account long-range forces between the substrate and the fluid, which prove to have important effects for submicrometer size drops. Profile measurements at the submicron scale allow direct estimation of the interaction potential between a fluid and a substrate.