We study the variation in localized surface plasmon resonance (LSPR) spectra (lambda(LSPR) approximate to 600 nm) as a function of dielectric coating thickness. Langmuir-Blodgett multilayers composed of 22-tricosenoic acid (n approximate to 1.53) were deposited onto short-range-ordered Au nanodisks and nanoholes on glass in air. For large dielectric coating thicknesses (d = 100-340 nm), the LSPRs exhibit a pronounced oscillatory behavior with a periodicity of similar to 190 nm. This is in agreement with a simple image-dipole model, which yields a periodicity of similar to lambda(LSPR)/2n. However, the amplitude of the dipolar plasmon resonance wavelength oscillation lambda(LSPR)(d) is surprisingly large, of the order 25-45 nm for d approximate to 300 nm, indicating the importance of finite size effects. The large LSPR shifts observed at such a large distance from the actual metal surface suggest the possibility of using comparatively thick dielectric films as spacer layers in bio/chemo LSPR sensor applications.