Recent theoretical work on the radio interferometry technique for dielectric layers less than one free space wavelength thick has indicated that there is a thickness for which no interference is observed. This thickness is about 0.2 free space wavelengths for ice, and it lies between the thickness that allows one single mode to propagate in the layer (>0.2 wavelengths) and a thickness that is essentially transparent to the wavelength being used (< or =0.2 wavelengths).Field work was done on the Juneau Icefield, Alaska; frequencies from 1 to 32 Mhz were used. At 1 and 2 Mhz, an interference pattern typical of a half-space of ice with a dielectric constant of 3.3 was observed, while at 4 Mhz essentially no interference was seen. At higher frequencies, the interference observed is typical of that of a layer overlying a half-space. The upper layer can be interpreted to have a thickness of 15 or 20 m (0.2 wavelengths at 4 Mhz) with a dielectric constant of 2.4. These results are for a layer of snow over a half-space of ice. The technique is therefore of potential interest in interpreting the nature of the snow layer overlying a glacier.