A new simple formula is derived as an approximation for the general exact integrals for the radial component of the electric field generated by a horizontal electric dipole in a half-space of water or earth near its boundary with air. The field in the water or earth is investigated as a function of radial distance from the source for εr = 80, 20, and 4, over wide ranges of conductivities and frequencies. Special attention is paid to the ranges in which the direct wave from the dipole produces an interference pattern of standing waves when it interacts with the lateral wave. For selected values of the parameters the radial electric field computed from the new simple formula is compared with the field evaluated numerically from the exact integrals. The agreement is excellent when the ratio of wave numbers characteristic of the denser half-space and air is large, quite good even when this ratio is as small as 2.