When a half-wave dipole antenna is installed one-half wavelength above ground, the:

The radiation pattern of a horizontal dipole is heavily influenced by its height above ground due to signal reflections. When an antenna is placed exactly one-half wavelength above the ground, the downward-radiated wave travels a half-wavelength to the ground, undergoes a 180-degree phase reversal upon reflection, and travels another half-wavelength back up. This combined travel distance of one full wavelength (360 degrees) plus the 180-degree reflection phase shift results in the reflected wave arriving exactly 180 degrees out of phase with the direct upward radiation. As a result, the vertical (straight up) radiation is effectively cancelled, pushing the RF energy into lower-angle lobes.