Farhan is correct that these "bug eyes" are part of the radar warning system, but unfortunately is incorrect as to what that system actually does.
Radar warning systems are commonly installed on military aircraft. Their primary purpose is to detect the upper-level radio frequencies employed by ground- and airborne-based active (i.e. radiation-emitting) radars, to include those used by radar-guided missiles such as the AIM-120 AMRAAM. Though each antenna is omnidirectional, radar warning systems typically consist of multiple antennas (usually four) each mounted pointing in a separate "quadrant" for maximum coverage and to determine where the signal is coming from.
The F-4 Phantom employed various iterations of radar warning systems over the years, to include the AN/APR-36, AN/APR-37, and ALR-46. The antennas pictured in the question constitute the aft-facing pair of one of these systems; the remaining front facing antennas are mounted one on each wingtip as seen below and captioned in the following image:
Port wing tip with bug-eye RWR dome and position light.
However, radar warning systems are almost universally passive in nature, meaning they do not emit radiation of their own, and can only sense radar signals being emitted by something else (and unfortunately not planes per se, nor smiles).