Air gap of the induction motor is inversely proportional to the power factor and efficiency. The airgap between stator and rotor decides amount of energy transferred from stator to rotor. Air gap increase the loss of fluxes transferred from stator to rotor. Thus efficiency decreases if air gap increases ,
now coming to the part of power factor :-
Power factor is defined as ratio between active or real power and the apparent power consumed by the load. If the load increases the power factor increases at full load power factor is 0.8–0.9 lagging for 3-phase IM.
Increasing air gap means less amount of fluxes linked with the armature winding which makes the EMF induced in the rotor low. But the apparent power driven by the constant load will be same thus the load will draw more current to make the apparant power same . More losses makes the output active power less .
Air gap between stator and rotor increases means magnetizing current drawn by stator itself increases . This magnetizing current lags almost 90 ° from the supply voltage . So to induce EMF more magnetizing flux is needed as air gap is high.
this no load fluxes increases the angle between supply voltage and load current it makes the power factor of the machine poor.