Have you ever had your kitchen dimmer switch turned down really low, and then the refrigerator cuts in and the lights go right out? The funny thing is that when the compressor turns off, the lights don't even come back on again. You've got to turn the dimmer up quite a bit to bring them back.
It works best in older houses where the fridge plug is on the same circuit as the overhead light, but you can often see it quite clearly even when they are on different circuits. I was at a friend's house the other day and I was showing them how this works, when something very unexpected happened. The fridge cut in and the lights got brighter. I thought we were imagining it but we watched for several cycles, and it kept happening. Then we tried turning on the microwave, and the lights got dimmer. But the fridge definitely made it get brighter.
I think I figured out what is going on, and the answer is kind of interesting. It's really a two-part question: part 1 is just why is a dimmer switch turned down low so very sensitive to small changes in line voltage; and part 2, why the anomalous result of the lights getting brighter?
I'm including a simplified schematic of the dimmer circuit for your edification: I'll give you my answer when we return.
(I found the schematic on this very impressive website.)